|
320.
Arrangements and Likelihood (with Thomas Kahle, Lukas Kühne,
Leonie Mühlherr and Maximilian Wiesmann), 20pp, submitted to
Vietnam Journal of Mathematics.
319.
Gram Matrices for Isotropic Vectors (with
Yassine El Maazouz and Svala Sverrisdóttir), 23pp, submitted to
Journal of the European Mathematical Society.
318.
Computing Arrangements of Hypersurfaces (with
Paul Breiding and Kexin Wang), 16pp, submitted to
Journal of Software for Algebra and Geometry.
317.
Kinematic Varieties for Massless Particles (with Smita Rajan and
Svala Sverrisdóttir), 19pp, submitted to
Le Matematiche.
316.
Spinor-Helicity Varieties (with Yassine El Maazouz and
Anaëlle Pfister), 28pp, submitted to
SIAM Journal on Applied Algebra and Geometry.
315.
Maximal Mumford Curves from Planar Graphs (with Mario Kummer and
Raluca Vlad), 22pp, submitted to Journal of Algebraic Geometry.
314.
Minimal Kinematics on M0n (with Nick Early and
Anaëlle Pfister), 18pp, submitted to Moduli.
313. The Chow-Lam Form (with Lizzie Pratt), 20pp, submitted to Journal of Symbolic Computation.
312. Positive del Pezzo Geometry (with
Nick Early, Alheydis Geiger, Marta Panizzut and Claudia Yun), 34pp,
submitted to
Annales de l’Institut Henri Poincaré Comb. Phys. Interact.
311. The Two Lives of the Grassmannian (with Karel Devriendt, Hannah Friedman and Bernhard Reinke), 18pp,
to appear in Acta Universitatis Sapientiae, Mathematica.
310. Algebraic Varieties in Quantum Chemistry (with Fabian Faulstich and Svala Sverrisdóttir), 27pp,
to appear in Foundations of Computational Mathematics.
309. Tropical Implicitization Revisited
(with Kemal Rose and Simon Telen), 18 pp,
chapter for a book about the OSCAR Computer Algebra System.
308. Self-Dual Matroids from
Canonical Curves (with Alheydis Geiger, Sachi Hashimoto and Raluca Vlad),
33pp, to appear in Experimental Mathematics.
307. Coupled Cluster Degree of the Grassmannian
(with Viktoriia Borovik and Svala Sverrisdóttir),
Journal of Symbolic Computation
128 (2025) 102396.
306. Gibbs
Manifolds (with Dmitrii Pavlov and Simon Telen),
Information Geometry
7 (2024) 691-717.
305.
Recovery of Plane Curves from Branch Points
(with Daniele Agostini, Hannah Markwig, Clemens Nollau,
Victoria Schleis, Javier Sendra-Arranz),
Discrete and Computational Geometry
72 (2024) 451-475.
304. Taylor Polynomials of
Rational Functions (with Aldo Conca, Simone Naldi and Giorgio Ottaviani),
Acta Mathematica Vietnamica
49 (2024) 19-37.
303.
Recovery from Power Sums
(with Hana Melánová and Rosa Winter),
Experimental Mathematics
33 (2024) 225-234.
302. Likelihood Geometry of Determinantal Point Processes (with Hannah Friedman and Maksym Zubkov),
Algebraic Statistics
15 (2024) 15-25.
301.
Subspaces Fixed by a Nilpotent Matrix
(with Marvin Hahn, Gabriele Nebe and Mima Stanojkovski),
Orbita Mathematicae
1 (2024) 1-15.
300.
Toric Geometry of Entropic Regularization
(with Simon Telen, François-Xavier Vialard and Max von Renesse),
Journal of Symbolic Computation
120 (2024) 102221.
299.
Making Waves
(with Marc Härkönen and Jonas Hirsch),
La Matematica
2 (2023) 593-615.
298.
Primary Decomposition with Differential Operators
(with Yairon Cid-Ruiz),
International Mathematics Research Notices
14 (2023) 12119-12147.
297.
D-Modules and Holonomic Functions
(with Anna-Laura Sattelberger), 36pp, presented at the
Math+ Fall School in Algebraic Geometry (FU Berlin, October 2019).
296. Moment Varieties for
Mixtures of Products (with Yulia Alexandr and Joe Kileel),
Proceedings of the International Symposium on Symbolic and Algebraic Computation (ISSAC 2023),
ACM, New York, 2023, 53-60.
295.
Linear PDE with Constant Coefficients
(with Rida Ait El Manssour and Marc Härkönen),
Glasgow Mathematical Journal
65 (2023) S2-S27.
294. Beyond Linear Algebra,
Proceedings of the International Congress of Mathematicians 2022,
Vol 6, EMS Press, 2023, 4820-4840.
293.
Four-Dimensional Lie Algebras Revisited
(with Laurent Manivel and Svala Sverrisdóttir),
Journal of Lie Theory
33 (2023) 703-712.
292.
Bayesian Integrals on Toric Varieties
(with Michael Borinsky, Anna-Laura Sattelberger and Simon Telen),
SIAM Journal on Applied Algebra and Geometry
7 (2023) 77-103.
291.
Quantum Correlations in the Minimal Scenario
(with Thinh Le, Chiara Meroni, Reinhard Werner and Timo Ziegler),
Quantum 7 (2023) 947.
290. Likelihood Degenerations
(with Daniele Agostini, Taylor Brysiewicz, Claudia Fevola,
Lukas Kühne, Simon Telen and Thomas Lam),
Advances in Mathematics
414 (2023) Paper No 108863.
289.
KP Solitons from Tropical Limits
(with Daniele Agostini, Claudia Fevola and Yelena Mandelshtam),
Journal of Symbolic Computation
114 (2023) 282-301.
288.
