Derangement Polynomials and Excedances of Type B

2008/09/04 by William Y. C. Chen, Chen, William Y. C., Robert L. Tang +3 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.0809.0741

openalex publication_date 2008/09/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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• Eulerian-type polynomials over Stirling permutations and box sorting algorithm

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