5 papers
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 $…
Equivariant inverse -polynomials of matroids
Alice L. L. Gao, Yun Li, Matthew H. Y. Xie
Motivated by the notion of the inverse -polynomial introduced by Ferroni, Matherne, Stevens, and Vecchi, we study the equivariant inverse -polynomial of a matroid equipped wi…
Equivariant inverse Kazhdan--Lusztig polynomials of thagomizer matroids
Alice L. L. Gao, Yun Li, Matthew H. Y. Xie
In this paper, we focus on the equivariant inverse Kazhdan--Lusztig polynomials of thagomizer matroids, a natural family of graphic matroids associated with the complete tripartite…
The inverse -polynomial of a matroid
Alice L. L. Gao, Xuan Ruan, Matthew H. Y. Xie
Motivated by the -polynomials of matroids, Ferroni, Matherne, Stevens, and Vecchi introduced the inverse -polynomial of a matroid. In this paper, we prove several fundamental…
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…