Derangement Polynomials and Excedances of Type B

Details Derangement Polynomials and Excedances of Type B Derangement Polynomials and Excedances of Type B

2008-09-04

arxiv.org/abs/0809.0741v1

Mathematics

Combinatorics

18 pages

Scientific paper

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.

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