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Cyclic sieving for longest reduced words in the hyperoctahedral group

Abstract : We show that the set $R(w_0)$ of reduced expressions for the longest element in the hyperoctahedral group exhibits the cyclic sieving phenomenon. More specifically, $R(w_0)$ possesses a natural cyclic action given by moving the first letter of a word to the end, and we show that the orbit structure of this action is encoded by the generating function for the major index on $R(w_0)$.
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https://hal.inria.fr/hal-01186256
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T. K. Petersen, L. Serrano. Cyclic sieving for longest reduced words in the hyperoctahedral group. 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), 2010, San Francisco, United States. pp.983-994. ⟨hal-01186256⟩

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