Cyclage, catabolism, and the affine Hecke algebra. (2009), Advisor: Mark Haiman. PDF
Cyclage, catabolism, and the affine Hecke algebra. Preprint (2009). PDF
A factorization theorem for affine Kazhdan-Lusztig basis elements. Preprint (2009). PDF
W-graph versions of tensoring with the Sn defining representation. Preprint (Revised 2009). PDF
The toric ideal of a graphic matroid is generated by quadrics.
Combinatorica, 28, no. 3 (2008), 283--297.
PDF
(with A. Berglund and P. Hersh) Combinatorics of multigraded Poincaré series for monomial rings. J. Algebra, 308, no. 1 (2007), 73--90. PS
A special case of Hadwiger's conjecture.
J. Combin. Theory Ser. B, 97, no. 6 (2007), 1056--1073.
PDF
A longer version that was my senior thesis: PDF
(with R. Durrett) Random Oxford graphs. Stochastic Process. Appl., 115, no. 8 (2005), 1257--1278. PDF
Cohomology of the complex Grassmannian. An expository paper for the final in Hutchings' algebraic topology class. PDF
Longest common subsequences and the Bernoulli matching model: numerical work and analyses of the R-reach simplification. For my spring semester undergraduate junior paper. PDF
combinatorics.txt Lots of functions from algebraic combinatorics including cyclage, catabolizability, and the standardization map of Lascoux and Schützenberger.
affineHecke.txt Some messy, slow, but quite general code to compute canonical bases for iterated restriction and inductions. Supports affine Weyl group computations in type A and was written to work for all types but it does not yet do so. Computes cells and the partial order on cells in terms of tableaux.
affineHeckeuserRes3H4.txt
An example using affineHecke.txt to compute the cells of
ResHK IndHJH triv, where K = {s1, s2}, J = {s2}, and H is the Hecke algebra of type A3.