English

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.

Keywords

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

R2 v1 2026-06-21T11:16:45.355Z