Geometry of Dependency Equilibria
(with Irem Portakal),
Rendiconti dell'Istituto di Matematica dell'Università
di Trieste 54 (2022) Art 5, 26 pages.
287.
Orders and Polytropes: Matrix Algebras from Valuations
(with Yassine El Maazouz, Marvin Hahn, Gabriele Nebe and Mima Stanojkovski),
Contributions to Algebra and Geometry
63 (2022) 515-531.
286.
Marginal Independence Models
(with Tobias Boege and Sonja Petrović),
Proceedings of the International Symposium on Symbolic and Algebraic Computation (ISSAC 2022),
ACM, New York, 2022, 263-271.
285.
Positivity Certificates via Integral Representations (with
Khazhgali Kozhasov and Mateusz Michalek), Facets
of Algebraic Geometry, Vol II, 84-114, London Math Soc Lecture Note
Ser 473, Cambridge University Press, 2022.
284.
Voronoi Cells of Varieties (with
Diego Cifuentes, Kristian Ranestad and Madeleine Weinstein),
Journal of Symbolic Computation
109 (2022) 351-366.
283.
Likelihood Equations and Scattering Amplitudes (with Simon Telen),
Algebraic Statistics 12 (2021) 167-186.
282.
Tangent Quadrics in Real 3-Space (with
Taylor Brysiewicz and Claudia Fevola),
Le Matematiche 76 (2021) 355-367.
281.
Jordan Algebras of Symmetric Matrices (with Arthur Bik and Henrik Eisenmann),
Le Matematiche 76 (2021) 337-353.
280.
Pencils of Quadrics: Old and New (with Claudia Fevola
and Yelena Mandelshtam),
Le Matematiche 76 (2021) 319-335.
279.
Primary Ideals and their Differential Equations
(with Yairon Cid-Ruiz and Roser Homs),
Foundations of Computational Mathematics
21 (2021) 1363-1399.
278.
Maximum Likelihood Estimation for Totally
Positive Log-Concave Densities (with
Elina Robeva, Ngoc Tran and Caroline Uhler),
Scandinavian Journal of Statistics
48 (2021) 817-844.
277. Theta Surfaces (with
Daniele Agostini, Türkü Özlüm Çelik and
Julia Struwe), Vietnam Journal of Mathematics
49 (2021) 319-347.
276.
The Dubrovin Threefold of an Algebraic Curve (with
Daniele Agostini and Türkü Özlüm Çelik),
Nonlinearity 34 (2021) 3783-3812.
275.
Bad Projections of the PSD Cone (with Yuhan Jiang),
Collectanea Mathematica
72 (2021) 261-280.
274.
K3 Polytopes and their Quartic Surfaces (with
Gabriele Balletti and Marta Panizzut),
Advances in Geometry
21 (2021) 85-98.
273.
Wasserstein Distance to Independence Models
(with Türkü Özlüm Çelik, Asgar Jamneshan,
Guido Montúfar and Lorenzo Venturello),
Journal of Symbolic Computation
104 (2021) 855-873.
272.
Discrete Statistical Models with Rational Maximum Likelihood Estimator
(with Eliana Duarte and Orlando Marigliano),
Bernoulli 27 (2021) 135-154.
271.
Moment Varieties of Measures on Polytopes (with
Kathlén Kohn and Boris Shapiro),
Annali della Scuola Normale Superiore di Pisa
21 (2020) 739-770.
270.
Brownian Motion Tree Models are Toric (with
Caroline Uhler and Piotr Zwiernik),
Kybernetika 56 (2020) 1154-1175.
269.
Algebraic Analysis of Rotation Data (with Michael Adamer, András
Lörincz and Anna-Laura Sattelberger),
Algebraic Statistics 11 (2020) 189-211.
268.
Estimating Linear Covariance Models with Numerical Nonlinear Algebra
(with Sascha Timme and Piotr Zwiernik),
Algebraic Statistics 11 (2020) 31-52.
267.
An Octanomial Model for Cubic Surfaces (with
Marta Panizzut and Emre Sertöz),
Le Matematiche 75 (2020) 517-536.
266.
Twenty-Seven Questions about the Cubic Surface (with Kristian Ranestad),
Le Matematiche 75 (2020) 411-424.
265.
The Schläfli Fan (with Michael Joswig and Marta Panizzut),
Discrete and Computational Geometry
64 (2020) 355-381.
264.
The Geometry of SDP-Exactness in Quadratic Optimization
(with Diego Cifuentes and Corey Harris),
Mathematical Programming, Ser. A
182 (2020) 399-428.
263. Optimal Transport to a Variety
(with Türkü Özlüm Çelik, Asgar Jamneshan,
Guido Montúfar and Lorenzo Venturello),
Mathematical Aspects of Computer and Information Sciences,
MACIS 2019, Istanbul, Springer Lecture Notes in Computer Science
11989 (2020) 364-381.
262.
3264 Conics in a Second (with Paul Breiding and Sascha Timme),
Notices of the American Mathematical Society
67 (2020) 30-37.
261.
Computing Convex Hulls of Trajectories (with Daniel Ciripoi,
Andreas Löhne and Nidhi Kaihnsa),
Revista de la Unión Matemática Argentina.
60 (2019) 637-662.
260.
The Geometry of Gaussoids (with Alessio D'Ali,
Tobias Boege and Thomas Kahle),
Foundations of Computational Mathematics
19 (2019) 775-812.
259. Schottky Algorithms: Classical Meets Tropical (with Lynn Chua and Mario Kummer), Mathematics of Computation
88 (2019) 2541-2558.
258.
Sixty-four Curves of Degree Six
(with Nidhi Kaihnsa, Mario Kummer, Daniel Plaumann and Mahsa Sayyary),
Experimental Mathematics
28 (2019) 132-150.
