Avoiding (m, m, m)-arrays of order n=2(k)
2012 (English)In: The Electronic Journal of Combinatorics, ISSN 1077-8926, Vol. 19, no 1, P63- p.Article in journal (Refereed) Published
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.
IdentifiersURN: urn:nbn:se:umu:diva-55037ISI: 000302381200004OAI: oai:DiVA.org:umu-55037DiVA: diva2:525263