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arXiv · 0809.0741

Derangement Polynomials and Excedances of Type B

William Y. C. Chen·Robert L. Tang·Alina F. Y. Zhao
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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.

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William Y. C. Chen, Robert L. Tang, Alina F. Y. Zhao. 2008-09-04. Derangement Polynomials and Excedances of Type B. https://arxiv.org/abs/0809.0741

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