Cyclic Sieving for Longest Reduced Words in the Hyperoctahedral Group

  • T. Kyle Petersen
  • Luis Serrano

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 $R(w_0)$.

Published
2010-04-30
Article Number
R67