matthias beck

some of matt's pictures

papers

  1. The reciprocity law for Dedekind sums via the constant Ehrhart coefficient, American Mathematical Monthly 106, no. 5 (1999), 459-462.
  2. A closer look at the number of lattice points in rational simplices, Electronic Journal of Combinatorics 6, no. 1 (1999), R 37 (9 pages).
  3. Counting lattice points by means of the residue theorem, Ramanujan Journal 4, no. 3 (2000), 299-310.
  4. (with Ira Gessel and Takao Komatsu) The polynomial part of a restricted partition function related to the Frobenius problem, Electronic Journal of Combinatorics 8, no. 1 (2001), N 7 (5 pages).
  5. Multidimensional Ehrhart reciprocity, Journal of Combinatorial Theory Series A 97, no. 1 (2002), 187-194.
  6. (with Sinai Robins) Explicit and efficient formulas for the lattice point count in rational polygons using Dedekind-Rademacher sums, Discrete & Computational Geometry 27 (2002), 443-459.
  7. (with Thomas Zaslavsky) A Shorter, simpler, stronger proof of the Meshalkin-Hochberg-Hirsch bounds on componentwise antichains, Journal of Combinatorial Theory Series A 100 (2002), 196-199.
  8. (with Ricardo Diaz and Sinai Robins) The Frobenius problem, rational polytopes, and Fourier-Dedekind sums, Journal of Number Theory 96 (2002), 1-21.
  9. (with Thomas Zaslavsky) A Meshalkin theorem for projective geometries, Journal of Combinatorial Theory Series A 102 (2003), 433-441.
  10. Dedekind cotangent sums, Acta Arithmetica 109, no. 2 (2003), 109-130.
  11. (with Moshe Cohen, Jessica Cuomo, and Paul Gribelyuk) The number of "magic" squares, cubes, and hypercubes, American Mathematical Monthly 110, no. 8 (2003), 707-717.
  12. (with David Einstein and Shelemyahu Zacks) Some Experimental Results on the Frobenius Problem, Experimental Mathematics 12, no. 3 (2003), 263-269. [PARI-GP program]
  13. (with Dennis Pixton) The Ehrhart polynomial of the Birkhoff polytope, Discrete & Computational Geometry 30, no. 4 (2003), 623-637.
  14. (with Sinai Robins) A formula related to the Frobenius problem in two dimensions, Number Theory. New York Seminar 2003 (D. Chudnovsky, G. Chudnovsky, M. Nathanson, eds.), pp. 17-23. Springer, Berlin, 2004.
  15. (with Shelemyahu Zacks) Refined upper bounds for the linear Diophantine problem of Frobenius, Advances in Applied Mathematics 32, no. 3 (2004), 454-467.
  16. (with Sinai Robins) Dedekind sums: a combinatorial-geometric viewpoint, Unusual Applications of Number Theory (M. B. Nathanson, ed.), DIMACS: Series in Discrete Mathematics and Theoretical Computer Science 64 (2004), 25-35.
  17. The partial-fractions method for counting solutions to integral linear systems, Discrete & Computational Geometry 32 (2004), 437-446 (special issue in honor of Louis Billera).
  18. (with Jesus A. Deloera, Mike Develin, Julian Pfeifle, and Richard Stanley) Coefficients and roots of Ehrhart polynomials, Contemporary Mathematics 374 (2005), 15-36 (Proceedings of the Summer Research Conference on Integer Points in Polyhedra, July 13 - July 17, 2003 in Snowbird, Utah).
  19. (with Beifang Chen, Lenny Fukshansky, Christian Haase, Allen Knutson, Bruce Reznick, Sinai Robins, and Achill Schuermann) Problems from the Cottonwood Room, Contemporary Mathematics 374 (2005), 179-191 (Proceedings of the Summer Research Conference on Integer Points in Polyhedra, July 13 - July 17, 2003 in Snowbird, Utah).
  20. (with Bruce C. Berndt, O-Yeat Chan, and Alexandru Zaharescu) Determinations of analogues of Gauss sums and other trigonometric sums, International Journal of Number Theory 1, no. 3 (2005), 333-356.
  21. (with Sinai Robins and Shelemyahu Zacks) Higher-dimensional Dedekind sums and their bounds arising from the discrete diagonal of the n-cube, Advances in Applied Mathematics 36, no. 1 (2006), 1-29.
  22. (with Xueqin Wang and Thomas Zaslavsky) A unifying generalization of Sperner's theorem, More Sets, Graphs and Numbers: A Salute to Vera Sos and Andras Hajnal (E. Gyari, G. O. H. Katona, and L. Lovasz, eds.) Bolyai Society Mathematical Studies 15, pp. 9-24. Springer, Berlin, and Janos Bolyai Mathematical Society, Budapest, 2006.
  23. (with M. Welleda Baldoni, Charles Cochet, and Michele Vergne) Volume computation for polytopes and partition functions for classical root systems, Discrete & Computational Geometry 35 (2006), 551-595. [Maple programs]
  24. (with Serkan Hosten) Cyclotomic Polytopes and Growth Series of Cyclotomic Lattices, Mathematical Research Letters 13, no. 4 (2006), 607-622.
  25. (with Thomas Zaslavsky) Inside-out polytopes, Advances in Mathematics 205, no. 1 (2006), 134-162.
  26. (with Thomas Zaslavsky) The number of nowhere-zero flows in graphs and signed graphs, Journal of Combinatorial Theory Series B 96, no. 6 (2006), 901-918.
  27. (with Thomas Zaslavsky) An enumerative geometry for magic and magilatin labellings, Annals of Combinatorics 10, no. 4 (2006), 395-413.
  28. Geometric proofs of polynomial reciprocity laws of Carlitz, Berndt, and Dieter, Diophantine analysis and related fields 2006, 11-18, Sem. Math. Sci. 35, Keio University, Yokohama, 2006.
  29. (with Frank Sottile) Irrational proofs for three theorems of Stanley, European Journal of Combinatorics 28, no. 1 (2007), 403-409.
  30. (with Steven Sam and Kevin Woods) Maximal periods of (Ehrhart) quasi-polynomials, Journal of Combinatorial Theory Series A 115, no. 3 (2008), 517-525.
  31. (with Benjamin Nill, Bruce Reznick, Carla Savage, Ivan Soprunov, and Zhiqiang Xu) Let me tell you my favorite lattice-point problem..., Contemporary Mathematics 452 (2008), 179-187 (Proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Integer Points in Polyhedra, June 2006, in Snowbird, Utah).
  32. (with Christian Haase and Asia Matthews) Dedekind-Carlitz polynomials as lattice-point enumerators in rational polyhedra, Mathematische Annalen 341, no. 4 (2008), 945-961.
  33. (with Christian Haase and Frank Sottile)

