Hecke insertion and maximal increasing and decreasing sequences in fillings of stack polyominoes

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:176

Article

Guo, Ting^1,2  Poznanovic, Svetlana³ 

[1] Hunan Normal Univ, Sch Math & Stat, MOE LCSM, Changsha, Hunan, Peoples R China

[2] Univ Vienna, Fac Math, Vienna, Austria

[3] Clemson Univ, Sch Math & Stat Sci, Clemson, SC 29631 USA

关键词: Maximal chains;    Hecke insertion;    K-theoretic jeu de taquin;    Stack polyominoes;   

DOI  :  10.1016/j.jcta.2020.105304

来源: Elsevier

【 摘 要 】

We prove that the number of 01-fillings of a given stack polyomino (a polyomino with justified rows whose lengths form a unimodal sequence) with at most one 1 per column which do not contain a fixed-size northeast chain and a fixed-size southeast chain, depends only on the set of row lengths of the polyomino. The proof is via a bijection between fillings of stack polyominoes which differ only in the position of one row and uses the Hecke insertion algorithm by Buch, Kresch, Shimozono, Tamvakis, and Yong and the jeu de taquin for increasing tableaux of Thomas and Yong. Moreover, our bijection gives another proof of the result by Chen, Guo, and Pang that the crossing number and the nesting number have a symmetric joint distribution over linked partitions. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free