PreprintCC BY 4.0arXiv
Real-rootedness of Kazhdan--Lusztig polynomials of sparse paving matroids
Abstract
We prove that every nonconstant Kazhdan--Lusztig polynomial of a sparse paving matroid has only simple negative zeros. For each rank d≥5, the Kazhdan--Lusztig polynomial of the uniform matroid of rank d−2 on d elements strictly interlaces those of all sparse paving matroids of rank d and corank at least two.
Related
- Unimodality of Kazhdan--Lusztig polynomials of sparse paving matroids
- Prescribed Turán sign patterns for inverse Kazhdan-Lusztig polynomials of matroids
- Real-rootedness of the Z-polynomials of sparse paving matroids and strict interlacing for uniform matroids
- Kazhdan--Lusztig Polynomials for permutations with Pid,w(1)=3 and Irreducible Singular Locus
- Hybrid Kazhdan-Lusztig basis and parabolic induction
BibTeX
@misc{zhang2026realrootedness,
title = {{Real-rootedness of Kazhdan--Lusztig polynomials of sparse paving matroids}},
author = {Philip B. Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.07099},
eprint = {2610.07099},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.07099},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Real-rootedness of Kazhdan--Lusztig polynomials of sparse paving matroids
AU - Philip B. Zhang
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.07099
UR - https://arxiv.org/abs/2610.07099
AB - We prove that every nonconstant Kazhdan--Lusztig polynomial of a sparse paving matroid has only simple negative zeros. For each rank d≥5, the Kazhdan--Lusztig polynomial of the uniform matroid of rank d−2 on d elements strictly interlaces those of all sparse paving matroids of rank d and corank at least two.
ER -