Publications (reverse chronological order)

  • The generalized Frobenius problem via restricted partition functions, The Electronic Journal of Combinatorics, to appear (2023). [pdf]
  • When is a numerical semigroup a quotient? (with Tristram Bogart and Christopher O'Neill), Bulletin of the Australian Mathematical Society (2023), 1-10. [pdf, publisher]
  • A plethora of polynomials: a toolbox for counting problems (with Tristram Bogart), The American Mathematical Monthly 129 (2022), 203-222. [pdf, publisher]
  • Periodic behavior in families of numerical and affine semigroups via parametric Presburger arithmetic (with Tristram Bogart and John Goodrick), Semigroup Forum 102 (2021), 340-356. [pdf, publisher]
  • A parametric version of LLL and some consequences: parametric shortest and closest vector problems (with Tristram Bogart and John Goodrick), SIAM Journal on Discrete Mathematics, 34 (2020), 2363-2387. [pdf, publisher]
  • Parametric Presburger arithmetic: complexity of counting and quantifier elimination (with Tristram Bogart, John Goodrick, and Danny Nyguyen), Mathematical Logic Quarterly 65 (2019), 237-250. [pdf, publisher]
  • The danger of testing by selecting controlled subsets, with applications to spoken-word recognition (with David Liben-Nowell, Julia Strand, Alexa Sharp, and Tom Wexler, Journal of Cognition 2(1):2 (2019). [pdf, publisher]
  • AdaM and GrahaM Play the Stock Market, The American Mathematical Monthly 125 (2018), p:1257. [pdf, publisher]
  • Parametric Presburger arithmetic: logic, combinatorics, and quasi-polynomial behavior (with Tristram Bogart and John Goodrick), Discrete Analysis (2017), #4. [pdf, publisher]
  • The parametric Frobenius problem (with Bjarke Hammersholt Roune), Electronic Journal of Combinatorics 22 (2015), #P2.36. [pdf, publisher]
  • Presburger arithmetic, rational generating functions, and quasi-polynomials, Journal of Symbolic Logic 80 (2015), 433-449. Extended abstract in Proceedings of ICALP '13, the International Colloquium on Automata, Languages and Programming. [full pdf, publisher, conf. pdf, conf. publisher]
  • The unreasonable ubiquitousness of quasi-polynomials, Electronic Journal of Combinatorics 21 (2014), #P1.44. Extended abstract in Proceedings of FPSAC '13, the International Conference on Formal Power Series and Algebraic Combinatorics. [full pdf, publisher, conf. pdf, conf. publisher]
  • Book Review of Symmetry: A Mathematical Exploration, by Kristopher Tapp. In The American Mathematical Monthly 120 (2013), 477-481. [pdf, publisher]
  • Computing Shapley value in supermodular coalitional games (with David Liben-Nowell, Alexa Sharp, and Tom Wexler), Proceedings of COCOON, the International Computing and Combinatorics Conference (2012). [pdf, publisher]
  • The price of civil society (with Russell Buehler, Zachary Goldman, David Liben-Nowell, Yuechao Pei, Jamie Quadri, Alexa Sharp, Sam Taggart, and Tom Wexler), Proceedings of WINE, the Workshop on Internet & Network Economics (2011). [pdf, publisher]
  • A finite calculus approach to Ehrhart polynomials (with Steven Sam), Electronic Journal of Combinatorics 17 (2010), #R68. [pdf, publisher]
  • An implementation of the Barvinok-Woods integer projection algorithm (with Matthias Koeppe and Sven Verdoolaege), Proceedings of the International Conference on Information Theory and Statistical Learning (2008), 53-59. [pdf]
  • Maximal periods of (Ehrhart) quasi-polynomials (with Matthias Beck and Steven Sam), Journal of Combinatorial Theory, Series A, 115 (2008), 517-525. [pdf, publisher]
  • Counting with rational generating functions (with Sven Verdoolaege), Journal of Symbolic Computation 43 (2008), 75-91. [pdf, publisher]
  • The probability of choosing primitive sets (with Sergi Elizalde), Journal of Number Theory 125 (2007), 39-49. [pdf, publisher]
  • Bounds on the number of inference functions of a graphical model (with Sergi Elizalde), Statistica Sinica 17 (2007), 1395-1415. Also in Proceedings of FPSAC, the International Conference on Formal Power Series and Algebraic Combinatorics (2006). [pdf, publisher, conference]
  • Parametric alignment of Drosophila genomes (with Colin Dewey, Peter Huggins, Bernd Sturmfels, and Lior Pachter), PLoS Computational Biology 2 (2006), 606-614. [pdf, publisher]
  • Computing the period of an Ehrhart quasi-polynomial, Electronic Journal of Combinatorics 12 (2005), #R34. [pdf, publisher]
  • Short rational generating functions and their applications to integer programming (with Ruriko Yoshida), SIAG/OPT Views and News 16 (2005), 15-19. [pdf]
  • Parametric Sequence Alignment (with Colin Dewey), in Algebraic Statistics for Computational Biology, Lior Pachter and Bernd Sturmfels, eds, Cambridge University Press (2005), 193-205. [publisher]
  • Neighborhood complexes, and generating functions for affine semigroups (with Herbert Scarf), Discrete and Computational Geometry 35 (2006), 385 - 403. [pdf, publisher]
  • The minimum period of the Ehrhart quasi-polynomial of a rational polytope (with Tyrrell McAllister), Journal of Combinatorial Theory, Series A, 109 (2005), 345-352. [pdf, publisher]
  • Rational Generating Functions and Lattice Point Sets, Ph.D. thesis, University of Michigan (2004). [pdf]
  • Short rational generating functions for lattice point problems (with Alexander Barvinok), Journal of the American Mathematical Society 16 (2003), 957-979. [pdf, publisher]

Unpublished manuscripts

Unpublished papers from my college days

  • Groovin’ with the Big Band(width) (with Dan Durand and Jacob Kline), UMAP Journal 21(3), (2000). Our winning paper in the Mathematical Contest in Modeling. [pdf]
  • Lengths of Systoles on Tileable Hyperbolic Surfaces, Rose Hulman Technical Report Series in Mathematics, MSTR 00-09 (2000). My paper from the REU at Rose-Hulman. [pdf]

Expository articles from college

  • Mathematical Melodies: The Beauty of Numbers, The Philomathesian, Wake Forest University, 6(2), 8-11 (Spring 2000). [pdf]
  • Art As War: Ruminations on the Aesthetics of Islamic Decoration, The Philomathesian, Wake Forest University, 5, 17-21 (Fall 1998). [pdf]

For more images, check out my talks. Website design adapted from openwebdesign.