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Discrete Mathematics & Theoretical Computer Science |
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.2828Cyclic sieving for longest reduced words in the hyperoctahedral groupArticle
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 $R(w_0)$.
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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