The Z-polynomial of a matroid
Combinatorics
2017-06-20 v1
Abstract
We introduce the Z-polynomial of a matroid, which we define in terms of the Kazhdan-Lusztig polynomial. We then exploit a symmetry of the Z-polynomial to derive a new recursion for Kazhdan-Lusztig coefficients. We solve this recursion, obtaining a closed formula for Kazhdan-Lusztig coefficients as alternating sums of multi-indexed Whitney numbers. For realizable matroids, we give a cohomological interpretation of the Z-polynomial in which the symmetry is a manifestation of Poincare duality.
Keywords
Cite
@article{arxiv.1706.05575,
title = {The Z-polynomial of a matroid},
author = {Nicholas Proudfoot and Ben Young and Yuan Xu},
journal= {arXiv preprint arXiv:1706.05575},
year = {2017}
}