257. Learning Paths from Signature Tensors (with Max Pfeffer and Anna Seigal),
SIAM Journal on Matrix Analysis and Applications
40 (2019) 394-416.
256.
Varieties of Signature Tensors (with
Carlos Améndola and Peter Friz),
Forum of Mathematics, Sigma
7 (2019) e10, 54 pp.
255.
Geometry of Log-Concave Density Estimation
(with Elina Robeva and Caroline Uhler),
Discrete and Computational Geometry
61 (2019) 136-160.
254.
Algebraic Identifiability of Gaussian Mixtures
(with Carlos Améndola and Kristian Ranestad),
International Mathematics Research Notices
21 (2018) 6556-6580.
253.
Learning Algebraic Varieties from Samples
(with Paul Breiding, Sara Kalisnik and Madeleine Weinstein),
Revista Matematica Complutense
31 (2018) 545-593;
News story, Lecture.
252. Real Space Sextics and their Tritangents
(with Avinash Kulkarni, Yue Ren and Mahsa Sayyary),
Proceedings of the International Symposium on Symbolic and Algebraic Computation (ISSAC 2018),
ACM, New York, 2018, 247-254.
251.
Distortion Varieties
(with Joe Kileel, Zuzana Kukelova and Tomas Pajdla),
Foundations of Computational Mathematics
18 (2018) 1043-1071.
250.
Nearest Points on Toric Varieties
(with Martin Helmer), Mathematica Scandinavica
122 (2018) 213-238.
249. Changing Views on Curves
and Surfaces (with Kathlén Kohn and Matthew Trager),
Acta Mathematica Vietnamica
43 (2018) 1-29.
248.
Fitness, Apprenticeship, and Polynomials,
In: Combinatorial Algebraic Geometry,
(eds. G. Smith and B. Sturmfels), Fields Institute
Communications, Springer, New York, vol 80, (2017) 1-19.
247.
A Clever Elimination Strategy for Efficient Minimal Solvers
(with Joe Kileel, Zuzana Kukelova and Tomas Pajdla), 13pp,
IEEE Conference on Computer Vision and Pattern Recognition 2017
(CVPR 2017).
246. General
Models for Rational Cameras and the Case of Two-Slit Projections
(with Matthew Trager, John Canny, Martial Hebert and Jean Ponce), 9pp,
IEEE Conference on Computer Vision and Pattern Recognition 2017
(CVPR 2017).
245.
How to Flatten a Soccer Ball
(with Kaie Kubjas and Pablo Parrilo), In: Homological and
Computational Methods
in Commutative Algebra, (eds. A. Conca, J. Gubeladze and
T. Römer), Springer INdAM series, vol 20,
(2017) 141-162
244.
Convexity in Tree Spaces (with Bo Lin, Xiaoxian Tang and Ruriko Yoshida),
SIAM Journal on Discrete Mathematics
31 (2017) 2015-2038.
243.
Real Rank Two Geometry
(with Anna Seigal), Journal of Algebra
484 (2017) 310-333.
242.
Real Rank Geometry of Ternary Forms
(with Mateusz Michalek, Hyunsuk Moon and Emanuele Ventura),
Annali di Matematica Pura ed Applicata
196 (2017) 1025-1054.
241.
Congruences and Concurrent Lines in Multi-View Geometry
(with Jean Ponce and Matthew Trager),
Advances in Applied Mathematics
88 (2017) 62-91.
240.
Eigenconfigurations of Tensors (with Hirotachi Abo and Anna Seigal),
in Algebraic and Geometric Methods in
Discrete Mathematics, Contemporary Mathematics,
vol 685, American Mathematical Society,
(2017) 1-25.
239.
On the Existence of Epipolar Matrices
(with Sameer Agarwal, Hon-Leung Lee and Rekha Thomas),
International Journal of Computer Vision
121 (2017) 403-415.
238.
Does Antibiotic Resistance Evolve in Hospitals?
(with Anna Seigal, Portia Mira and Miriam Barlow),
Bulletin of Mathematical Biology
79 (2017) 191-208;
News story.
237.
The Hurwitz Form of a Projective Variety,
Journal of Symbolic Computation
79 (2017) 186-196.
236.
Tropicalization of Del Pezzo surfaces
(with Qingchun Ren and Kristin Shaw),
Advances in Mathematics
300 (2016) 156-189.
235. Tensors and their Eigenvectors,
Notices of the American Mathematical Society
63 (2016) 604-606.
234. Symmetric Matrices, Catalan Paths, and Correlations (with Emmanuel Tsukerman and Lauren Williams),
Journal of Combinatorial Theory, Series A
144 (2016) 496-510.
233. Rigid Multiview Varieties
(with Michael Joswig, Joe Kileel and André Wagner),
International Journal of Algebra and Computation
26 (2016) 775-788.
232. Moment Varieties of Gaussian Mixtures
(with Carlos Améndola and Jean-Charles Faugère),
Journal of Algebraic Statistics 7
(2016) 14-28.
231.
Maximum Likelihood Estimates for Gaussian Mixtures Are Transcendental
(with Carlos Améndola and Mathias Drton),
Mathematical Aspects of Computer and Information Sciences,
(eds. I. Kotsireas, S. Rump and C. Yap),
MACIS 2015, Berlin, (2016) 579-590.
230. Computing the Chow Variety of Quadratic Space Curves
(with Peter Bürgisser, Kathlén Kohn and Pierre Lairez),
Mathematical Aspects of Computer and Information Sciences,
(eds. I. Kotsireas, S. Rump and C. Yap),
MACIS 2015, Berlin, (2016) 130-136.
229. Exponential Varieties
(with Mateusz Michalek, Caroline Uhler and Piotr Zwiernik),
Proceedings of the London Mathematical Society
112 (2016) 27-56.
228.
