Derangement Polynomials and Excedances of Type B
Combinatorics
2008-09-05 v1
Abstract
Adopting the definition of excedances of type B due to Brenti, we give a type B analogue of the q-derangement polynomials. The connection between q-derangement polynomials and Eulerian polynomials naturally extends to the type B case. Based on this relation, we derive some basic properties of the q-derangement polynomials of type B, including the generating function formula, the Sturm sequence property, and the asymptotic normal distribution. We also show that the q-derangement polynomials are almost symmetric in the sense that the coefficients possess the spiral property.
Cite
@article{arxiv.0809.0741,
title = {Derangement Polynomials and Excedances of Type B},
author = {William Y. C. Chen and Robert L. Tang and Alina F. Y. Zhao},
journal= {arXiv preprint arXiv:0809.0741},
year = {2008}
}
Comments
18 pages