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dc.contributor.authorCavenagh, Nicholas J.en_NZ
dc.contributor.authorDonovan, Diane M.en_NZ
dc.contributor.authorDemirkale, Fatihen_NZ
dc.date.accessioned2017-11-26T23:04:19Z
dc.date.available2017en_NZ
dc.date.available2017-11-26T23:04:19Z
dc.date.issued2017en_NZ
dc.identifier.citationCavenagh, N. J., Donovan, D. M., & Demirkale, F. (2017). Orthogonal trades in complete sets of MOLS. The Electronic Journal of Combinatorics, 24(3).en
dc.identifier.issn1077-8926en_NZ
dc.identifier.urihttps://hdl.handle.net/10289/11516
dc.description.abstractLet Bₚ be the Latin square given by the addition table for the integers modulo an odd prime p (i.e. the Cayley table for (Zₚ, +)). Here we consider the properties of Latin trades in Bₚ which preserve orthogonality with one of the p−1 MOLS given by the finite field construction. We show that for certain choices of the orthogonal mate, there is a lower bound logarithmic in p for the number of times each symbol occurs in such a trade, with an overall lower bound of (log p)² / log log p for the size of such a trade. Such trades imply the existence of orthomorphisms of the cyclic group which differ from a linear orthomorphism by a small amount. We also show that any transversal in Bₚ hits the main diagonal either p or at most p − log₂ p – 1 times. Finally, if p ≡ 1 (mod 6) we show the existence of a Latin square which is orthogonal to Bₚ and which contains a 2 × 2 subsquare.
dc.format.mimetypeapplication/pdf
dc.language.isoen
dc.publisherThe Electronic Journal of Combinatoricsen_NZ
dc.relation.urihttp://www.combinatorics.org/ojs/index.php/eljc/article/view/v24i3p15en_NZ
dc.subjectmathematicsen_NZ
dc.subjectMOLSen_NZ
dc.subjecttradeen_NZ
dc.subjectorthomorphismen_NZ
dc.subjecttransversalen_NZ
dc.subjectOrthogonal array
dc.subjectMOLS
dc.subjecttrade
dc.subjectorthomorphism
dc.subjecttransversal
dc.titleOrthogonal trades in complete sets of MOLSen_NZ
dc.typeJournal Article
dc.relation.isPartOfThe Electronic Journal of Combinatoricsen_NZ
pubs.elements-id201206
pubs.issue3en_NZ
pubs.volume24en_NZ
uow.identifier.article-noP3.15


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