The Euclidean distance degree of an algebraic variety (with Jan Draisma, Emil Horobet,
Giorgio Ottaviani, and Rekha Thomas),
Foundations of Computational Mathematics
16 (2016) 99-149.
227.
Algebraic Systems Biology: a Case Study for the Wnt Pathway
(with Elizabeth Gross, Heather Harrington and Zvi Rosen),
Bulletin of Mathematical Biology
78 (2016) 21-51.
226.
Decomposing Tensors into Frames
(with Luke Oeding and Elina Robeva),
Advances in Applied Mathematics
73 (2016) 125-153.
225.
Duality of Multiple Root Loci (with Hwangrae Lee), Journal
of Algebra 446 (2016) 499-526.
224.
Cayley-Bacharach Formulas
(with Qingchun Ren and Jurgen Richter-Gebert),
American Mathematical Monthly
122 (2015) 845-854.
223.
Generic Spectrahedral Shadows (with Rainer Sinn),
SIAM Journal on Optimization
25 (2015) 1209-1220.
222.
Quartic spectrahedra
(with John Christian Ottem, Kristian Ranestad, and Cynthia Vinzant),
Mathematical Programming, Ser. B,
151 (2015) 585-612.
221.
A Family of Quasisymmetry Models
(with Maria Kateri and Fatemeh Mohammadi),
Journal of Algebraic Statistics
6 (2015) 1-16.
220. Rational Design of Antibiotic Treatment Plans:
A Treatment Strategy for Managing Evolution and Reversing Resistance
(with Portia Mira, Kristina Crona, Devin Greene, Juan Meza and Miriam Barlow),
PLoS One
10(5) (2015) e0122283
219.
Tensors of nonnegative rank two
(with Elizabeth Allman, John Rhodes and Piotr Zwiernik),
Linear Algebra and its Applications
473 (2015) 37-53.
218.
Moduli of Tropical Plane Curves
(with Sarah Brodsky, Ralph Morrison and Michael Joswig),
Research in the Mathematical Sciences
2:4 (2015)
217.
Fixed points of the EM algorithm and nonnegative rank boundaries
(with Kaie Kubjas and Elina Robeva),
Annals of Statistics
43 (2015) 422-461.
216.
Exact solutions in structured low-rank approximation
(with Pierre-Jean Spaenlehauer and Giorgio Ottaviani),
SIAM Journal on Matrix Analysis and Applications
35 (2014) 1521-1542.
215.
Hypersurfaces and their singularities in partial
correlation testing
(with Shaowei Lin, Caroline Uhler and Peter Bühlmann),
Foundations of Computational Mathematics
5 (2014) 1079-1116.
214.
Tropicalization of classical moduli spaces
(with Steven Sam and Qingchun Ren),
Mathematics in Computer Science
8 (2014) 119-145.
213.
Maximum likelihood for matrices with rank constraints
(with Jonathan Hauenstein and Jose Rodriguez),
Journal of Algebraic Statistics
5 (2014) 18-38.
212.
Likelihood geometry (with June Huh),
in Combinatorial Algebraic Geometry
(eds. Aldo Conca et al.),
Lecture Notes in Mathematics 2108,
Springer, (2014) 63-117.
211.
The universal Kummer threefold
(with Gus Schrader, Steven Sam and Qingchun Ren),
Experimental Mathematics
22 (2013) 327-362.
210.
A Hilbert scheme in computer vision
(with Chris Aholt and Rekha Thomas),
Canadian Journal of Mathematics
65 (2013) 961-988.
209.
Mixed discriminants
(with Eduardo Cattani, Maria Angelica Cueto, Alicia Dickenstein
and Sandra Di Rocco),
Mathematische Zeitschrift
274 (2013) 761-778.
208.
Capacity pre-log of noncoherent SIMO channels via Hironaka's theorem
(with V. Morgenshtern, E. Riegler, W. Yang, G. Durisi, S. Lin and
H. Bolcskei),
IEEE Transactions on Information Theory
59 (2013) 4213-4229.
207.
The entropic discriminant
(with Raman Sanyal and Cynthia Vinzant),
Advances in Mathematics
244 (2013) 678-707.
206.
Elliptic curves in honeycomb form (with Melody Chan),
in "Tropical Geometry", Proceedings Castro Urdiales 2011,
editors E. Brugallé, M.A. Cueto, A. Dickenstein, E.M. Feichtner
and I. Itenberg, American Mathematical Society,
Contemporary Mathematics
589 (2013) 87-107.
205.
Monomials, binomials, and Riemann-Roch
(with Madhusudan Manjunath),
Journal of Algebraic Combinatorics
37 (2013) 737-756.
204.
Toric cubes (with Alex Engström and Patricia Hersh),
Circolo Matematico di Palermo
62 (2013) 67-78.
203.
Binary cumulant varieties (with Piotr Zwiernik),
Annals of Combinatorics
17 (2013) 229-250.
202.
Combinatorial types of tropical eigenvectors (with Ngoc Tran),
Bulletin of the London Mathematical Society
45 (2013) 27-36.
201.
Matrices with eigenvectors in a given subspace (with Giorgio Ottaviani),
Proceedings of the American Mathematical Society
141 (2013) 1219-1232.
200.
The number of eigenvalues of a tensor (with Dustin Cartwright),
Linear Algebra and its Applications
438 (2013) 942-952.
199.
Geometry of higher-order Markov chains,
Journal of Algebraic Statistics
3 (2012) 1-10.
198.
Algebraic boundaries of Hilbert's SOS cones
(with Grigoriy Blekherman, Jonathan Hauenstein, John Christian Ottem
and Kristian Ranestad), Compositio Mathematica
148 (2012) 1717-1735.
197.
Graphical models for correlated defaults
(with I.O. Filiz, X. Guo and J. Morton),
Mathematical Finance
22 (2012) 621-644.
