Alexander Wilson

A mathematician next to his slides showing a colorful matrix Taken by Tom Roby at the Discrete Math Day workshop at Smith College
This site was last updated on February 20, 2025. It was created using Jekyll with interactive components running on p5.js.

Research

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.
A proper edge-coloring of a tree on 7 vertices along with the corresponding coloring group
From Coloring Groups
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
An example of applying super RSK inserting a value into a tableau
From Super Multiset RSK and a Mixed Multiset Partition Algebra

Selected Slides

Publications and preprints

  1. The defective parking space and defective Kreweras numbers (with Rebecca E. Garcia, Pamela E. Harris, Alex Moon, Aaron Ortiz, Lauren J. Quesada, Cynthia Marie Rivera Sánchez, Dwight Anderson Williams II), Algebraic Combinatorics, submitted [arXiv:2405.14635]
  2. The support of Kostant's weight multiplicity formula is an order ideal in the weak Bruhat order (with Portia X. Anderson, Esther Banaian, Melanie J. Ferreri, Owen C. Goff, Kimberly P. Hadaway, Pamela E. Harris, Kimberly J. Harry, Nicholas Mayers, Shiyun Wang), preprint [arXiv:2412.16820]
  3. Centralizers in the Plactic Monoid (with Bruce E. Sagan), Semigroup Forum, submitted [arXiv:2410.20460] [GitHub]
  4. Coloring Groups (with Ben Adenbaum), Discrete Mathematics & Theoretical Computer Science, vol. 26:2 (2024) [arXiv 2312.03092] [GitHub]
  5. 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]
  6. A Diagram-Like Basis for the Multiset Partition Algebra, Algebraic Combinatorics, Volume 7 (2024) no. 4, pp. 1225-1259. [arXiv 2307.01353]
  7. The Multiset Partition Algebra: Diagram-Like Bases and Representations. Ph.D. Thesis, Dartmouth College 2023 [pdf]
  8. Closed Forms of Recursive Polynomials and Applications (with M. Haver, K. Lee, W. McDermott, W. Yu, A. Zeleke), Ars Combinatoria, 142 (2019), 175-195.