8 papers
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 and of a classical simple Lie algebra , Kostant's weight multiplicity formula gives the multiplicity of the weight in the irreducible…
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…
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…
On some discrete statistics of parking functions
Ari Cruz, Pamela E. Harris, Kimberly J. Harry +5
Recall that is a parking function if its nondecreasing rearrangement satisfies for all . In thi…
Computing the -Multiplicity of the Positive Roots of 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 in the adjoint representati…
Interval and -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…
Flattened Stirling Permutations
Adam Buck, Jennifer Elder, Azia A. Figueroa +3
Recall that a Stirling permutation is a permutation on the multiset such that any numbers appearing between repeated values of must be greater than …
Counting Parking Sequences and Parking Assortments Through Permutations
Spencer J. Franks, Pamela E. Harris, Kimberly Harry +2
Parking sequences (a generalization of parking functions) are defined by specifying car lengths and requiring that a car attempts to park in the first available spot after its pref…