196. Commutative algebra of statistical ranking (with Volkmar Welker),
Journal of Algebra
361 (2012) 264-286.
195.
Computing linear matrix representations of Helton-Vinnikov curves
(with Daniel Plaumann and Cynthia Vinzant),
in Mathematical Methods in Systems, Optimization and Control,
(eds. Harry Dym, Mauricio de Oliveira, Mihai Putinar),
Operator Theory: Advances and Applications", Vol 222, Birkhauser,
Basel, 2012, pp. 259-277.
194. The central
curve in linear programming (with Jesus De Loera and Cynthia Vinzant),
Foundations of Computational Mathematics
12 (2012) 509-540.
193.
On the convex hull of a space curve (with Kristian Ranestad),
Advances in Geometry 12 (2012) 157-178.
192.
Mustafin varieties (with D. Cartwright, M. Haebich and A. Werner),
Selecta Mathematica
17 (2011) 757-793.
191.
Noncoherent SIMO pre-log via resolution of singularities
(with E. Riegler, V. Morgenshtern, G. Durisi, S. Lin and
H. Bolcskei), 6 pp.,
2011 IEEE International Symposium on Information Theory, St. Petersburg, Russia.
190.
Orbitopes (with R. Sanyal and F. Sottile),
Mathematika
57 (2011) 275-314.
189.
The convex hull of a variety (with K. Ranestad),
in: "Notions of Positivity and the Geometry of Polynomials",
(eds. Petter Branden, Mikael Passare and Mihai Putinar),
Trends in Mathematics, Springer Verlag, Basel, 2011,
pp. 331-344.
188.
Tropical quadrics through three points (with S. Brodsky),
Linear Algebra and its Applications
435 (2011) 1778-1785.
187.
Quartic curves and their bitangents (with D. Plaumann and
C. Vinzant), Journal of Symbolic Computation
46 (2011) 712-733.
186.
Dualities in convex algebraic geometry (with P. Rostalski),
Rendiconti di Mathematica, Serie VII
30 (2010) 285-327.
185.
Siphons in chemical reaction networks (with A. Shiu),
Bulletin of Mathematical Biology
72 (2010) 1448-1463.
184.
Geometry of the restricted Boltzmann machine (with M.A. Cueto
and J. Morton), in Algebraic Methods in Statistics and Probability,
(eds. M. Viana and H. Wynn), American Mathematical Society,
Contemporary Mathematics 516 (2010) 135-153.
183.
Multivariate Gaussians, semidefinite matrix completion, and
convex algebraic geometry (with C. Uhler),
Annals of the Institute of Statistical Mathematics
62 (2010) 603-638.
182.
Blow-ups of P^(n-3) at n points and spinor varieties (with M. Velasco),
Journal of Commutative Algebra 2 (2010)
223-244.
181.
The Hilbert scheme of the diagonal in a product of projective spaces (with D. Cartwright),
International Mathematics Research Notices
9 (2010) 1741-1771.
180.
Sagbi bases of Cox-Nagata rings (with Z. Xu),
Journal of the European Mathematical Society
12 (2010) 429-459.
179.
Commuting birth-death processes (with S. Evans and C. Uhler),
Annals of Applied Probability
20 (2010) 238-266.
178. The algebraic degree of semidefinite programming (with J. Nie and K. Ranestad), Mathematical Programming
122 (2010) 379-405.
177.
Polynomial relations among principal minors of a 4x4 matrix
(with S. Lin), Journal of Algebra
322 (2009) 4121-4131.
176.
Reconstructing spatiotemporal gene expression data from partial observations (with D. Cartwright, S. Brady, D. Orlando, and P. Benfey),
Bioinformatics
25 (2009) 2581-2587.
175.
Computer algebra in systems biology,
(with R. Laubenbacher), American Mathematical Monthly
116 (2009) 882-891.
German version:
Computeralgebra in der Systembiologie,
Informatik-Spektrum 32(1) (2009) 27-32.
174.
Toric dynamical systems,
(with G. Craciun, A. Dickenstein and A. Shiu),
Journal of Symbolic Computation
44 (2009) 1551-1565.
173.
Marginal likelihood integrals for mixtures of independence models (with S. Lin and Z. Xu), Journal of Machine Learning Research
10 (2009) 1611-1631.
172.
Convex rank tests and semigraphoids (with
J. Morton, L. Pachter, A. Shiu and O. Wienand),
SIAM Journal on Discrete Mathematics
23 (2009) 1117-1134.
171.
Matrix cubes parametrized by eigenvalues (with J. Nie),
SIAM Journal on Matrix Analysis and Applications
31 (2009) 755-766.
170.
Normal toric ideals of low codimension,
(with P. Dueck and S. Hosten),
Journal of Pure and Applied Algebra
213 (2009) 1636-1641.
169.
Tropical mathematics, (with D. Speyer), Mathematics Magazine
82 (2009) 163-173.
168.
How to draw tropical planes (with S. Hermann, A. Jensen and M. Joswig),
Electronic Journal of Combinatorics
16(2) (2009) R6.
167. Comparison of pattern detection methods in microarray time series of the segmentation clock,
(with M-L. Dequeant, 12 others, and O. Pourquie),
PLoS ONE 3(8) (2008) e2856.
166.
Elimination theory for tropical varieties (with J. Tevelev),
Mathematical Research Letters
15 (2008) 543-562.
165.
Open problems in algebraic statistics, in
Emerging Applications of Algebraic Geometry,
(editors M. Putinar and S. Sullivant),
I.M.A. Volumes in Mathematics and its Applications,
149, Springer, New York, 2008, pp. 351-364.
164.
The hyperdeterminant and triangulations of the 4-cube,
(with P. Huggins, J. Yu and D. Yuster),
Mathematics of Computation
77 (2008) 1653-1679.
