Multicover Ucycles
type: Item
instance of: scholarly article
title: Multicover Ucycles
zbMATH Open document ID: 0816.05001
DOI: 10.1016/0012-365X(95)91427-R
published in: Discrete Mathematics
publication date: 1995-07-02T00:00:00Z
review text: A universal cycle, or Ucycle, for \(k\)-subsets of \([n]= \{1,2,\dots, n\}\) is a cyclic sequence of \((\begin{smallmatrix} n\\ k\end{smallmatrix})\) integers with the property that every \(k\)-subsets of \([n]\) appears exactly once consecutively in the sequence. A \(t\)-cover Ucycle for \(k\)-subsets of \([n]\) is a cyclic sequence of \(t(\begin{smallmatrix} n\\ k\end{smallmatrix})\) integers with the property that every \(k\)-subset of \([n]\) appears exactly \(t\)-times consecutively in the sequence. The author investigates the minimal number \(t= U(n, k)\) for which there is a \(t\)-cover Ucycle. For example: (a) \(U(n, 4)\leq 2\) if \(n\equiv 2\pmod 4\). (b) \(U(n,5)\leq 2\) if \(n\geq 16\) is relatively prime to 5 and \(n\not\equiv 2\pmod 3\).
reviewed by: V.Peteanu
Mathematics Subject Classification ID: 05A05
Mathematics Subject Classification ID: 05C70
Mathematics Subject Classification ID: 05C38
Mathematics Subject Classification ID: 05C45
zbMATH DE Number: 719463
zbMATH Keywords: universal cycle
zbMATH Keywords: \(t\)-cover Ucycle
author: Glenn H. Hurlbert
MaRDI profile type: Publication
cites work: Universal cycles for combinatorial structures
cites work: Q5834367
cites work: A Survey of Full Length Nonlinear Shift Register Cycle Algorithms
cites work: On Universal Cycles for k-Subsets of an n-Set
cites work: Universal cycles of \(k\)-subsets and \(k\)-permutations
cites work: Notes on Binomial Coefficients I-A Generalization of Lucas' Congruence†
cites work: Q5808057
Wikidata QID: Q126671746
full work available at URL: 0012-365x(95)91427-r
OpenAlex ID: W2914663802
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description: scientific article; zbMATH DE number 719463