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Perfect Skolem sets
Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, TCSLAB - Theoretical Computer Science Laboratory.
2008 (English)In: Discrete Mathematics, ISSN 0012-365X, E-ISSN 1872-681X, Vol. 308, no 9, 1653-1664 p.Article in journal (Refereed) Published
Abstract [en]

A Skolem sequence is a sequence s1, s2, ..., s2 n (where si ? A = { 1, ..., n }), each si occurs exactly twice in the sequence and the two occurrences are exactly si positions apart. A set A that can be used to construct Skolem sequences is called a Skolem set. The problem of deciding which sets of the form A = { 1, ..., n } are Skolem sets was solved by Thoralf Skolem in the late 1950s. We study the natural generalization where A is allowed to be any set of n positive integers. We give necessary conditions for the existence of Skolem sets of this generalized form. We conjecture these necessary conditions to be sufficient, and give computational evidence in favor of our conjecture. We investigate special cases of the conjecture and prove that the conjecture holds for some of them. We also study enumerative questions and show that this problem has strong connections with problems related to permutation displacements. © 2007 Elsevier B.V. All rights reserved.

Place, publisher, year, edition, pages
2008. Vol. 308, no 9, 1653-1664 p.
Keyword [en]
Design theory, Permutation displacement, Skolem sequence
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:liu:diva-46166DOI: 10.1016/j.disc.2006.12.003OAI: oai:DiVA.org:liu-46166DiVA: diva2:267062
Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2017-12-13

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Nordh, Gustav

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