Geodesic
Cyclic sieving for longest reduced words in the hyperoctahedral group
The electronic journal of combinatorics, Tome 17 (2010)

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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 $R(w_0)$.
DOI : 10.37236/339
Classification : 05E10, 05E18 
T. Kyle Petersen; Luis Serrano. Cyclic sieving for longest reduced words in the hyperoctahedral group. The electronic journal of combinatorics, Tome 17 (2010). doi: 10.37236/339
@article{10_37236_339,
     author = {T. Kyle Petersen and Luis Serrano},
     title = {Cyclic sieving for longest reduced words in the hyperoctahedral group},
     journal = {The electronic journal of combinatorics},
     year = {2010},
     volume = {17},
     doi = {10.37236/339},
     zbl = {1228.05299},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/339/}
}
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