matthias beck

professor of mathematics
kumi does math
san francisco state university


  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. How to change coins, M&M's, or chicken nuggets: The linear Diophantine problem of Frobenius, Resources for Teaching Discrete Mathematics: Classroom Projects, History Modules, and Articles (B. Hopkins, ed.), pp. 65-74. Mathematical Association of America, 2009.
  34. (with Christian Haase and Frank Sottile)

    Mathematical Intelligencer 31, no. 1 (2009), 9-17.
  35. (with Christian Haase and Steven Sam) Grid graphs, Gorenstein polytopes, and domino stackings, Graphs and Combinatorics 25, no. 4 (2009), 409-426.
  36. (with Alan Stapledon) On the log-concavity of Hilbert series of Veronese subrings and Ehrhart series, Mathematische Zeitschrift 264, no. 1 (2010), 195-207.
  37. (with Mary Halloran) Finite trigonometric character sums via discrete Fourier analysis, International Journal of Number Theory 6, no. 1 (2010), 51-67.
  38. (with Thomas Zaslavsky) Six little squares and how their numbers grow, Journal of Integer Sequences 13 (2010), Article 10.6.2.
  39. (with Sinai Robins and Steven Sam) Positivity theorems for solid-angle polynomials, Beiträge zur Algebra und Geometrie 51, no. 2 (2010), 493-507. Corrigendum in Beiträge zur Algebra und Geometrie 56, no. 2 (2015), 775–776.
  40. (with Ira Gessel, Sunyoung Lee, and Carla Savage) Symmetrically constrained compositions, Ramanujan Journal 23 (2010), 355-369.
  41. (with Andrew Van Herick) Enumeration of 4x4 magic squares, Mathematics of Computation 80 (2011), 617-621.
  42. (with Federico Ardila, Serkan Hosten, Julian Pfeifle, and Kim Seashore) Root polytopes and growth series of root lattices, SIAM Journal on Discrete Mathematics 25 (2011), 360-378.
  43. (with Curtis Kifer) An extreme family of generalized Frobenius numbers, Integers: the Electronic Journal of Combinatorial Number Theory 11 (2011), A 24.
  44. (with Anastasia Chavez) Bernoulli-Dedekind sums, Acta Arithmetica 149 (2011), 65-82.
  45. (with Ben Braun) Nowhere-harmonic colorings of graphs, Proceedings of the American Mathematical Society 140 (2012), 47-63.
  46. Combinatorial reciprocity theorems, Jahresbericht der DMV 114, no. 1 (2012), 3-22.
  47. (with Tristram Bogart and Tu Pham) Enumeration of Golomb rulers and acyclic orientations of mixed graphs, Electronic Journal of Combinatorics 19, no. 3 (2012), P42 (13 pages).
  48. (with Yvonne Kemper) Flows on simplicial complexes, Discrete Mathematics & Theoretical Computer Science Proc. AR (2012), 817-826 (Proceedings of FPSAC'12).
  49. (with Ben Braun and Nguyen Le) Mahonian partition identities via polyhedral geometry, From Fourier Analysis and Number Theory to Radon Transforms and Geometry: In Memory of Leon Ehrenpreis (H. Farkas, R. Gunning, M. Knopp, and B. A. Taylor, eds.), Developments in Mathematics 28 (2013), 41-54.
  50. (with Pallavi Jayawant and Tyrrell McAllister) Lattice-point generating functions for free sums of convex sets, Journal of Combinatorial Theory Series A 120 (2013), 1246-1262.
  51. (with Ben Braun) Euler-Mahonian statistics via polyhedral geometry, Advances in Mathematics 244 (2013), 925-954.
  52. (with Jessica De Silva, Gabriel Dorfsman-Hopkins, Joseph Pruitt, and Amanda Ruiz) The combinatorics of interval-vector polytopes, Electronic Journal of Combinatorics 20, no. 3 (2013), P22 (12 pages).
  53. (with Thomas Bliem, Ben Braun, and Carla Savage) Lattice point generating functions and symmetric cones, Journal of Algebraic Combinatorics 38, no. 3 (2013), 543-566.
  54. (with Felix Breuer, Logan Godkin, and Jeremy Martin) Enumerating colorings, tensions and flows in cell complexes, Journal of Combinatorial Theory Series A 122 (2014), 82-106.
  55. (with Florian Kohl) Rademacher-Carlitz polynomials, Acta Arithmetica 163 (2014), 379-393.
  56. (with Abdelmejid Bayad) Relations for Bernoulli-Barnes numbers and Barnes zeta functions, International Journal of Number Theory 10 (2014), 1321-1335.
  57. (with Alyssa Cuyjet, Gordon Rojas Kirby, Molly Stubblefield, and Michael Young) Nowhere-zero k-flows on graphs, Annals of Combinatorics 18 (2014), 579-583.
  58. (with Daniel Blado, Joseph Crawford, Taina Jean-Louis, and Michael Young) On weak chromatic polynomials of mixed graphs, Graphs and Combinatorics 31 (2015), 91-98.
  59. (with Neville Robbins) Variations on a generating-function theme: Enumerating compositions with parts avoiding an arithmetic sequence, American Mathematical Monthly 122 (2015), 256-263.
