Geodesic
Cyclic sieving for longest reduced words in the hyperoctahedral group
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010) (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 $R(w_0)$. 
@article{DMTCS_2010_special_259_a23,
     author = {Petersen, T. K. and Serrano, L.},
     title = {Cyclic sieving for longest reduced words in the hyperoctahedral group},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010)},
     year = {2010},
     doi = {10.46298/dmtcs.2828},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2828/}
}
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Petersen, T. K.; Serrano, L. Cyclic sieving for longest reduced words in the hyperoctahedral group. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010) (2010). doi : 10.46298/dmtcs.2828. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2828/

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