Excedance numbers for the permutations of type \(B\)
type: Item
instance of: scholarly article
title: Excedance numbers for the permutations of type \(B\)
zbMATH Open document ID: 1267.05016
author: Alina F. Y. Zhao
published in: The Electronic Journal of Combinatorics
publication date: 2013-06-07T00:00:00Z
full work available at URL: v20i2p28
review text: Summary: This work provides a study on the multidistribution of type \(B\) excedances, fixed points and cycles on the permutations of type \(B\). We derive the recurrences and closed formulas for the distribution of signed excedances on type \(B\) permutations as well as derangements via combinatorial construction. Based on this result, we obtain the recurrence and generating function for the signed excedance polynomial and disclose some relationships with Euler numbers and Springer numbers, respectively.
Mathematics Subject Classification ID: 05A05
Mathematics Subject Classification ID: 05A19
zbMATH DE Number: 6171943
zbMATH Keywords: type \(B\) permutation
zbMATH Keywords: type \(B\) excedance
zbMATH Keywords: type \(B\) derangement
zbMATH Keywords: fixed point
zbMATH Keywords: cycle
zbMATH Keywords: Euler number
zbMATH Keywords: Springer number
zbMATH Keywords: multidistribution
MaRDI profile type: Publication
cites work: The calculus of snakes and the combinatorics of Bernoulli, Euler and Springer numbers of Coxeter groups
cites work: Statistics on the multi-colored permutation groups
cites work: On the excedance number of colored permutation groups
cites work: \(q\)-Eulerian polynomials arising from Coxeter groups
cites work: A class of \(q\)-symmetric functions arising from plethysm
cites work: An involution on derangements
cites work: Derangement polynomials and excedances of type \(B\)
cites work: On the descent numbers and major indices for the hyperoctahedral group
cites work: On certain combinatorial expansions of the Eulerian polynomials
cites work: On derangement polynomials of type \(B\). II
cites work: Two involutions for signed excedance numbers
cites work: Exceedingly deranging!
cites work: Q5629638
cites work: Q4344108
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description: scientific article; zbMATH DE number 6171943