163.
Toric geometry of cuts and splits
(with S. Sullivant),
Michigan Mathematical Journal
57 (2008) 689-709.
162.
Three counterexamples on semigraphoids
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161.
Tropical implicitization and mixed fiber polytopes (with J. Yu)
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Semidefinite representation of the k-ellipse (with
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159.
Affine buildings and tropical convexity,
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158.
Conjunctive Bayesian networks
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Bernoulli 13 (2007) 893-909.
157.
Towards the human genotope (with P. Huggins and L. Pachter),
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156.
Epistasis and shapes of fitness landscapes,
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Statistica Sinica
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155.
Hyperdeterminantal relations among symmetric principal minors,
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The cyclohedron test for finding periodic genes in time course
expression studies (with J. Morton, L. Pachter and A. Shiu),
Statistical Applications in Genetics and Molecular Biology
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153. Tropical discriminants,
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Journal of the American Mathematical Society
20 (2007) 1111-1133.
152. Analysis
of epistatic interactions and fitness
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Computing the integer programming gap (with S. Hosten),
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The Newton polytope of the implicit equation
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149.
Algebraic factor analysis: tetrads, pentads and beyond,
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148.
The mathematics of phylogenomics (with L. Pachter),
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147.
Computing tropical varieties (with T. Bogart, A. Jensen,
D. Speyer and R. Thomas), Journal of Symbolic Computation
42 (2007) 54-73.
146.
Monomial dynamical systems over finite fields
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145.
Geometry of rank tests,
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8 pp., Proceedings of the conference
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144.
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242 (2006) 409-420.
143.
An algebraic geometry approach to nonlinear parametric optimization in
control (with I. Fotiou, P. Rostalski and M. Morari),
American Control Conference,
Minneapolis, MN, June 2006, pp. 3618-3623.
142.
The maximum likelihood degree,
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141.
Combinatorial secant varieties (with S. Sullivant),
Quarterly Journal of Pure and Applied Mathematics
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140.
Minimizing polynomials via sum of squares over the gradient ideal
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Mathematical Programming
106 (2006) 587-606.
139.
Parametric alignment of Drosophila genomes,
(with C. Dewey, P. Huggins, K. Woods and L. Pachter),
PLOS Computational Biology,
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138.
On the toric algebra of graphical models (with D. Geiger and C. Meek),
Annals of Statistics
34 (2006) 1463-1492
137.
Resultants in genetic linkage analysis (with I. Hallgrimsdottir),
Journal of Symbolic Computation 41
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136.
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135.
Matroid polytopes, nested sets and Bergman fans,
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Portugaliae Mathematica
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134.
What is a Grobner basis?,
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Phylogenetic algebraic geometry,
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in Projective Varieties
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A. Geramita, B. Harbourne, R-M. Roig and K. Ranestad),
De Gruyter, Berlin, 2005, pp. 237-255
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Solving the likelihood equations,
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Foundations of Computational Mathematics.
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131.
On the tropical rank of a matrix (with F. Santos and M. Develin),
in Discrete and Computational Geometry, (eds. J.E. Goodman,
J. Pach and E. Welzl), Mathematical Sciences Research
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The graph of monomial ideals (with K. Altmann),
Journal of Pure and Applied Algebra
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129.
First steps in tropical geometry (with J. Richter-Gebert and
T. Theobald), in
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128.
Toric ideals of phylogenetic invariants, (with S. Sullivant),
Journal of Computational Biology
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127.
Algebraic geometry of Bayesian networks
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39 (2005) 331-355.
126.
Parametric inference for biological sequence analysis
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Proceedings of the National Academy of Sciences
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125.
Tropical geometry of statistical models
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124.
Algebraic recipes for integer programming,
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123.
Short rational functions for toric algebra (with J. A. De Loera,
D. Haws, R. Hemmecke, P. Huggins, and R. Yoshida),
Journal of Symbolic Computation
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122.
The tropical Grassmannian (with D. Speyer),
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121.
Classification of six-point metrics
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120.
Multigraded Hilbert schemes (with M. Haiman),
Journal of Algebraic Geometry 13
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119. Supernormal
vector configurations (with S. Hosten and
D. Maclagan), Journal of Algebraic Combinatorics
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118. Tropical Convexity (with M. Develin), Documenta
Mathematica 9 (2004) 1-27.
117. Algebraic unimodular counting (with J. De
Loera), Mathematical Programming, Series B,
96 (2003) 183-203.
116. Minimizing polynomial functions (with P.
Parrilo), Proceedings of the DIMACS Workshop on
Algorithmic and Quantitative Aspects of Real Algebraic
Geometry in Mathematics and Computer Science (March
2001), (eds. S. Basu and L. Gonzalez-Vega), American
Mathematical Society, 2003, pp. 83-100.
115. Higher Lawrence Configurations (with F. Santos),
Journal of Combinatorial Theory, Series A,
103 (2003) 151-164.
114. Alexander duality in subdivisions of Lawrence
polytopes (with F. Santos), Advances in Geometry,
3 (2003) 177-189.
113. Algorithms for the toric Hilbert scheme
(with M. Stillman and R. Thomas), in
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Algorithms Comput. Math., 8, Springer, Berlin, 2002, pp. 179--214.
112. Ideals, varieties and Macaulay 2, in
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Algorithms Comput. Math., 8, Springer, Berlin, 2002, pp. 3--15.
111. Toric hyperkahler varieties (with T. Hausel),
Documenta Mathematica 7
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110. Elimination theory in codimension two (with
A. Dickenstein), Journal of Symbolic Computation
34 (2002) 119-135.
