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Promotion and cyclic sieving via webs

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Abstract

We show that Schützenberger’s promotion on two and three row rectangular Young tableaux can be realized as cyclic rotation of certain planar graphs introduced by Kuperberg. Moreover, following work of the third author, we show that this action admits the cyclic sieving phenomenon.

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Correspondence to T. Kyle Petersen.

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Petersen, T.K., Pylyavskyy, P. & Rhoades, B. Promotion and cyclic sieving via webs. J Algebr Comb 30, 19–41 (2009). https://doi.org/10.1007/s10801-008-0150-3

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Keywords

  • Promotion
  • Webs
  • Cyclic sieving