19 citations · 21 across the 13 of their papers we have counts for
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Unimodality of Kazhdan--Lusztig polynomials of sparse paving matroids
Matthew H. Y. Xie, Zuo-Ru Zhang
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 coefficie…
Nonnegativity of the -polynomial of split matroids
Alice L. L. Gao, Matthew H. Y. Xie
We prove that the -polynomial of every split matroid has nonnegative coefficients, establishing Speyer's conjecture for a class closed under taking minors and containing all pav…
Infinite log-concavity of the Boros--Moll sequences
Matthew H. Y. Xie, Philip B. Zhang
Let be the Boros--Moll coefficient sequence. We prove that, for every integer , the polynomial \[ M_n(x)=\sum_{i=0}^n \bigl(d_i(n)^2-d_{i-1}(n)d_{i+1}(n)\…
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…