Pietro Mongelli
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Excedances in classical and affine Weyl groups
dmtcs:3029 -
Discrete Mathematics & Theoretical Computer Science,
January 1, 2012,
DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)
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https://doi.org/10.46298/dmtcs.3029
Excedances in classical and affine Weyl groupsArticle
Authors: Pietro Mongelli 1
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Pietro Mongelli
1 Dipartimento di Matematica "Guido Castelnuovo" [Roma I]
Based on the notion of colored and absolute excedances introduced by Bagno and Garber we give an analogue of the derangement polynomials. We obtain some basic properties of these polynomials. Moreover, we define an excedance statistic for the affine Weyl groups of type $\widetilde{B}_n, \widetilde {C}_n$ and $\widetilde {D}_n$ and determine the generating functions of their distributions. This paper is inspired by one of Clark and Ehrenborg (2011) in which the authors introduce the excedance statistic for the group of affine permutations and ask if this statistic can be defined for other affine groups.
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