7 papers
From Unit Interval Orders to Totally Nonnegative Matrices: Permanental Inequalities and Bruhat-Increasing Bijections
Sihong Pan, Mark Skandera, Jiayuan Wang
Given an matrix and subsets of , let denote the -submatrix of . We prove that,…
On the Impossibility of Parabolic Factorization of certain Kazhdan-Lusztig Basis Elements
Tommy Parisi, Mark Skandera, Ben Spahiu +1
For w in the symmetric group S_n, let C_w be the corresponding modified, signless Kazhdan-Lusztig basis element of the type-A Hecke algebra H_n(q). An extension [Ann. Comb. 25, no.…
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…
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…
Coincidences between intervals in two partial orders on complex reflection groups
Joel Brewster Lewis, Jiayuan Wang
In a finite real reflection group, the reflection length of each element is equal to the codimension of its fixed space, and the two coincident functions determine a partial order…