A recurrence relation for the ``inv'' analogue of \(q\)-Eulerian polynomials
type: Item
instance of: scholarly article
title: A recurrence relation for the ``inv'' analogue of \(q\)-Eulerian polynomials
zbMATH Open document ID: 1189.05005
author: Chak-On Chow
published in: The Electronic Journal of Combinatorics
publication date: 2010-06-16T00:00:00Z
full work available at URL: https://eudml.org/doc/229679
full work available at URL: v17i1n22.html
review text: We study in the present work a recurrence relation, which has long been overlooked, for the \(q\)-Eulerian polynomial \(A_n^{\text{des},\text{inv}}(t,q)=\sum_{\sigma\in{\mathfrak S}_n} t^{\text{des}(\sigma)}q^{\text{inv}(\sigma)}\), where \(\text{des}(\sigma)\) and \(\text{inv}(\sigma)\) denote, respectively, the descent number and inversion number of \(\sigma\) in the symmetric group \({\mathfrak S}_n\) of degree \(n\). We give an algebraic proof and a combinatorial proof of the recurrence relation.
Mathematics Subject Classification ID: 05A05
Mathematics Subject Classification ID: 05A15
zbMATH DE Number: 5721431
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5721431