7 papers · 1 filter
Permanental Inequalities and Unit Interval Orders
Sihong Pan, Mark Skandera, Jiayuan Wang
Given a square matrix, the permanent is a determinant-like function without signs. In this paper, we study inequalities involving permanents of certain submatrices. We first focus…
On Kazhdan--Lusztig basis elements having no reversal factorization
Tommy Parisi, Ben Spahiu, Mark Skandera +1
For in the symmetric group , let be the corresponding modified, signless Kazhdan--Lusztig basis element of the type- Hecke algebra . An extensi…
Hook immanantal inequalities for totally nonnegative matrices
Mark Skandera
Given a weakly decreasing positive integer sequence summing to , let denote the irreducible character of the symmetric group indexed by…
Hyperoctahedral group characters and a type-BC analog of graph coloring
Mark Skandera
We state combinatorial formulas for hyperoctahedral group () character evaluations of the form $Ï( {{\widetilde C}_w}^{\negthickspace\negthickspace BC}\negthickspac…
A generalization of Deodhar's defect statistic for Iwahori--Hecke algebras of type
Gavin Hobbs, Tommy Parisi, Mark Skandera +1
Let be the Iwahori--Hecke algebra corresponding to any Coxeter group. Deodhar's defect statistic [Geom. Dedicata 36, (1990) pp.95--119] allows one to expand products of simple…
LLT Polynomials and Hecke Algebra Traces
Alejandro H. Morales, Mark A. Skandera, Jiayuan Wang
We show that coefficients in unicellular LLT polynomials are evaluations of Hecke algebra traces at Kazhdan-Lusztig basis elements. We express these in terms of traditional trace b…