Equivalence class universal cycles for permutations
type: Item
instance of: scholarly article
title: Equivalence class universal cycles for permutations
zbMATH Open document ID: 0844.05004
DOI: 10.1016/0012-365X(94)00314-9
author: Garth Isaak
author: Glenn H. Hurlbert
published in: Discrete Mathematics
publication date: 1996-03-25T00:00:00Z
review text: The paper sets out to construct a complete family of universal cycles of \(n\)-permutations using \(n+ 1\) symbols, and an equivalence relation based on differences. The notion of universal cycles as cyclic representations of combinatorial objects, a generalization of de Bruijn cycles, is of recent (1990's) interest---and the universal cycles for permutations examined in this paper is an example of this. Having set up the equivalence classes, the authors then construct a directed graph---which proves to be Eulerian. An Eulerian cycle provides the desired universal cycle for their example.
Mathematics Subject Classification ID: 05A05
Mathematics Subject Classification ID: 05C99
Mathematics Subject Classification ID: 05C38
zbMATH DE Number: 858106
zbMATH Keywords: universal cycles
zbMATH Keywords: de Bruijn cycles
zbMATH Keywords: permutations
zbMATH Keywords: Eulerian cycle
reviewed by: R. Scurr
MaRDI profile type: Publication
cites work: Universal cycles for combinatorial structures
cites work: Universal cycles of \(k\)-subsets and \(k\)-permutations
cites work: Q4722111
description: scientific article; zbMATH DE number 858106