Oliver Pechenik - Cyclic Sieving of Increasing Tableaux

dmtcs:12815 - Discrete Mathematics & Theoretical Computer Science, January 1, 2013, DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013) - https://doi.org/10.46298/dmtcs.12815
Cyclic Sieving of Increasing TableauxArticle

Authors: Oliver Pechenik 1

  • 1 Department of Mathematics [Urbana]

An $\textit{increasing tableau}$ 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. Using the jeu de taquin for increasing tableaux of [Thomas–Yong '09], we then present a new instance of the cyclic sieving phenomenon of [Reiner–Stanton–White '04].


Volume: DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)
Section: Proceedings
Published on: January 1, 2013
Imported on: November 21, 2016
Keywords: increasing tableaux,cyclic sieving phenomenon,K-promotion,Schröder path,Schröder number,noncrossing partition,[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
Funding:
    Source : OpenAIRE Graph
  • EMSW21-MCTP: Research Experience for Graduate Students; Funder: National Science Foundation; Code: 0838434

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