A cycle lemma for permutation inversions
type: Item
instance of: scholarly article
title: A cycle lemma for permutation inversions
zbMATH Open document ID: 1009.05007
DOI: 10.1016/S0012-365X(02)00254-6
published in: Discrete Mathematics
publication date: 2002-12-02T00:00:00Z
review text: The permutations of the multiset \(\{ 1^{m_1},2^{m_2}\}\) of size \(n=m_1+m_2\) can be enumerated by the number of inversions. For \(d=\gcd(m_1,m_2)\), the authors give a combinatorial proof that the remainders modulo \(n/d\) of the numbers of inversions are equally distributed, and the remainders modulo \(m_1/d\) of the numbers of inversions of permutations whose first term is 1 are equally distributed. These results provide combinatorial interpretations of some properties of the Gaussian binomial coefficients.
Mathematics Subject Classification ID: 05A15
Mathematics Subject Classification ID: 05A05
Mathematics Subject Classification ID: 05A10
zbMATH DE Number: 1838971
zbMATH Keywords: multiset
zbMATH Keywords: permutation
zbMATH Keywords: inversion
zbMATH Keywords: major index
zbMATH Keywords: cyclic shift
zbMATH Keywords: greatest common divisor
zbMATH Keywords: Gaussian binomial coefficient
author: S. Brunetti
author: A. Del Lungo
author: F. Del Ristoro
reviewed by: David Grabiner
MaRDI profile type: Publication
Wikidata QID: Q124808048
Recommended article: Q4502529
Recommended article: On inversions and cycles in permutations
Recommended article: A new universal cycle for permutations
Recommended article: A permutation regularity lemma
Recommended article: Inversions in \(k\)-sorted permutations
Recommended article: Q4238400
Recommended article: On the constructions of \(n\)-cycle permutations
Recommended article: The cycle lemma and some applications
description: scientific article; zbMATH DE number 1838971