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Cyclic sieving of increasing tableaux and small Schröder paths

Authors
Journal
Journal of Combinatorial Theory Series A
0097-3165
Publisher
Elsevier
Volume
125
Identifiers
DOI: 10.1016/j.jcta.2014.04.002
Disciplines
  • Mathematics

Abstract

Abstract 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 Schröder 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.

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