7 papers
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…
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…