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dc.contributor.authorCavenagh, Nicholas J.en_NZ
dc.date.accessioned2018-09-03T04:01:28Z
dc.date.available2018-07-01en_NZ
dc.date.available2018-09-03T04:01:28Z
dc.date.issued2018en_NZ
dc.identifier.citationCavenagh, N. J. (2018). Lower bounds on the sizes of defining sets in full n-Latin squares and full designs. Graphs and Combinatorics, 34(4), 571–577. https://doi.org/10.1007/s00373-018-1895-7en
dc.identifier.issn0911-0119en_NZ
dc.identifier.urihttps://hdl.handle.net/10289/12058
dc.description.abstractThe full n-Latin square is the n×n array with symbols 1, 2, . . . , n in each cell. In this paper we show, as part of a more general result,that any defining set for the full n-Latin square has size n³(1 − o(1)). The full design N(v, k) is the unique simple design with parameters (v,k,{v-2 \atopwithdelims ()k-2}); that is, the design consisting of all subsets of size k from a set of size v. We show that any defining set for the full design N(v, k) has size {v\atopwithdelims ()k}(1-o(1)) (as v-k becomes large). These results improve existing results and are asymptotically optimal. In particular, the latter result solves an open problem given in (Donovan, Lefevre, et al, 2009), in which it is conjectured that the proportion of blocks in the complement of a full design will asymptotically approach zero.
dc.format.mimetypeapplication/pdf
dc.language.isoenen_NZ
dc.publisherSpringer Japan KKen_NZ
dc.rights© Springer Japan KK, part of Springer Nature 2018.This is the author's accepted version. The final publication is available at Springer via dx.doi.org/10.1007/s00373-018-1895-7
dc.subjectScience & Technologyen_NZ
dc.subjectPhysical Sciencesen_NZ
dc.subjectMathematicsen_NZ
dc.subjectFull designsen_NZ
dc.subjectFull n-Latin squaresen_NZ
dc.subjectDefining setsen_NZ
dc.titleLower bounds on the sizes of defining sets in full n-Latin squares and full designsen_NZ
dc.typeJournal Article
dc.identifier.doi10.1007/s00373-018-1895-7en_NZ
dc.relation.isPartOfGraphs and Combinatoricsen_NZ
pubs.begin-page571
pubs.elements-id203655
pubs.end-page577
pubs.issue4en_NZ
pubs.publication-statusPublisheden_NZ
pubs.volume34en_NZ
dc.identifier.eissn1435-5914en_NZ


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