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.
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 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]
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