Cyclic sieving for longest reduced words in the hyperoctahedral group

T. K. Petersen; L. Serrano

doi:10.46298/dmtcs.2828

T. K. Petersen ; L. Serrano - Cyclic sieving for longest reduced words in the hyperoctahedral group

dmtcs:2828 - Discrete Mathematics & Theoretical Computer Science, January 1, 2010, DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010) - https://doi.org/10.46298/dmtcs.2828

Cyclic sieving for longest reduced words in the hyperoctahedral groupConference paper

Authors: T. K. Petersen ¹; L. Serrano ²

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 $R(w_0)$ .

https://doi.org/10.46298/dmtcs.2828

Source: HAL:hal-01186256v1

Volume: DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010)

Section: Proceedings

Published on: January 1, 2010

Imported on: January 31, 2017

Keywords: Cyclic sieving,hyperoctahedral group,standard Young tableau,shifted staircase,reduced word,[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]

Funding:

Source : OpenAIRE Graph

Algebraic Combinatorics; Funder: National Science Foundation; Code: 0555880

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