Barycentric subdivisions and derangement polynomials for the even-signed permutation groups
Abstract
The derangement polynomial for the symmetric group enumerates derangements by the number of excedances. It can be interpreted as the local -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.
Cite
@article{arxiv.1212.1266,
title = {Barycentric subdivisions and derangement polynomials for the even-signed permutation groups},
author = {Christina Savvidou},
journal= {arXiv preprint arXiv:1212.1266},
year = {2013}
}
Comments
This paper has been withdrawn by the author due to an error in the proof of the main theorem that cancels the theorem. It will be replaced by a new article with similar content