19 citations · 31 across the 18 of their papers we have counts for
23 papers
Distributions of Mesh Patterns of Short Lengths on Separable Permutations
Alice L. L. Gao, Sergey Kitaev, Ya-Xing Li +1
This paper contributes to the long line of research on the distribution of mesh patterns in permutations. We extend these studies to separable permutations and carry out a comprehe…
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…
Lascoux series, parking functions and noncrossing partitions
Alice L. L. Gao, Xin-Bei Liu, Arthur L. B. Yang +1
In the study of the generating series of Demazure characters, Lascoux used isobaric divided differences to define a family of polynomials indexed by permutations…
Inverse Kazhdan--Lusztig polynomials of fan matroids
Alice L. L. Gao, Ya-Xing Li, Yun Li
The inverse Kazhdan--Lusztig polynomial of a matroid was introduced by Gao and Xie, and the inverse -polynomial of a matroid was introduced by Ferroni, Matherne, Stevens, and Ve…
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…
Distribution of statistics on separable permutations restricted by a flat POP
Alice L. L. Gao, Sergey Kitaev, Ya-Xing Li +1
Finding distributions of statistics in pattern-avoiding permutations has attracted significant attention in the literature. In particular, Chen, Kitaev, and Zhang derived functiona…
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…
The combinatorics behind the leading Kazhdan-Lusztig coefficients of braid matroids
Alice L. L. Gao, Nicholas Proudfoot, Arthur L. B. Yang +1
Ferroni and Larson gave a combinatorial interpretation of the braid Kazhdan-Lusztig polynomials in terms of series-parallel matroids. As a consequence, they confirmed an explicit f…
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…
On partially ordered patterns of length 4 and 5 in permutations
Alice L. L. Gao, Sergey Kitaev
Partially ordered patterns (POPs) generalize the notion of classical patterns studied widely in the literature in the context of permutations, words, compositions and partitions. I…
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…
On a Greedy Algorithm to Construct Universal Cycles for Permutations
Alice L. L. Gao, Sergey Kitaev, Wolfgang Steiner +1
A universal cycle for permutations of length is a cyclic word or permutation, any factor of which is order-isomorphic to exactly one permutation of length , and containing a…
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…
On pattern avoiding indecomposable permutations
Alice L. L. Gao, Sergey Kitaev, Philip B. Zhang
Comtet introduced the notion of indecomposable permutations in 1972. A permutation is indecomposable if and only if it has no proper prefix which is itself a permutation. Indecompo…
On 132-representable Graphs
Alice L. L. Gao, Sergey Kitaev, Philip B. Zhang
A graph is word-representable if there exists a word over the alphabet such that letters and alternate in if and only if is an edge in . Wor…
Enumeration of Corners in Tree-like Tableaux
Alice L. L. Gao, Emily X. L. Gao, Patxi Laborde-Zubieta +1
In this paper, we confirm conjectures of Laborde-Zubieta on the enumeration of corners in tree-like tableaux and in symmetric tree-like tableaux. In the process, we also enumerate…
Enumeration of Corners in Tree-like Tableaux and a Conjectural (a,b)-analogue
Alice L. L. Gao, Emily X. L. Gao, Patxi Laborde-Zubieta +1
In this paper, we confirm a conjecture of Laborde-Zubieta on the enumeration of corners in tree-like tableaux. Our proof is based on Aval, Boussicault and Nadeau's bijection betwee…
Avoiding vincular patterns on alternating words
Alice L. L. Gao, Sergey Kitaev, Philip B. Zhang
A word is alternating if either (when the word is up-down) or (when the word is down-up). The study of altern…
Pattern-avoiding alternating words
Emma L. L. Gao, Sergey Kitaev, Philip B. Zhang
A word is alternating if either (when the word is up-down) or (when the word is down-up). In this paper, we i…