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dc.contributor.authorCavenagh, Nicholas J.en_NZ
dc.contributor.authorRamadurai, Reshmaen_NZ
dc.date.accessioned2017-05-22T00:25:37Z
dc.date.available2016-08-04en_NZ
dc.date.available2017-05-22T00:25:37Z
dc.date.issued2017en_NZ
dc.identifier.citationCavenagh, N., & Ramadurai, R. (2017). On the Distances between Latin Squares and the Smallest Defining Set Size. Journal of Combinatorial Designs, 25(4), 147–158. https://doi.org/10.1002/jcd.21529en
dc.identifier.issn1063-8539en_NZ
dc.identifier.urihttps://hdl.handle.net/10289/11068
dc.description.abstractIn this note, we show that for each Latin square L of order n≥2 , there exists a Latin square L’≠L of order n such that L and L’ differ in at most 8√n cells. Equivalently, each Latin square of order n contains a Latin trade of size at most 8√n. We also show that the size of the smallest defining set in a Latin square is Ω(n³/²).
dc.format.mimetypeapplication/pdf
dc.language.isoenen_NZ
dc.publisherWileyen_NZ
dc.rightsThis is an author’s accepted version of an article published in the journal: Journal of combinatorial designs. © 2017 Wiley.
dc.subjectScience & Technologyen_NZ
dc.subjectPhysical Sciencesen_NZ
dc.subjectMathematicsen_NZ
dc.subjectLatin squareen_NZ
dc.subjectLatin tradeen_NZ
dc.subjectdefining seten_NZ
dc.subjectcritical seten_NZ
dc.subjectHamming distanceen_NZ
dc.subjectLatin square
dc.subjectLatin trade
dc.subjectdefining set
dc.subjectHamming distance
dc.titleOn the Distances between Latin Squares and the Smallest Defining Set Sizeen_NZ
dc.typeJournal Article
dc.identifier.doi10.1002/jcd.21529en_NZ
dc.relation.isPartOfJournal of combinatorial designsen_NZ
pubs.begin-page147
pubs.elements-id143506
pubs.end-page158
pubs.issue4en_NZ
pubs.publication-statusPublisheden_NZ
pubs.volume25en_NZ
dc.identifier.eissn1520-6610en_NZ


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