The skew, relative, and classical derangements
type: Item
instance of: scholarly article
title: The skew, relative, and classical derangements
zbMATH Open document ID: 0863.05001
DOI: 10.1016/0012-365X(95)00116-E
published in: Discrete Mathematics
publication date: 1997-05-28T00:00:00Z
review text: A derangement on a set \([n]= \{1,\dots,n\}\) is a permutation \(i_1i_2 \dots i_n\), such that \(i_k\neq k\) for each \(k\). Their number is \(D_n\). A relative derangement \(j_1j_2 \dots j_n\) is a permutation such that \(j_k+ 1\neq j_{k+1}\) for each \(k\). The number of these objects is \(Q_n\). Brualdi showed that \(Q_n=D_n + D_{n-1}\). The reviewed paper gives a bijective proof for this nice correspondence. The main tools are the so-called skew derangements, which are one-to-one maps \(f:X\to Y\) (for \(|X|= |Y|)\) such that for every \(x\in X\) the relation \(f(x)\neq x\) holds.
Mathematics Subject Classification ID: 05A05
Mathematics Subject Classification ID: 05A15
zbMATH DE Number: 955158
zbMATH Keywords: derangement
zbMATH Keywords: permutation
author: William Y. C. Chen
reviewed by: Péter L. Erdős
MaRDI profile type: Publication
cites work: Q3996998
cites work: Q3669422
cites work: Matchings, Derangements, Rencontres
cites work: Q3748279
description: scientific article; zbMATH DE number 955158