Publications of Lorenz Halbeisen

Preliminary remark:
You may download the ps-files (ps) as well as the pdf-files (pdf) of all articles which are accepted or already published. Notice that these files may differ from the published articles. Further, the abstract of every paper is available in HTML.

Diploma, Thesis, Habilitation, and Book

• Vergleiche zwischen unendlichen Kardinalzahlen in einer Mengenlehre ohne Auswahlaxiom,
  Diplomarbeit, 1990, University of Zürich (Set Theory without the Axiom of Choice)

• Ramsey properties of reals and partitions,
  Ph.D. ETH No. 10828 (1994), ETH Zürich (Generalized Ramsey Theory)

• Combinatorial properties of sets of partitions (ps) (deutsches Autor-Referat),
  Habilitation (2003) at the University of Bern (Combinatorial Set Theory)

• Combinatorial Set Theory: with a gentle introduction to forcing (ps) (pdf)
  Springer-Verlag (London), 2011 [book details] [errata]

Research

Infinite Combinatorics

Combinatorial Set Theory, Generalized Ramsey Theory, Set Theory without the Axiom of Choice, Combinatorics of Forcing Constructions, Combinatorial Methods in Banach Space Theory, Set-Theoretic Topology, Combinatorial Aspects of Algebra

1. Consequences of arithmetic for set theory (ps) (pdf) [abstract] (with Saharon Shelah),
   The Journal of Symbolic Logic 59 (1994) 30-40.

2. Mathias absoluteness and the Ramsey property (ps) (pdf) [abstract] (with Haim Judah),
   The Journal of Symbolic Logic 61 (1996) 177-193.

3. On shattering, splitting and reaping partitions (ps) (pdf) [abstract],
   Mathematical Logic Quarterly 44 (1998) 123-134.

4. Symmetries between two Ramsey properties (ps) (pdf) [abstract],
   Archive for Mathematical Logic 37(4) (1998) 241-260.

5. The cardinality of Hamel bases of Banach spaces (ps) (pdf) [abstract] (with Norbert Hungerbühler),
   East-West Journal of Mathematics 2 (2000) 153-159.

6. Techniques for approaching the dual Ramsey property in the projective hierarchy (ps) (pdf) [abstract] (with Benedikt Löwe),
   Pacific Journal of Mathematics 200(1) (2001) 119-145.

7. Ramseyan ultrafilters (ps) (pdf) [abstract],
   Fundamenta Mathematicae 169(3) (2001) 233-248.

8. Ultrafilter spaces on the semilattice of partitions (ps) (pdf) [abstract] (with Benedikt Löwe),
   Topology and its Applications 115(3) (2001) 317-332.

9. On the complexity of Hamel bases of infinite dimensional Banach spaces (ps) (pdf) [abstract],
   Colloquium Mathematicum 89 (2001) 133-134.

10. Relations between some cardinals in the absence of the axiom of choice (ps) (pdf) [abstract] (with Saharon Shelah),
    The Bulletin of Symbolic Logic 7(2) (2001) 237-261.

11. On continuously Urysohn and strongly separating spaces (ps) (pdf) [abstract] (with Norbert Hungerbühler),
    Topology and its Applications 118(3) (2002) 329-335.

12. A result in dual Ramsey theory (ps) (pdf) [abstract] (with Pierre Matet),
    Journal of Combinatorial Theory (A) 100 (2002) 394-398.

13. Making doughnuts of Cohen reals (ps) (pdf) [abstract],
    Mathematical Logic Quarterly 49(2) (2003) 173-178.

14. A generalization of the dual Ellentuck theorem (ps) (pdf) [abstract] (with Pierre Matet),
    Archive for Mathematical Logic 42(2) (2003) 103-128.

15. On the cardinality of smallest spanning sets of rings (ps) (pdf) [abstract] (with Nadia Boudi),
    Quaestiones Mathematicae 26 (2003) 321-325.

16. On a theorem of Banach and Kuratowski and K-Lusin sets (ps) (pdf) [abstract] (with Tomek Bartoszynski),
    Rocky Mountain Journal of Mathematics 33(4) (2003) 1223-1231.

17. A set-theoretic approach to complete minimal systems in Banach spaces of bounded functions (ps) (pdf) [abstract],
    Matematychni Studii 20(2) (2003) 162-166.

18. On asymptotic models in Banach spaces (ps) (pdf) [abstract] (with Edward Odell),
    Israel Journal of Mathematics 139 (2004) 253-291.

19. Silver measurability and its relation to other regularity properties (ps) (pdf) [abstract] (with Jörg Brendle and Benedikt Löwe),
    Mathematical Proceedings of the Cambridge Philosophical Society 138(1) (2005) 135-149.