109. Binomial residues (with E. Cattani and
A. Dickenstein), Annales de l'Institute Fourier
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108.Syzygies of oriented matroids (with I. Novik
and A. Postnikov), Duke Mathematical Journal
111 (2002) 287-317.
107.Grobner bases of abelian matrix groups, in
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Geometry, and Engineering, (eds. E. Green, S.
Hosten, R. Laubenbacher, V. Powers), Contemporary
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RI, 2001, pp. 141-143.
106.Rational hypergeometric functions (with
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105. Syzygies of unimodular Lawrence ideals,
(with D. Bayer and S. Popescu), Journal fur
die Reine und Angewandte Mathematik 534
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104. A
sagbi basis for the quantum Grassmannian,
(with F. Sottile), Journal for Pure and Applied
Algebra 158 (2001) 347-366.
103. Four counterexamples in combinatorial algebraic
geometry, Journal of Algebra 230
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102. Generic and cogeneric monomial ideals (with
E. Miller and K. Yanagawa), Journal of Symbolic
Computation 28 (2000) 691-708.
101. Solving algebraic equations in terms of
${\cal A$-hypergeometric series, Discrete
Mathematics 210 (2000) 171-181.
100. Monomial ideals and planar graphs (with
E. Miller), in "Applied Algebra, Algebraic
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Proceedings of AAECC-13 (Honolulu, November 1999),
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99. Cutting corners (with S. Onn), Advances
in Applied Mathematics 23
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98. The Co-Scarf resolution, in "Commutative
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97. Hypergeometric polynomials and integer programming
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96. Numerical Schubert calculus (with B. Huber
and F. Sottile), Journal of Symbolic Computation
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95. Syzygies of codimension $2$ lattice ideals,
(with I. Peeva), Mathematische Zeitschrift
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94. Cellular resolution of monomial modules (with
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Mathematik 502 (1998) 123-140.
93. Grobner deformations of regular holonomic
systems (with M. Saito and N.Takayama), Proceedings
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92. Polynomial equations and convex polytopes,
American Mathematical Monthly 105
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91. Monomial resolutions (with D. Bayer and
I. Peeva), Mathematical Research Letters
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90. Residues and resultants (with E. Cattani
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Sciences of the University of Tokyo 5
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89. Lattice walks and primary decomposition (with
P. Diaconis and D. Eisenbud), Mathematical Essays
in Honor of Gian-Carlo Rota, eds. B. Sagan and
R. Stanley, Progress in Mathematics, Vol. 161,
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88. Algebraic algorithms for sampling from conditional
distributions (with P. Diaconis), Annals
of Statistics 26 (1998)
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87. Generic lattice ideals (with I. Peeva),
Journal of the American Mathematical Society
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86. Non-commutative Grobner bases for commutative
algebras (with D. Eisenbud and I. Peeva), Proceedings
of the American Mathematical Society 126
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85. How to shell a monoid (with I. Peeva and
V. Reiner), Mathematische Annalen 310
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84. Grobner bases and hypergeometric functions,
(with N. Takayama), in Grobner Bases and Applications
(Proc. of the Conference 33 Years of Grobner Bases),
B. Buchberger and F. Winkler (eds.), Cambridge
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83. A toric ring with irrational Poincare-Betti
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82. Equations defining toric varieties, Algebraic
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81. Introduction to resultants, in: D. Cox, B.
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80. Variation of cost functions in integer programming,
(with R.R. Thomas), Mathematical Programming
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79. Computing Hopf bifurcations (with J. Guckenheimer,
M. Myers), SIAM J. Numerical Analysis
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78. Structural Grobner basis detection (with
M. Wiegelmann), Applicable Algebra in Engineering,
Communication and Computing (AAECC Journal) 8
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77. Bernstein's Theorem in affine space (with
B. Huber), Discrete and Computational Geometry
17 (1997) 137-141.
76. Intersection theory on toric varieties (with
W. Fulton), Topology 36
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75. A normal form algorithm for modules over $k[x,y]/\langle
x y \rangle$ (with R. Laubenbacher), Journal
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74. Binomial ideals (with D. Eisenbud), Duke
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73.
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72. Computing multidimensional residues (with
E. Cattani, A. Dickenstein), in Algorithms in
Algebraic Geometry and Applications, (eds. L.
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71. Primitive partition identities (with P. Diaconis,
R. Graham), in Combinatorics, Paul Erdos is Eighty,
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1996, pp. 173-192.
70. The polytope of all triangulations of a point
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69. Initial complexes of prime ideals (with M.
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68. On vector partition functions, J. of Combinatorial
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67. Grobner bases and triangulations of the second
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15 (1995) 409-424.
66. A polyhedral method for solving sparse polynomial
systems (with B. Huber), Mathematics of Computation
64 (1995) 1541-1555.
65. Grobner bases of lattices, corner polyhedra,
and integer programming (with R. Weismantel,
G. Ziegler), Beitrage zur Algebra und Geometrie
36 (1995), 281-298.
64. GRIN: An implementation of Grobner bases for
integer programming (with S.Hosten), in ``Integer
Programming and Combinatorial Optimization'',
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the IV. IPCO Conference (Copenhagen, May 1995),
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63. Bounds for degrees of projective schemes,
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62. Introduction
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61. Intersection
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R. MacPherson, F. Sottile), Journal of Algebraic
Geometry 4 (1995) 181-193.
60. Viro's theorem for complete intersections,
Annali della Scuola Normale Superiore di Pisa.
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59. On the number of real roots of a sparse polynomial, in Hamiltonian and Gradient Flows: Algorithms
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RI, 1994, pp. 137-143.
58. Iterated fibre polytopes (with L.J. Billera),
Mathematika 41 (1994)
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57. Cellular strings on polytopes (with L. Billera,
M. Kapranov), Proceedings of the Amer. Math.
Soc. 122 (1994) 549-555.
