Research — Alexander N. Wilson

I am primarily interested in algebraic combinatorics, which aims to answer questions about algebraic structures through the use of combinatorial objects like graphs or tableaux. In particular, I apply these techniques to the area of representation theory.

Slides from Recent Talks

Representation Theory through Parking Functions (UWM Graduate Student Colloquium)

Publications, Preprints, and Selected Slides

Topics:

A Pollak Proof for the Number of Weakly Increasing Parking Functions (with J. Carlos Martinez Mori Pamela E. Harris). preprint. [arXiv:2511.20796]
Kronecker Coefficients, Crystals, and Bitableaux (with Nate Harman). preprint. [arXiv:2507.14026] [Slides, SSMC Jun 6, 2024 (20min survey talk)]
Costello Divisibility: Exploration of a Comedic Division Algorithm (with Sam Thiel). College Mathematics Journal, to appear. [pdf]
The defective parking space and defective Kreweras numbers (with R. E. Garcia, P. E. Harris, A. Moon, A. Ortiz, L. J. Quesada, C. M. Rivera Sánchez, D. A. Williams II) . Discrete Mathematics & Theoretical Computer Science, submitted. [arXiv:2405.14635]
The support of Kostant's weight multiplicity formula is an order ideal in the Bruhat order (with P. X. Anderson, E. Banaian, M. J. Ferreri, O. C. Goff, K. P. Hadaway, P. E. Harris, K. J. Harry, N. Mayers, S. Wang) . Journal of Combinatorics, to appear. [arXiv:2412.16820] [Slides, UW Madison Combinatorics Seminar Jan 27, 2025]
Centralizers in the Plactic Monoid (with Bruce E. Sagan). Proceedings of FPSAC 2025, Sém. Lothar. Combin. 93B (2025), 12pp.
Centralizers in the Plactic Monoid (with Bruce E. Sagan). Semigroup Forum (2025). [arXiv:2410.20460] [GitHub]
Coloring Groups (with Ben Adenbaum). Discrete Mathematics & Theoretical Computer Science, vol. 26:2 (2024). [arXiv:2312.03092] [GitHub]
Super Multiset RSK and a Mixed Multiset Partition Algebra . Electronic Journal of Combinatorics, 31 (2024), no. 4, Paper No. 4.45. [arXiv:2308.07238] [GitHub] [Slides, AMS Eastern Fall Sectional 2024]
A Diagram-Like Basis for the Multiset Partition Algebra . Algebraic Combinatorics, Volume 7 (2024) no. 4, pp. 1225-1259. [arXiv:2307.01353] [Slides, UW Milwaukee Colloquium Feb 14, 2025]
The Multiset Partition Algebra: Diagram-Like Bases and Representations . Ph.D. Thesis, Dartmouth College 2023. [pdf]
Closed Forms of Recursive Polynomials and Applications (with M. Haver, K. Lee, W. McDermott, W. Yu, A. Zeleke) . Ars Combinatoria, 142 (2019), 175-195.

Pictures

A lexicographic bitableau decomposed into three skew shapes. This decomposition corresponds to a restriction of a $\mathfrak{gl}_{3\cdot2}$-crystal structure to a $\mathfrak{gl}_2$-crystal structure. From Kronecker Coefficients, Crystals, and Bitableaux
A poset illustrating a recursive structure of Weyl alternation sets in type A From The support of Kostant's weight multiplicity formula is an order ideal in the weak Bruhat order
My coauthors' (facetious) reviews of Kostant's weight multiplicity formula. The study of the Weyl alternation set is meant to address the last comment about how large the Weyl groups are to sum over. From The support of Kostant's weight multiplicity formula is an order ideal in the weak Bruhat order