  60. (with Ben Braun, Matthias Köppe, Carla Savage, and Zafeirakis Zafeirakopoulos) s-Lecture hall partitions, self-reciprocal polynomials, and Gorenstein cones, Ramanujan Journal 36 (2015), 123-147.
  61. (with Jessica Delgado, Joseph Gubeladze, and Mateusz Michalek) Very ample and Koszul segmental fibers, Journal of Algebraic Combinatorics 42 (2015), 165-182.
  62. (with Ana Berrizbeitia, Michael Dairyko, Claudia Rodriguez, Amanda Ruiz, and Schuyler Veeneman) Parking functions, Shi arrangements, and mixed graphs, American Mathematical Monthly 122 (2015), 660-673.
  63. (with George Andrews and Neville Robbins) Partitions with fixed differences between largest and smallest parts, Proceedings of the American Mathematical Society 143 (2015), 4283-4289.
  64. (with Mela Hardin) A bivariate chromatic polynomial for signed graphs, Graphs and Combinatorics 31 (2015), 1211-1221.
  65. (with Erika Meza, Bryan Nevarez, Alana Shine, and Michael Young) The chromatic polynomials of signed Petersen graphs, Involve 8 (2015), 825-831.
    [sage code]
  66. (with Ben Braun, Matthias Köppe, Carla Savage, and Zafeirakis Zafeirakopoulos) Generating functions and triangulations for lecture hall cones, SIAM Journal on Discrete Mathematics 30 (2016), 1470-1479.
  67. Stanley's major contributions to Ehrhart theory, The Mathematical Legacy of Richard P. Stanley (P. Hersh, T. Lam, P. Pylyavskyy and V. Reiner, eds.), AMS, 2016, pp. 53-63.
  68. (with Juan Auli and Abdelmejid Bayad) Reciprocity theorems for Bettin-Conrey sums, Acta Arithmetica 181 (2017), 297-319.
  69. (with Katharina Jochemko and Emily McCullough) h*-polynomials of zonotopes, Transactions of the American Mathematical Society 371 (2019), 2021-2042.
  70. (with Serkan Hosten and Matthias Schymura) Lonely runner polyhedra, Integers: the Electronic Journal of Combinatorial Number Theory 19 (2019), A 29 (13 pages).
  71. (with Christian Haase, Akihiro Higashitani, Johannes Hofscheier, Katharina Jochemko, Lukas Katthän, and Mateusz Michalek) Smooth centrally symmetric polytopes in dimension 3 are IDP, Annals of Combinatorics 23 (2019), 255-262.
  72. (with Leonardo Bardomero) Frobenius coin-exchange generating functions, American Mathematical Monthly 127 (2020), 308-315.
  73. (with Maryam Farahmand, Gina Karunaratne, and Sandra Zuniga Ruiz) Bivariate order polynomials, Graphs and Combinatorics 36 (2020), 921-931.
  74. (with Federico Ardila and Jodi McWhirter) The arithmetic of Coxeter permutahedra, Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales 44, no. 173 (2020), 1152-1166.
  75. (with Paul Gunnells and Evgeny Materov) Weighted lattice point sums in lattice polytopes, unifying Dehn-Sommerville and Ehrhart-Macdonald, Discrete & Computational Geometry 65, no. 2 (2021), 365-384.
  76. (with Emerson Leon) Binomial inequalities for chromatic, flow, and tension polynomials, Discrete & Computational Geometry 66, no. 2 (2021), 464-474.
  77. (with Ben Braun and Andrés Vindas-Meléndez) Decompositions of Ehrhart h*-polynomials for rational polytopes, Discrete & Computational Geometry 68, no. 1 (2022), 50-71 and Séminaire Lotharingien de Combinatoire, 85B (2021), Article 38 (Proceedings of FPSAC'21).
  78. (with Sophia Elia and Sophie Rehberg) Rational Ehrhart theory, Integers: the Electronic Journal of Combinatorial Number Theory 23 (2023), A 60 (31 pages) and Séminaire Lotharingien de Combinatoire, 86B (2022), Article 44 (Proceedings of FPSAC'22).
  79. (with Esme Bajo) Boundary h*-polynomials of rational polytopes, SIAM Journal on Discrete Mathematics 37 (2023), no. 3, 1952-1969.
  80. (with Ellinor Janssen and Katharina Jochemko) Lattice zonotopes of degree 2, Beiträge zur Algebra und Geometrie 64 (2023), 1011-1025.
  81. (with Sampada Kolhatkar) Bivariate chromatic polynomials of mixed graphs, Discrete Mathematics & Theoretical Computer Science 25 (2023), no. 2, Article 2 (10 pages).
  82. (with Danai Deligeorgaki, Max Hlavacek, and Jerónimo Valencia-Porras, Inequalities for f*-vectors of lattice polytopes, Advances in Geometry 24 (2024), no. 2, 141-150, and Séminaire Lotharingien de Combinatoire 89B (2023), Article 43 (Proceedings of FPSAC'23).
  83. (with Matthias Schymura) Deep lattice points in zonotopes, lonely runners, and lonely rabbits, International Mathematics Research Notices 2024, no. 8, 6553–6578.
  84. (with Max Hlavacek) Signed poset polytopes.
  85. (with Esme Bajo and Andrés Vindas-Meléndez) q-chromatic polynomials.

department of mathematics
san francisco state university
1600 holloway ave
san francisco, ca 94132