7 papers
Lower and upper bounds of Schur characters
Zhuowei Lin, Candice X. T. Zhang, Zhong-Xue Zhang
Characterizations of lower and upper bounds for dual characters of flagged Weyl modules have attracted considerable interest. In this paper, we establish explicit pattern avoidance…
Combinatorial relations among restricted and half Eulerian polynomials of types , , and
Zhong-Xue Zhang
In this paper, we study relations among several types of Eulerian polynomials from a combinatorial viewpoint. We establish an identity between the restricted Eulerian polynomials o…
A symmetric function approach to log-concavity of independence polynomials
Ethan Y. H. Li, Grace M. X. Li, Arthur L. B. Yang +1
As introduced by Gutman and Harary, the independence polynomial of a graph serves as the generating polynomial of its independent sets. In 1987, Alavi, Malde, Schwenk and Erdős con…
Strongly nice property and Schur positivity of graphs
Ethan Y. H. Li, Grace M. X. Li, Arthur L. B. Yang +1
Motivated by the notion of nice graphs, we introduce the concept of strongly nice property, which can be used to study the Schur positivity of symmetric functions. We show that a g…
Stanley's conjecture on the Schur positivity of distributive lattices
Grace M. X. Li, Dun Qiu, Arthur L. B. Yang +1
In this paper we solve an open problem on distributive lattices, which was proposed by Stanley in 1998. This problem was motivated by a conjecture due to Griggs, which equivalently…
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…