Cyclic sieving of increasing tableaux and small Schroder paths

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:125

Article

Pechenik, Oliver

关键词: Cyclic sieving phenomenon;    Increasing tableau;    Schroder path;    Schroder number;    Jeu de taquin;    Frieze pattern;    Promotion;   

DOI  :  10.1016/j.jcta.2014.04.002

来源: Elsevier

【 摘 要 】

An increasing tableau is a semistandard tableau with strictly increasing rows and columns. It is well known that the Catalan numbers enumerate both rectangular standard Young tableaux of two rows and also Dyck paths. We generalize this to a bijection between rectangular 2-row increasing tableaux and small Schroder paths. We demonstrate relations between the jeu de taquin for increasing tableaux developed by H. Thomas and A. Yong and the combinatorics of tropical frieze patterns. We then use this jeu de taquin to present new instances of the cyclic sieving phenomenon of V. Reiner, D. Stanton, and D. White, generalizing results of D. White and of J. Stembridge. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free