5 papers
A Pollak Proof for the Number of Weakly Increasing Parking Functions
Pamela E. Harris, J. Carlos MartÃnez Mori, Alexander N. Wilson
We develop a circular-street argument, in the style of Pollak, to obtain a new proof that there are weakly increasing parking functions of length…
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 irreduci…
Kronecker Coefficients, Crystals, and Bitableaux
Nate Harman, Alexander N. Wilson
What might a combinatorial interpretation of the Kronecker coefficients even look like? We introduce a class of combinatorial objects called bitableaux, which we believe are a natu…
Centralizers in the plactic monoid
Bruce E. Sagan, Alexander N. Wilson
Let u be a word over the positive integers. Motivated in part by a question from representation theory, we study the centralizer set of u which is C(u) = {w | uw is Knuth-equivalen…
Coloring Groups
Ben Adenbaum, Alexander Wilson
We introduce coloring groups, which are permutation groups obtained from a proper edge coloring of a graph. These groups generalize the generalized toggle groups of Striker (which…