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dc.contributor.authorCavenagh, Nicholas J.en_NZ
dc.contributor.authorWanless, Ian M.en_NZ
dc.date.accessioned2018-07-30T23:32:53Z
dc.date.available2017-06-30en_NZ
dc.date.available2018-07-30T23:32:53Z
dc.date.issued2017en_NZ
dc.identifier.citationCavenagh, N. J., & Wanless, I. M. (2017). Latin squares with no transversals. Electronic Journal of Combinatorics, 24(2).en
dc.identifier.issn1077-8926en_NZ
dc.identifier.urihttps://hdl.handle.net/10289/11995
dc.description.abstractAk-plex in a latin square of ordernis a selection of kn entries that includes k representatives from each row and column and k occurrences of each symbol. A 1-plex is also known as a transversal. It is well known that if n is even then Bₙ, the addition table for the integers modulo n, possesses no transversals. We show that there are a great many latin squares that are similar to Bₙ and have no transversal. As a consequence, the number of species of transversal-free latin squares is shown to be at least nⁿ³⁼²⁽¹⁼²ᵒ⁽¹⁾ for even n→∞. We also produce various constructions for latin squares that have no transversal but do have a k-plex for some odd k >1. We prove a 2002 conjecture of the second author that for all even orders n >4 there is a latin square of order n that contains a 3-plex but no transversal. We also show that for odd k and m≥2, there exists a latin square of order 2km with a k-plex but no k'-plex for odd k'< k.
dc.format.mimetypeapplication/pdf
dc.language.isoenen_NZ
dc.rights© 2017 copyright is held by the authors.
dc.subjectScience & Technologyen_NZ
dc.subjectPhysical Sciencesen_NZ
dc.subjectMathematics, Applieden_NZ
dc.subjectMathematicsen_NZ
dc.subjectlatin squareen_NZ
dc.subjecttransversalen_NZ
dc.subjectplexen_NZ
dc.subjecttriplexen_NZ
dc.titleLatin squares with no transversalsen_NZ
dc.typeJournal Article
dc.relation.isPartOfElectronic Journal of Combinatoricsen_NZ
pubs.elements-id200442
pubs.issue2en_NZ
pubs.organisational-group/Waikato
pubs.organisational-group/Waikato/2018 PBRF
pubs.organisational-group/Waikato/FCMS
pubs.organisational-group/Waikato/FCMS/2018 PBRF - FCMS
pubs.organisational-group/Waikato/FCMS/Mathematics and Statistics
pubs.publication-statusPublisheden_NZ
pubs.volume24en_NZ
uow.identifier.article-noARTN P2.45


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