Publication:
Embedding partial Latin squares in Latin squares with many mutually orthogonal mates

dc.contributor.coauthorDonovan, Diane
dc.contributor.coauthorGrannell, Mike
dc.contributor.departmentDepartment of Mathematics
dc.contributor.kuauthorYazıcı, Emine Şule
dc.contributor.kuprofileFaculty Member
dc.contributor.yokid27432
dc.date.accessioned2024-11-09T13:44:55Z
dc.date.issued2020
dc.description.abstractIn this paper it is shown that any partial Latin square of order n can be embedded in a Latin square of order at most 16n2 which has at least 2n mutually orthogonal mates. Further, for any t⩾2, it is shown that a pair of orthogonal partial Latin squares of order n can be embedded in a set of t mutually orthogonal Latin squares (MOLS) of order a polynomial with respect to n. A consequence of the constructions is that, if N(n) denotes the size of the largest set of MOLS of order n, then N(n2)⩾N(n)+2. In particular, it follows that N(576)⩾9, improving the previously known lower bound N(576)⩾8.
dc.description.fulltextYES
dc.description.indexedbyWoS
dc.description.indexedbyScopus
dc.description.issue6
dc.description.openaccessYES
dc.description.publisherscopeInternational
dc.description.sponsoredbyTubitakEuTÜBİTAK
dc.description.sponsorshipScientific and Technological Research Council of Turkey (TÜBİTAK)
dc.description.versionAuthor's final manuscript
dc.description.volume343
dc.formatpdf
dc.identifier.doi10.1016/j.disc.2020.111835
dc.identifier.embargoNO
dc.identifier.filenameinventorynoIR02846
dc.identifier.issn0012-365X
dc.identifier.linkhttps://doi.org/10.1016/j.disc.2020.111835
dc.identifier.quartileQ3
dc.identifier.scopus2-s2.0-85078899203
dc.identifier.urihttps://hdl.handle.net/20.500.14288/3557
dc.identifier.wos528203800014
dc.keywordsEmbeddings
dc.keywordsEmbeddings of orthogonal partial Latin squares
dc.keywordsEmbeddings of partial Latin squares
dc.keywordsOrthogonal partial Latin squares
dc.languageEnglish
dc.publisherElsevier
dc.relation.grantno116F166
dc.relation.urihttp://cdm21054.contentdm.oclc.org/cdm/ref/collection/IR/id/9497
dc.sourceDiscrete Mathematics
dc.subjectMathematics
dc.titleEmbedding partial Latin squares in Latin squares with many mutually orthogonal mates
dc.typeJournal Article
dspace.entity.typePublication
local.contributor.authorid0000-0001-6824-451X
local.contributor.kuauthorYazıcı, Emine Şule
local.publication.orgunit1College of Sciences
local.publication.orgunit2Department of Mathematics
relation.isOrgUnitOfPublication2159b841-6c2d-4f54-b1d4-b6ba86edfdbe
relation.isOrgUnitOfPublication.latestForDiscovery2159b841-6c2d-4f54-b1d4-b6ba86edfdbe

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