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Small Latin Squares, Quasigroups and Loops

McKay, Brendan; Meynert, Alison; Myrvold, Wendy

Description

We present the numbers of isotopy classes and main classes of Latin squares, and the numbers of isomorphism classes of quasigroups and loops, up to order 10. The best previous results were for Latin squares of order 8 (Kolesova, Lam, and Thiel, 1990), quasigroups of order 6 (Bower, 2000), and loops of order 7 (Brant and Mullen, 1985). The loops of order 8 have been independently found by "QSCGZ" and Guérin (unpublished, 2001). We also report on the most extensive search so far for a triple of...[Show more]

dc.contributor.authorMcKay, Brendan
dc.contributor.authorMeynert, Alison
dc.contributor.authorMyrvold, Wendy
dc.date.accessioned2015-12-08T22:36:21Z
dc.identifier.issn1063-8539
dc.identifier.urihttp://hdl.handle.net/1885/35217
dc.description.abstractWe present the numbers of isotopy classes and main classes of Latin squares, and the numbers of isomorphism classes of quasigroups and loops, up to order 10. The best previous results were for Latin squares of order 8 (Kolesova, Lam, and Thiel, 1990), quasigroups of order 6 (Bower, 2000), and loops of order 7 (Brant and Mullen, 1985). The loops of order 8 have been independently found by "QSCGZ" and Guérin (unpublished, 2001). We also report on the most extensive search so far for a triple of mutually orthogonal Latin squares (MOLS) of order 10. Our computations show that any such triple must have only squares with trivial symmetry groups.
dc.publisherJohn Wiley & Sons Inc
dc.sourceJournal of Combinatorial Designs
dc.subjectKeywords: Isotopy; Latin square; Loop; Main class; Orthogonal; Quasigroup
dc.titleSmall Latin Squares, Quasigroups and Loops
dc.typeJournal article
local.description.notesImported from ARIES
local.identifier.citationvolume15
dc.date.issued2007
local.identifier.absfor010104 - Combinatorics and Discrete Mathematics (excl. Physical Combinatorics)
local.identifier.ariespublicationU3594520xPUB122
local.type.statusPublished Version
local.contributor.affiliationMcKay, Brendan, College of Engineering and Computer Science, ANU
local.contributor.affiliationMeynert, Alison, University of Victoria
local.contributor.affiliationMyrvold, Wendy, University of Victoria
local.description.embargo2037-12-31
local.bibliographicCitation.issue2
local.bibliographicCitation.startpage98
local.bibliographicCitation.lastpage119
local.identifier.doi10.1002/jcd.20105
dc.date.updated2015-12-08T09:49:38Z
local.identifier.scopusID2-s2.0-33847786535
CollectionsANU Research Publications

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