56. A note on lattice simplices and toric varieties,
(with S. Onn), American Journal of Mathematics
116 (1994) 1337-1339.
55. Minimal polynomials and sparse resultants,
(with J. Yu), in "Zero-Dimensional Schemes",
(eds. F. Orecchia and L. Chiantini), Proceedings
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54. A quantitative Steinitz Theorem (with S.
Onn), Beitrage zur Algebra und Geometrie
35 (1994) 125-129.
53. Finding sparse systems of parameters (with
D. Eisenbud), Journal of Pure and Applied
Algebra 94 (1994) 143-157.
52. On the Newton polytope of the resultant, Journal
of Algebraic Combinatorics 3
(1994) 207-236.
51. Multigraded resultants of Sylvester type,
(with A. Zelevinsky), Journal of Algebra
163 (1994) 115-127.
50. A note on polynomial reduction (with A. Reeves),
Journal of Symbolic Computation 11
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49. Product formulas for resultants and Chow forms,
(with P. Pedersen), Mathematische Zeitschrift
214 (1993) 377-396.
48. Sparse elimination theory,
in "Computational
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1993, pp. 264-298.
47. Non-extremal Camion bases (with R.G. Bland,
C.W. Ko), Linear Algebra and its Applications
187 (1993) 195-199.
46. Extension spaces of oriented matroids (with
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10 (1993) 23-45.
45. Minkowski addition of polytopes: Computational
complexity and applications to Grobner bases,
(with P. Gritzmann), SIAM J. Discrete Math.
6 (1993) 246-269.
44. Duality and minors of secondary polyhedra,
(with L.J. Billera, I.M. Gel'fand), Journal
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43. Maximal minors and their leading terms (with
A. Zelevinsky), Advances in Mathematics
98 (1993) 65-112.
42. Asymptotic analysis of toric ideals, Memoirs
of the Faculty of Sciences, Kyushu University,
Series A: Mathematics 46, No. 2, (1992) 217-228.
41. Chow polytopes and general resultants (with
M. Kapranov, A. Zelevinsky), Duke Mathematical
Journal 67 (1992) 189-218.
40. Algorithms for the Quillen-Suslin theorem,
(with A. Logar), Journal of Algebra
145 (1992) 231-239.
39. Fiber polytopes (with L.J. Billera), Annals
of Mathematics 135 (1992)
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38. Unimodular fans, toric manifolds and linear
codes (with P. Kleinschmidt and N. Schwartz),
in "Discrete and Computational Geometry:
Papers from the DIMACS Special Year", (eds.
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Math. Soc.. Providence, 1991, pp. 179-186.
37. Computing combinatorial decompositions of
rings (with N. White), Combinatorica
11 (1991), 275-293.
36. Quotients of toric varieties (with M. Kapranov,
A. Zelevinsky), Mathematische Annalen
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35. Computational algebraic geometry of projective
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34. On the synthetic factorization of projectively
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33. Grobner bases of toric varieties, Tohoku
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32. On the topology and geometric construction
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325 (1991) 389-412.
31. Smooth toric varieties with small Picard number
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30. Stanley decompositions of the bracket ring,
(with N. White), Math. Scandinavica 67
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29. Constructions and complexity of secondary
polytopes (with L.J. Billera, P. Filliman), Advances
in Mathematics 83 (1990)
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28. Grobner bases and Stanley decompositions of
determinantal rings, Mathematische Zeitschrift
205 (1990) 137-144.
27. The intrinsic spread of a configuration in
$R^d$ (with J.E. Goodman, R. Pollack), Journal
American Math. Society 3
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26. All $11_3$- and $12_3$-configurations are
rational (with N. White), Aequationes Mathematicae
39 (1990) 254-260.
25. Nonrealizability proofs in computational geometry,
(with J. Bokowski, J. Richter), Discrete Comput.
Geometry 5 (1990) 333-350.
24. Lawrence polytopes (with M. Bayer), Canadian
J. Mathematics 17 (1990)
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23. On the existence of certain smooth toric varieties,
(with J. Gretenkort, P. Kleinschmidt), Discrete
Comput. Geometry 5 (1990)
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22. Coordinate representation of order types requires
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on Theory of Computing, Seattle, 1989, pp.
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21. Introduction to invariant theory in superalgebras,
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Theory and Tableaux, I.M.A. Volumes in Mathematics
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20. Proposal for a geometric algebra software
package (with T. Havel, N. White), SIGSAM
Bulletin 23 (1989) 13-15.
19. Grobner bases and invariant theory (with
N. White), Advances in Mathematics 76
(1989) 245-259.
18. On the matroid stratification of Grassmann
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75 (1989) 202-211.
17. Computing final polynomials and final syzygies
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der Mathematik 15 (1989)
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16. An infinite family of minor-minimal nonrealizable
$3$-chirotopes (with J. Bokowski), Mathematische
Zeitschrift 200 (1989) 583-589.
15. Arrangements of lines and pseudolines without
adjacent triangles (with D. Ljubic, J.P. Roudneff),
J. Combinatorial Theory A 50
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14. Uniform oriented matroids without the isotopy
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White), Discrete Comput. Geometry 4
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13. Neighborly polytopes and oriented matroids,
European J. Combinatorics 9
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12. Tridiagonalization of complex matrices and
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11. Totally positive matrices and cyclic polytopes,
Linear Alg. Appl. 107
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10. Simplicial cells in arrangements and mutations
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9. Some applications of affine Gale diagrams to
polytopes with few vertices, SIAM J. Discrete
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7. Cyclic polytopes and $d$-order curves, Geometriae
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6. Boundary complexes of convex polytopes cannot
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5. Polytopal and non-polytopal spheres - An algorithmic
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4. On the decidability of diophantine problems
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3. Reell realisierbare orientierte Matroide (with
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