My research focuses on using polynomials to do discrete math. It's as simple as that. Below is my work.
Journal Articles
Permutations with a Given X-Descent Set
Growth Rates of Permutations with Given Descent or Peak Set European Journal of Combinatorics , 131, 104246, 2026. — w/ Justin Troyka
Revisiting Rédei Berge Symmetric Functions via Matrix Algebra Electronic Journal of Combinatorics , Vol 32(4), P.4.43, 2025. — w/ John Irving
Partition Rank and Partition Lattices Order , Vol 42, pages 371-388, 2025.
Sets Avoiding Full-Rank Three-Point Patterns in (Fq n )k Are Exponentially Small Australasian Journal of Combinatorics , 85(3): 423-429, 2023.
Burning Graph Classes Graphs and Combinatorics , 38(4), Article 121, 2022. — w/ Vibha Rohilla
On Distinct Distances Between a Variety and a Point Set Electronic Journal of Combinatorics , 29(3), P3.21, 2022. — w/ Bryce McLaughlin
Factorization Length Distribution For Affine Semigroups III: Modular Equidistribution for Numerical Semigroups with Arbitrarily Many Generators Journal of the Australian Mathematical Society , 113(1): 21-35, 2022. — w/ Stephan Ramon Garcia, Christopher O'Neill, Timothy Wesley
Factorization Length Distribution For Affine Semigroups II: Asymptotic Behavior for Numerical Semigroups with Arbitrarily Many Generators Journal of Combinatorial Theory, Series A , 178: 105358, 2021. — w/ Stephan Ramon Garcia, Christopher O'Neill, Samuel Yih
Weighted Means of B-Splines, Positivity of Divided Differences, and Complete Homogeneous Symmetric Polynomials Linear Algebra and its Applications , 608: 68-83, 2021. — w/ Albrecht Böttcher, Stephan Ramon Garcia, Christopher O'Neill
Counting Peaks on Graphs Australasian Journal of Combinatorics , 75(2): 174-189, 2019. — w/ Alex Diaz-Lopez, Lucas Everham, Pamela E. Harris, Erik Insko, Vince Marcantonio
Descent Polynomials Discrete Mathematics , 342: 1674-1686, 2019. — w/ Alex Diaz-Lopez, Pamela E. Harris, Erik Insko, Bruce Sagan
Sparse Neural Codes and Convexity Involve , 12(5): 737-754, 2019. — w/ R. Amzi Jeffs, Natchanon Suaysom, Aleina Wachtel, Nora Youngs
Lattice Point Visibility On Power Functions INTEGERS , 18: A90, 2018. — w/ Pamela E. Harris
Homomorphisms Preserving Neural Ideals Journal of Pure and Applied Algebra , 222(11): 3470-3482, 2018. — w/ R. Amzi Jeffs, Nora Youngs
The q-analog of Kostant's partition function and the highest root of the classical Lie algebras Australasian Journal Of Combinatorics , 71(1): 68-91, 2018. — w/ Pamela E. Harris, Erik Insko
A Proof of the Peak Polynomial Positivity Conjecture Journal of Combinatorial Theory Series A , 149: 21-29, 2017. — w/ Alex Diaz-Lopez, Pamela E. Harris, Erik Insko
What makes a neural code convex? SIAM Journal on Applied Algebra and Geometry , 1(1): 222-238, 2017. — w/ Carina Curto, Elizabeth Gross, Jack Jeffries, Katherine Morrison, Zvi Rosen, Anne Shiu, Nora Youngs
Low Degree Nullstellensatz Certificates for 3-Colorability Electronic Journal of Combinatorics , 23(1): P1.6, 2016. — w/ Bo Li, Benjamin Lowenstein
Chromatic Bounds on Orbital Chromatic Roots Electronic Journal of Combinatorics , 21(4): P4.17, 2014. — w/ Dae Hyun Kim, Alexander H. Mun
Strong Nonnegativity and Sums of Squares on Real Varieties Journal of Pure and Applied Algebra , 217(5): 843-850, 2013. — w/ Brian Osserman
On Volumes of Permutation Polytopes Fields Institute Communications , Discrete Geometry and Optimization, 55-77, 2013. — w/ Katherine Burggraf, Jesus De Loera
On The Hardness of Counting and Sampling Center Strings IEEE/ACM Transactions on Computational Biology and Bioinformatics , 9(6): 1843-1846, 2012. — w/ Christina Boucher
Recognizing Graph Theoretic Properties with Polynomial Ideals Electronic Journal of Combinatorics , 17(1): R114, 2010. — w/ Christopher Hillar, Jesus De Loera, Peter N. Malkin
Asymptotics of Largest Components in Combinatorial Structures Algorithmica , 46(3-4): 493-503, 2006. — w/ Daniel Panario, Bruce Richmond, Jacki Whitely
Conference Articles
New Perspectives on Flexibility in Simple Temporal Planning ICAPS 2018 , 18 pp., 2018. — w/ Jim Boerkoel, Amy Huang, Liam Lloyd
A Proof of the Peak Polynomial Positivity Conjecture FPSAC 2017 , 10 pp., 2017. — w/ Alex Diaz-Lopez, Pamela E. Harris, Erik Insko
On The Hardness of Counting and Sampling Center Strings SPIRE 2010 , 128-135, 2010. — w/ Christina Boucher
Distribution of the Number of Encryptions in Revocation Schemes for Stateless Receivers DMTCS / 5th Colloquium on Math & CS , 195-206, 2008. — w/ Christopher Eagle, Zhicheng Gao, Daniel Panario, Bruce Richmond
