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Avoiding (m, m, m)-arrays of order n=2(k)
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2012 (English)In: The Electronic Journal of Combinatorics, ISSN 1097-1440, E-ISSN 1077-8926, Vol. 19, no 1, P63- p.Article in journal (Refereed) Published
Abstract [en]

An (m, m, m)-array of order n is an n x n array such that each cell is assigned a set of at most m symbols from f 1,...,n g such that no symbol occurs more than m times in any row or column. An (m, m, m)-array is called avoidable if there exists a Latin square such that no cell in the Latin square contains a symbol that also belongs to the set assigned to the corresponding cell in the array. We show that there is a constant gamma such that if m <= gamma 2(k) and k >= 14, then any (m, m, m)-array of order n = 2(k) is avoidable. Such a constant gamma has been conjectured to exist for all n by Haggkvist.

Place, publisher, year, edition, pages
2012. Vol. 19, no 1, P63- p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-55037ISI: 000302381200004OAI: oai:DiVA.org:umu-55037DiVA: diva2:525263
Available from: 2012-05-07 Created: 2012-05-07 Last updated: 2017-12-07Bibliographically approved

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http://www.combinatorics.org/ojs/index.php/eljc/article/view/v19i1p63/pdf

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Andrén, Lina J

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