Cyclic sieving for longest reduced words in the hyperoctahedral group

Details Cyclic sieving for longest reduced words in the hyperoctahedral group Cyclic sieving for longest reduced words in the hyperoctahedral group

2009-05-16

arxiv.org/abs/0905.2650v1

Mathematics

Combinatorics

10 pages

Scientific paper

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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