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Discrete Mathematics & Theoretical Computer Science |
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.
Source : ScholeXplorer
IsRelatedTo ARXIV 2010.09513 Source : ScholeXplorer IsRelatedTo DOI 10.1016/j.disc.2021.112716 Source : ScholeXplorer IsRelatedTo DOI 10.48550/arxiv.2010.09513
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