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dc.contributor.authorBritz, Thomas
dc.contributor.authorCavenagh, Nicholas J.
dc.contributor.authorSørensen, Henrik Kragh
dc.date.accessioned2015-04-29T04:50:52Z
dc.date.available2015-03-30
dc.date.available2015-04-29T04:50:52Z
dc.date.issued2015-03-30
dc.identifier.citationBritz, T., Cavenagh, N. J., & Sørensen, H. K. (2015). Maximal partial Latin cubes. Electronic Journal of Combinatorics, 22(1).en
dc.identifier.urihttps://hdl.handle.net/10289/9306
dc.description.abstractWe prove that each maximal partial Latin cube must have more than 29.289% of its cells filled and show by construction that this is a nearly tight bound. We also prove upper and lower bounds on the number of cells containing a fixed symbol in maximal partial Latin cubes and hypercubes, and we use these bounds to determine for small orders n the numbers k for which there exists a maximal partial Latin cube of order n with exactly k entries. Finally, we prove that maximal partial Latin cubes of order n exist of each size from approximately half-full (n3/2 for even n ≥ 10 and (n3 + n)/2 for odd n ≥21) to completely full, except for when either precisely 1 or 2 cells are empty.
dc.format.mimetypeapplication/pdf
dc.language.isoeng
dc.publisherElectronic Journal of Combinatorics
dc.relation.urihttp://www.combinatorics.org/ojs/index.php/eljc/article/view/v22i1p81
dc.rights© 2015 the authors
dc.titleMaximal partial Latin cubes
dc.typeJournal Article
dc.relation.isPartOfElectronic Journal of Combinatorics
pubs.elements-id119594
pubs.issue1
pubs.publisher-urlhttp://www.combinatorics.org/ojs/index.php/eljc/article/view/v22i1p81
pubs.volume22
dc.identifier.eissn1077-8926
uow.identifier.article-noP1.81


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