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arXiv · 0905.2650

Cyclic sieving for longest reduced words in the hyperoctahedral group

T. Kyle Petersen·Luis Serrano
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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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T. Kyle Petersen, Luis Serrano. 2009-05-16. Cyclic sieving for longest reduced words in the hyperoctahedral group. https://arxiv.org/abs/0905.2650

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