6 papers
Varieties of chain complexes and mixed dimer covers
Portia X. Anderson, Esther Banaian, Melanie J. Ferreri +3
A quiver representation consists of a collection of vector spaces along with a set of arrows, which are linear maps between these spaces. In this work, we study quiver representati…
A Pollak Proof for the Number of Weakly Increasing Parking Functions
Pamela E. Harris, J. Carlos Martínez 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…
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…
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…
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…