3 papers
math.CO2026
Real-rootedness of Kazhdan--Lusztig and -polynomials of thagomizer matroids and graphic matroids of
Philip B. Zhang
Let , and let denote the Kazhdan--Lusztig polynomial of its graphic matroid. We prove that, whenever and , the polynomial $P_n(x)+λx…
math.CO2026
Equivariant Kazhdan--Lusztig Polynomials of Thagomizer Matroids with a Hyperoctahedral Group Action
Matthew H. Y. Xie, Philip B. Zhang, Michael X. X. Zhong
The thagomizer matroid, realized as the graphic matroid of the complete tripartite graph , has full automorphism group isomorphic to the hyperoctahedral group whenever $…
math.CO2025
Log-concavity of inverse Kazhdan-Lusztig polynomials of paving matroids
Matthew H. Y. Xie, Philip B. Zhang
Gao and Xie (2021) conjectured that the inverse Kazhdan-Lusztig polynomial of any matroid is log-concave. Although the inverse Kazhdan-Lusztig polynomial may not always have only r…