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Extending partial latin cubes
Austin Peay State University.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2014 (English)In: Ars combinatoria, ISSN 0381-7032, Vol. 113, 405-414 p.Article in journal (Refereed) Published
Abstract [en]

In the spirit of Ryser's theorem, we prove sufficient conditions on k, and m so that k xexm Latin boxes, i.e. partial Latin cubes whose filled cells form a k x x m rectangular box, can be extended to akxnxm latin box, and also to akxnxn latin box, where n is the number of symbols used, and likewise the order of the Latin cube. We also prove a partial Evans type result for Latin cubes, namely that any partial Latin cube of order n with at most n 1 filled cells is completable, given certain conditions on the spatial distribution of the filled cells.

Place, publisher, year, edition, pages
2014. Vol. 113, 405-414 p.
National Category
Discrete Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-50292ISI: 000329883500036OAI: oai:DiVA.org:umu-50292DiVA: diva2:461585
Available from: 2011-12-05 Created: 2011-12-05 Last updated: 2017-12-08Bibliographically approved

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