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5 papers · 1 filter
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…
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…
Congruences on the Number of Restricted -ary Partitions
Qing-Hu Hou, Hai-Tao Jin, Yan-Ping Mu +1
Andrews, Brietzke, Rødseth and Sellers proved an infinite family of congruences on the number of the restricted -ary partitions when is a prime. In this note, we show that t…
On the Enumeration of -Core Partitions
Jane Y. X. Yang, Michael X. X. Zhong, Robin D. P. Zhou
Anderson established a connection between core partitions and order ideals of certain posets by mapping a partition to its -set. In this paper, we give a characterization of the…
On Permutations with Bounded Drop Size
Joanna N. Chen, William Y. C. Chen
The maximum drop size of a permutation of is defined to be the maximum value of . Chung, Claesson, Dukes and Graham obtained polynomials $P_k(x)…