papers
- The reciprocity law for Dedekind sums via the constant Ehrhart coefficient,
American Mathematical Monthly 106, no. 5 (1999), 459-462.
- A closer look at the number of lattice points in rational simplices,
Electronic Journal of Combinatorics 6, no. 1 (1999), R 37 (9 pages).
- Counting lattice points by means of the residue theorem,
Ramanujan Journal 4, no. 3 (2000), 299-310.
- (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).
- Multidimensional Ehrhart reciprocity,
Journal of Combinatorial Theory Series A 97, no. 1 (2002), 187-194.
- (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.
- (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.
- (with Ricardo Diaz and
Sinai Robins)
The Frobenius problem, rational polytopes, and Fourier-Dedekind sums,
Journal of Number Theory 96 (2002), 1-21.
- (with Thomas Zaslavsky)
A Meshalkin theorem for projective geometries,
Journal of Combinatorial Theory Series A 102 (2003), 433-441.
- Dedekind cotangent sums,
Acta Arithmetica 109, no. 2 (2003), 109-130.
- (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.
- (with David Einstein and Shelemyahu Zacks)
Some Experimental Results on the Frobenius Problem,
Experimental Mathematics 12, no. 3 (2003), 263-269.
[PARI-GP program]
- (with Dennis Pixton)
The Ehrhart polynomial of the Birkhoff polytope,
Discrete & Computational Geometry 30, no. 4 (2003), 623-637.
- (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.
- (with Shelemyahu Zacks)
Refined upper bounds for the linear Diophantine problem of Frobenius,
Advances in Applied Mathematics 32, no. 3 (2004), 454-467.
- (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.
- 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).
- (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).
- (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).
- (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.
- (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.
- (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.
- (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]
- (with Serkan Hosten)
Cyclotomic Polytopes and Growth Series of Cyclotomic Lattices,
Mathematical Research Letters 13, no. 4 (2006), 607-622.
- (with Thomas Zaslavsky)
Inside-out polytopes,
Advances in Mathematics 205, no. 1 (2006), 134-162.
- (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.
- (with Thomas Zaslavsky)
An enumerative geometry for magic and magilatin labellings,
Annals of Combinatorics 10, no. 4 (2006), 395-413.
- 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.
- (with Frank Sottile)
Irrational proofs for three theorems of Stanley,
European Journal of Combinatorics 28, no. 1 (2007), 403-409.
- (with Steven Sam and Kevin Woods)
Maximal periods of (Ehrhart) quasi-polynomials,
Journal of Combinatorial Theory Series A 115, no. 3 (2008), 517-525.
- (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).
- (with Christian Haase and Frank Sottile)
to appear in Mathematical Intelligencer.
- (with Christian Haase and Asia Matthews)
Dedekind-Carlitz polynomials as lattice-point enumerators in rational polyhedra,
to appear in Mathematische Annalen.
- (with Mike Develin)
On Stanley's reciprocity theorem for rational cones.
- (with Richard Ehrenborg)
Ehrhart-Macdonald reciprocity extended.
- (with Christian Haase and Steven Sam)
Grid graphs, Gorenstein polytopes, and domino stackings.
- (with Mary Halloran)
Finite trigonometric character sums via discrete Fourier analysis.
- (with Alan Stapledon)
Asymptotics of Ehrhart delta-vectors.
- (with Thomas Zaslavsky)
Six little squares and how their numbers grow.
