Year: 2026
Type: preprint
Abstract: We prove that the Kazhdan--Lusztig polynomial of a loopless sparse paving matroid is unimodal. When the rank is at least five and the corank is positive, we show that the coefficient sequence is strictly unimodal except for three explicitly determined parameter triples, each giving two equal maximal coefficients. We also determine the modes and classify the degenerate loopless sparse paving matroids of positive rank and corank.
Source: arXiv (Cornell University)
Authors: Xie, Matthew H. Y., Zhang, Zuo-Ru
Institutions: Tianjin University of Technology, Hebei Normal University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7215100286