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A bijection on core partitions and a parabolic quotient of the affine symmetric group
Chris Berg, Brant Jones, Monica Vazirani
Let be fixed positive integers. In an earlier work, the first and third authors established a bijection between -cores with first part equal to and -co…
Leading coefficients of Kazhdan--Lusztig polynomials for Deodhar elements
Brant C. Jones
We show that the leading coefficient of the Kazhdan--Lusztig polynomial known as is always either 0 or 1 when is a Deodhar element of a finite Weyl group.…
Kazhdan--Lusztig polynomials for maximally-clustered hexagon-avoiding permutations
Brant C. Jones
We provide a non-recursive description for the bounded admissible sets of masks used by Deodhar's algorithm to calculate the Kazhdan--Lusztig polynomials of type ,…
The enumeration of maximally clustered permutations
Hugh Denoncourt, Brant C. Jones
The maximally clustered permutations are characterized by avoiding the classical permutation patterns 3421, 4312, and 4321. This class contains the freely-braided permutations and…
Embedded factor patterns for Deodhar elements in Kazhdan-Lusztig theory
Sara C. Billey, Brant C. Jones
The Kazhdan-Lusztig polynomials for finite Weyl groups arise in the geometry of Schubert varieties and representation theory. It was proved very soon after their introduction that…