Kimberly J. Harry

collaborators

6 papers

math.RT2024

The support of Kostant's weight multiplicity formula is an order ideal in the weak Bruhat order

Portia X. Anderson, Esther Banaian, Melanie J. Ferreri +7

For integral weights $λ$ and $μ$ of a classical simple Lie algebra $g$ , Kostant's weight multiplicity formula gives the multiplicity of the weight $μ$ in the irreducible…

math.CO2024

Enumerating runs, valleys, and peaks in Catalan words

Jean-Luc Baril, Pamela E. Harris, Kimberly J. Harry +2

We provide generating functions, formulas, and asymptotic expressions for the number of Catalan words based on the number of runs of ascents (descents), runs of weak ascents (desce…

math.CO2024

On the Lucky and Displacement Statistics of Stirling Permutations

Laura Colmenarejo, Aleyah Dawkins, Jennifer Elder +5

Stirling permutations are parking functions, and we investigate two parking function statistics in the context of these objects: lucky cars and displacement. Among our results, we…

math.CO2023

On some discrete statistics of parking functions

Ari Cruz, Pamela E. Harris, Kimberly J. Harry +5

Recall that $α = (a_{1}, a_{2}, \dots, a_{n}) \in [n]^{n}$ is a parking function if its nondecreasing rearrangement $β = (b_{1}, b_{2}, \dots, b_{n})$ satisfies $b_{i} \leq i$ for all $1 \leq i \leq n$ . In thi…

math.RT2023

Computing the $q$ -Multiplicity of the Positive Roots of $sl_{r + 1} (C)$ and Products of Fibonacci Numbers

Kimberly J. Harry

Using Kostant's weight multiplicity formula, we describe and enumerate the terms contributing a nonzero value to the multiplicity of a positive root $μ$ in the adjoint representati…

math.CO2023

Interval and $ℓ$ -interval Rational Parking Functions

Tomás Aguilar-Fraga, Jennifer Elder, Rebecca E. Garcia +12

Interval parking functions are a generalization of parking functions in which cars have an interval preference for their parking. We generalize this definition to parking functions…