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dc.contributor.authorCavenagh, Nicholas J.
dc.contributor.authorStones, Douglas S.
dc.date.accessioned2011-03-10T03:50:40Z
dc.date.available2011-03-10T03:50:40Z
dc.date.issued2011
dc.identifier.citationCavenagh, N.J. & Stones, D.S. (2011). Near-automorphisms of Latin squares. Journal of Combinatorial Designs, 19(5), 365-377.en_NZ
dc.identifier.urihttps://hdl.handle.net/10289/5155
dc.description.abstractWe define a near-automorphism α of a Latin square L to be an isomorphism such that L and αL differ only within a 2 × 2 subsquare. We prove that for all n≥2 except n∈{3, 4}, there exists a Latin square which exhibits a near-automorphism. We also show that if α has the cycle structure (2, n − 2), then L exists if and only if n≡2 (mod 4), and can be constructed from a special type of partial orthomorphism. Along the way, we generalize a theorem by Marshall Hall, which states that any Latin rectangle can be extended to a Latin square. We also show that if α has at least 2 fixed points, then L must contain two disjoint non-trivial subsquares.en_NZ
dc.language.isoen
dc.publisherWileyen_NZ
dc.relation.urihttp://onlinelibrary.wiley.com/doi/10.1002/jcd.20282/abstracten_NZ
dc.subjectintercalateen_NZ
dc.subjectLatin squareen_NZ
dc.subjectpartial orthomorphismen_NZ
dc.subjectnear-automorphismen_NZ
dc.titleNear-automorphisms of Latin squaresen_NZ
dc.typeJournal Articleen_NZ
dc.identifier.doi10.1002/jcd.20282en_NZ
dc.relation.isPartOfJournal of Combinatorial Designsen_NZ
pubs.begin-page365en_NZ
pubs.elements-id35778
pubs.end-page377en_NZ
pubs.issue5en_NZ
pubs.volume19en_NZ


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