20. A number-theoretic conjecture and its implication for set theory (ps) (pdf) [abstract],
    Acta Mathematica Universitatis Comenianae 74(2) (2005) 243-254.

21. On bases in Banach spaces (ps) (pdf) [abstract] (with Tomek Bartoszynski, Mirna Dzamonja, Eva Murtinova, Anatolij Plichko, all-5-pic),
    Studia Mathematica, 170(2) (2005) 147-171.

22. Families of almost disjoint Hamel bases (ps) (pdf) [abstract],
    Extracta Mathematicae, 20(2) (2005) 199-202.

23. A playful approach to Silver and Mathias forcings (ps) (pdf) [abstract],
    Foundations of the Formal Sciences V: Infinite Games (Papers of a Conference held in Bonn, November 26-29, 2004)
    College Publications: Studies in Logic (vol. 11), London (2007), 123-142.

24. Non-separable Banach spaces with non-meager Hamel basis (ps) (pdf) [abstract] (with Taras Banakh and Mirna Dzamonja),
    Studia Mathematica, 189(1) (2008), 27-34.

25. Comparing cardinalities in Zermelo's system (ps) (pdf) [abstract],
    Cahiers du Centre de Logique, 17 (2010), 9-19.




Finite Combinatorics

Number Theory, Extremal Combinatorics, Graph Theory, Ramsey Theory, Enumerative Combinatorics, Design Theory, Combinatorics on Words, Dynamical Systems, Geometry

26. The general counterfeit coin problem (ps) (pdf) [abstract] (with Norbert Hungerbühler),
    Discrete Mathematics 147 (1995) 139-150.

27. The Josephus problem (ps) (pdf) [abstract] (with Norbert Hungerbühler),
    Journal de Théorie des Nombres de Bordeaux 9 (1997) 303-318.

28. Optimal bounds for the length of rational Collatz cycles (ps) (pdf) [abstract] (with Norbert Hungerbühler),
    Acta Arithmetica LXXVIII (1997) 227-239.

29. Packings in complete graphs (ps) (pdf) [abstract] (with Norbert Hungerbühler),
    Ars Combinatoria 48 (1998) 97-110.

30. Powers and polynomials in Z_m (ps) (pdf) [abstract] (with Norbert Hungerbühler and Hans Läuchli),
    Elemente der Mathematik 54(3) (1999) 118-129.

31. Über das Mischen von Spielkarten, ein mathematisches Menü (ps) (pdf) [abstract] (with Stephanie Gloor),
    Elemente der Mathematik 54(4) (1999) 156-162.

32. On generalized Carmichael numbers (ps) (pdf) [abstract] (with Norbert Hungerbühler),
    Hardy-Ramanujan Journal 22 (1999) 8-22.

33. Number theoretic aspects of a combinatorial function (ps) (pdf) [abstract] (with Norbert Hungerbühler),
    Notes on Number Theory and Discrete Mathematics 5 (1999) 138-150.

34. Generation of isospectral graphs (ps) (pdf) [abstract] (with Norbert Hungerbühler),
    Journal of Graph Theory 31 (1999) 255-265.

35. Reconstruction of weighted graphs by their spectrum (ps) (pdf) [abstract] (with Norbert Hungerbühler),
    European Journal of Combinatorics 21 (2000) 641-650.

36. On periodic billiard trajectories in obtuse triangles (ps) (pdf) [abstract] (with Norbert Hungerbühler),
    SIAM Review 42(4) (2000) 657-670.

37. Dual form of combinatorial problems and Laplace techniques (ps) (pdf) [abstract] (with Norbert Hungerbühler),
    The Fibonacci Quarterly 38 (2000) 395-407.

38. An application of van der Waerden's Theorem in additive number theory (ps) (pdf) [abstract] (with Norbert Hungerbühler),
    INTEGERS: The Electronic Journal of Combinatorial Number Theory 0 (2000) #A07, 5 pages.

39. Can Kirkman's schoolgirls walk abreast by forming arithmetic progressions? (ps) (pdf) [abstract],
    The American Mathematical Monthly 110(3) (2003) 228-231.

40. Fans and bundles in the graph of pairwise sums and products (ps) (pdf) [abstract],
    The Electronic Journal of Combinatorics 11(1) (2004) #R6, 11 pages.

41. Avoiding arithmetic progressions in cyclic groups (ps) (pdf) [abstract] (with Stephanie Halbeisen),
    Elemente der Mathematik 60(3) (2005) 114-123.

42. Minimal generating sets of groups, rings, and fields (ps) (pdf) [abstract] (with Martin Hamilton and Pavel Ruzicka),
    Quaestiones Mathematicae 30(3) (2007) 355-363.

43. A simple proof of Poncelet's theorem (ps) (pdf) [abstract] (with Norbert Hungerbühler),
    The American Mathematical Monthly (to appear)