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Cyclic Sieving of Increasing Tableaux

Abstract : 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].
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https://hal.inria.fr/hal-01229744
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Oliver Pechenik. Cyclic Sieving of Increasing Tableaux. 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), 2013, Paris, France. pp.325-336. ⟨hal-01229744⟩

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