Alexander N. Wilson

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.

Publications, Preprints, and Selected Slides

  1. Kronecker Coefficients, Crystals, and Bitableaux (with Nate Harman). preprint. [arXiv:2507.14026] [Slides, SSMC Jun 6, 2024 (20min survey talk)]
  2. 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]
  3. The support of Kostant's weight multiplicity formula is an order ideal in the weak 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) . preprint. [arXiv:2412.16820] [Slides, UW Madison Combinatorics Seminar Jan 27, 2025]
  4. Centralizers in the Plactic Monoid (with Bruce E. Sagan). Proceedings of FPSAC 2025, Sém. Lothar. Combin. 93B (2025), 12pp.
  5. Centralizers in the Plactic Monoid (with Bruce E. Sagan). Semigroup Forum (2025). [arXiv:2410.20460] [GitHub]
  6. Coloring Groups (with Ben Adenbaum). Discrete Mathematics & Theoretical Computer Science, vol. 26:2 (2024). [arXiv:2312.03092] [GitHub]
  7. 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]
  8. 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]
  9. The Multiset Partition Algebra: Diagram-Like Bases and Representations . Ph.D. Thesis, Dartmouth College 2023. [pdf]
  10. 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

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