2018/02/11 by Linyuan Lü, Lu, Linyuan, Matthew H. Y. Xie +3 · 2 citations
Computer Science · Mathematics · #05A15(Primary) 05B35 #26C10(Secondary) #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Geometry and complex manifolds #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1802.03711
openalex publication_date 2018/02/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Kazhdan-Lusztig polynomial of a matroid was introduced by Elias, Proudfoot and Wakefield, whose properties need to be further explored. In this paper we prove that the Kazhdan-Lusztig polynomials of fan matroids coincide with Motzkin polynomials, which was recently conjectured by Gedeon. As a byproduct, we determine the Kazhdan-Lusztig polynomials of graphic matroids of squares of paths. We further obtain explicit formulas of the Kazhdan-Lusztig polynomials of wheel matroids and whirl matroids. We prove the real-rootedness of the Kazhdan-Lusztig polynomials of these matroids, which provides positive evidence for a conjecture due to Gedeon, Proudfoot and Young. Based on the results on the Kazhdan-Lusztig polynomials, we also determine the Z-polynomials of fan matroids, wheel matroids and whirl matroids, and prove their real-rootedness, which provides further evidence in support of a conjecture of Proudfoot, Xu, and Young.