liu.seSearch for publications in DiVA
Change search
ReferencesLink to record
Permanent link

Direct link
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, 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
URN: urn:nbn:se:liu:diva-46166DOI: 10.1016/j.disc.2006.12.003OAI: diva2:267062
Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2011-01-10

Open Access in DiVA

No full text

Other links

Publisher's full text

Search in DiVA

By author/editor
Nordh, Gustav
By organisation
The Institute of TechnologyTCSLAB - Theoretical Computer Science Laboratory
In the same journal
Discrete Mathematics
Engineering and Technology

Search outside of DiVA

GoogleGoogle Scholar
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Altmetric score

Total: 13 hits
ReferencesLink to record
Permanent link

Direct link