- 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 Asia Matthews) Dedekind-Carlitz polynomials as lattice-point enumerators in rational polyhedra,
*Mathematische Annalen*341, no. 4 (2008), 945-961. - 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. - (with Christian Haase and Frank Sottile)

*Mathematical Intelligencer*31, no. 1 (2009), 9-17. - (with Christian Haase and Steven Sam)
Grid graphs, Gorenstein polytopes, and domino stackings,
*Graphs and Combinatorics*25, no. 4 (2009), 409-426. - (with Alan Stapledon)
On the log-concavity of Hilbert series of Veronese subrings and Ehrhart series,
*Mathematische Zeitschrift*264, no. 1 (2010), 195-207. - (with Mary Halloran) Finite trigonometric character sums via discrete Fourier analysis,
*International Journal of Number Theory*6, no. 1 (2010), 51-67. - (with Thomas Zaslavsky) Six little squares and how their numbers grow,
*Journal of Integer Sequences*13 (2010), Article 10.6.2. - (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. - (with Ira Gessel, Sunyoung Lee, and Carla Savage)
Symmetrically constrained compositions,
*Ramanujan Journal*23 (2010), 355-369. - (with Andrew Van Herick) Enumeration of 4x4 magic squares,
*Mathematics of Computation*80 (2011), 617-621. - (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. - (with Curtis Kifer)
An extreme family of generalized Frobenius numbers,
*Integers: the Electronic Journal of Combinatorial Number Theory*11 (2011), A 24. - (with Anastasia Chavez)
Bernoulli-Dedekind sums,
*Acta Arithmetica*149 (2011), 65-82. - (with Ben Braun)
Nowhere-harmonic colorings of graphs,
*Proceedings of the American Mathematical Society*140 (2012), 47-63. -
Combinatorial reciprocity theorems,
*Jahresbericht der DMV*114, no. 1 (2012), 3-22. - (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). - (with Yvonne Kemper)
Flows on simplicial complexes,
*Discrete Mathematics & Theoretical Computer Science*Proc. AR (2012), 817-826 (Proceedings of FPSAC'12). - (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. - (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. - (with Ben Braun)
Euler-Mahonian statistics via polyhedral geometry,
*Advances in Mathematics*244 (2013), 925-954. - (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). - (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. - (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. - (with Florian Kohl)
Rademacher-Carlitz polynomials,
*Acta Arithmetica*163 (2014), 379-393. - (with Abdelmejid Bayad)
Relations for Bernoulli-Barnes numbers and Barnes zeta functions,
*International Journal of Number Theory*10 (2014), 1321-1335. - (with Alyssa Cuyjet, Gordon Rojas Kirby, Molly Stubblefield, and Michael Young)
Nowhere-zero
**k**-flows on graphs,*Annals of Combinatorics*18 (2014), 579-583. - (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. - (with Neville Robbins)
Variations on a generating-function theme: Enumerating compositions with parts avoiding an arithmetic sequence,
*American Mathematical Monthly*122 (2015), 256-263. - (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. - (with Jessica Delgado, Joseph Gubeladze, and Mateusz Michalek)
Very ample and Koszul segmental fibers,
*Journal of Algebraic Combinatorics*42 (2015), 165-182. - (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. - (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. - (with Mela Hardin)
A bivariate chromatic polynomial for signed graphs,
*Graphs and Combinatorics*31 (2015), 1211-1221. - (with Erika Meza, Bryan Nevarez, Alana Shine, and Michael Young)
The chromatic polynomials of signed Petersen graphs,
*Involve*8 (2015), 825-831.

[sage code] - (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. - 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. - (with Juan Auli and Abdelmejid Bayad)
Reciprocity theorems for Bettin-Conrey sums,
*Acta Arithmetica*181 (2017), 297-319. - (with Katharina Jochemko and Emily McCullough)
*h**-polynomials of zonotopes,*Transactions of the American Mathematical Society*371 (2019), 2021-2042. - (with Serkan Hosten and Matthias Schymura)
Lonely runner polyhedra,
*Integers: the Electronic Journal of Combinatorial Number Theory*19 (2019), A 29 (13 pages). - (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. - (with Leonardo Bardomero)
Frobenius coin-exchange generating functions,
*American Mathematical Monthly*127 (2020), 308-315. - (with Maryam Farahmand, Gina Karunaratne, and Sandra Zuniga Ruiz)
Bivariate order polynomials,
*Graphs and Combinatorics*36 (2020), 921-931. - (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. - (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. - (with Emerson Leon)
Binomial inequalities for chromatic, flow, and
tension polynomials,
*Discrete & Computational Geometry*66, no. 2 (2021), 464-474. - (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). - (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). - (with Esme Bajo)
Boundary h*-polynomials of rational
polytopes,
*SIAM Journal on Discrete Mathematics*37 (2023), no. 3, 1952-1969. - (with Ellinor Janssen and Katharina Jochemko)
Lattice zonotopes of degree 2,
*Beiträge zur Algebra und Geometrie*64 (2023), 1011-1025. - (with Sampada Kolhatkar) Bivariate chromatic polynomials of mixed graphs,
*Discrete Mathematics & Theoretical Computer Science*25 (2023), no. 2, Article 2 (10 pages). - (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). - (with Matthias Schymura)
Deep lattice points in zonotopes, lonely runners, and lonely rabbits,
*International Mathematics Research Notices*2024, no. 8, 6553–6578. - (with Mitsuki Hanada, Max Hlavacek, John Lentfer, Andrés Vindas-Meléndez, and Katie Waddle) Polyhedral geometry of refined q,t-Catalan numbers, to appear in Journal of Combinatorics.
- (with Max Hlavacek) Signed poset polytopes,
- (with Esme Bajo and Andrés Vindas-Meléndez) q-chromatic polynomials.
- (with Eleonore Bach and Sophie Rehberg) Acyclotopes and tocyclotopes.
- (with Danai Deligeorgaki) Canon permutation posets.

department of mathematics

san francisco state university

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san francisco, ca 94132

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