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arXiv · 1212.1266

Barycentric subdivisions and derangement polynomials for the even-signed permutation groups

Christina Savvidou
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Abstract

The derangement polynomial for the symmetric group enumerates derangements by the number of excedances. It can be interpreted as the local $h$-polynomial, in the sense of Stanley, of the barycentric subdivision of the simplex. Motivated by this interpretation, we define a derangement polynomial for the even-signed permutation group. The coefficients of this polynomial are nonnegative, symmetric and unimodal. We show that they enumerate derangements in the even-signed permutation group according to a notion of excedance, which is analogous to the one introduced by Brenti for signed permutations. We also give an explicit formula for the corresponding exponential generating function.

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Christina Savvidou. 2013-01-21. Barycentric subdivisions and derangement polynomials for the even-signed permutation groups. https://arxiv.org/abs/1212.1266

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