A Combinatorial Formula for Kazhdan-Lusztig Polynomials of Sparse Paving Matroids
Combinatorics
2020-06-19 v1
Abstract
We prove the positivity of Kazhdan-Lusztig polynomials for sparse paving matroids, which are known to be logarithmically almost all matroids, but are conjectured to be almost all matroids. The positivity follows from a remarkably simple combinatorial formula we discovered for these polynomials using skew young tableaux. This supports the conjecture that Kazhdan-Lusztig polynomials for all matroids have non-negative coeffiecients. In special cases, such as uniform matroids, our formula has a nice combinatorial interpretation.
Cite
@article{arxiv.2006.10209,
title = {A Combinatorial Formula for Kazhdan-Lusztig Polynomials of Sparse Paving Matroids},
author = {Kyungyong Lee and George D. Nasr and Jamie Radcliffe},
journal= {arXiv preprint arXiv:2006.10209},
year = {2020}
}