    Mathematical Intelligencer 31, no. 1 (2009), 9-17.
  34. (with Alan Stapledon) On the log-concavity of Hilbert series of Veronese subrings and Ehrhart series, Mathematische Zeitschrift 264, no. 1 (2010), 195-207.
  35. (with Mary Halloran) Finite trigonometric character sums via discrete Fourier analysis, to appear in International Journal of Number Theory.
  36. (with Christian Haase and Steven Sam) Grid graphs, Gorenstein polytopes, and domino stackings, to appear in Graphs and Combinatorics.
  37. (with Andrew Van Herick) Enumeration of 4x4 magic squares, to appear in Mathematics of Computation.
  38. (with Mike Develin) On Stanley's reciprocity theorem for rational cones.
  39. (with Richard Ehrenborg) Ehrhart-Macdonald reciprocity extended.
  40. (with Federico Ardila, Serkan Hosten, Julian Pfeifle, and Kim Seashore) Root polytopes and growth series of root lattices
  41. (with Sinai Robins and Steven Sam) Positivity theorems for solid-angle polynomials
  42. (with Ira Gessel, Sunyoung Lee, and Carla Savage) Symmetrically constrained compositions
  43. (with Thomas Zaslavsky) Six little squares and how their numbers grow.

all of my papers are also available at the mathematics arXiv
reviews can be found at mathSciNet

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