19 citations · 21 across the 13 of their papers we have counts for
17 papers
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…
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…
Induced log-concavity of equivariant matroid invariants
Alice L. L. Gao, Ethan Y. H. Li, Matthew H. Y. Xie +2
Inspired by the notion of equivariant log-concavity, we introduce the concept of induced log-concavity for a sequence of representations of a finite group. For an equivariant matro…
The equivariant inverse Kazhdan-Lusztig polynomials of uniform matroids
Alice L. L. Gao, Matthew H. Y. Xie, Arthur L. B. Yang
Motivated by the concepts of the inverse Kazhdan-Lusztig polynomial and the equivariant Kazhdan-Lusztig polynomial, Proudfoot defined the equivariant inverse Kazhdan-Lusztig polyno…
The inverse Kazhdan-Lusztig polynomial of a matroid
Alice L. L. Gao, Matthew H. Y. Xie
In analogy with the classical Kazhdan-Lusztig polynomials for Coxeter groups, Elias, Proudfoot and Wakefield introduced the concept of Kazhdan-Lusztig polynomials for matroids. It…
Equivariant Kazhdan-Lusztig polynomials of thagomizer matroids
Matthew H. Y. Xie, Philip B. Zhang
The equivariant Kazhdan-Lusztig polynomial of a matroid was introduced by Gedeon, Proudfoot, and Young. Gedeon conjectured an explicit formula for the equivariant Kazhdan-Lusztig p…
The Kazhdan-Lusztig polynomials of uniform matroids
Alice L. L. Gao, Linyuan Lu, Matthew H. Y. Xie +2
The Kazhdan-Lusztig polynomial of a matroid was introduced by Elias, Proudfoot, and Wakefield [{\it Adv. Math. 2016}]. Let denote the uniform matroid of rank on a set…
Kazhdan-Lusztig polynomials of fan matroids, wheel matroids and whirl matroids
Linyuan Lu, Matthew H. Y. Xie, Arthur L. B. Yang
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-…
Schur positivity and log-concavity related to longest increasing subsequences
Alice L. L. Gao, Matthew H. Y. Xie, Arthur L. B. Yang
Chen proposed a conjecture on the log-concavity of the generating function for the symmetric group with respect to the length of longest increasing subsequences of permutations. Mo…
The Smith normal form of a specialized Giambelli-type matrix
Alice L. L. Gao, Matthew H. Y. Xie, Arthur L. B. Yang
In the study of determinant formulas for Schur functions, Hamel and Goulden introduced a class of Giambelli-type matrices with respect to outside decompositions of partition diagra…
Melham's Conjecture on Odd Power Sums of Fibonacci Numbers
Brian Y. Sun, Matthew H. Y. Xie, Arthur L. B. Yang
Ozeki and Prodinger showed that the odd power sum of the first several consecutive Fibonacci numbers of even order is equal to a polynomial evaluated at certain Fibonacci number of…