Greco-Latin squares as bijections

dc.contributor.advisor Jonathan Smith
dc.contributor.author Fiedler, James
dc.contributor.department Mathematics
dc.date 2018-08-22T22:47:50.000
dc.date.accessioned 2020-06-30T07:47:38Z
dc.date.available 2020-06-30T07:47:38Z
dc.date.copyright Mon Jan 01 00:00:00 UTC 2007
dc.date.issued 2007-01-01
dc.description.abstract <p>A Latin square of order n is an n-by-n array of n symbols, which we take to be the integers 0 to n-1, such that no symbol is repeated in any row or column. Two Latin squares of the same order are orthogonal if, when overlapped, no ordered pair of symbols occurs more than once. Equivalently, the Latin squares together form a bijection on the set of n-squared coordinates. In this thesis the question of what this bijection is in terms of projective planes is investigated. The major result here is a new necessary and sufficient condition such that two ternary rings correspond to the same plane.</p>
dc.format.mimetype application/pdf
dc.identifier archive/lib.dr.iastate.edu/rtd/15841/
dc.identifier.articleid 16840
dc.identifier.contextkey 7051129
dc.identifier.doi https://doi.org/10.31274/rtd-180813-17044
dc.identifier.s3bucket isulib-bepress-aws-west
dc.identifier.submissionpath rtd/15841
dc.identifier.uri https://dr.lib.iastate.edu/handle/20.500.12876/69514
dc.language.iso en
dc.source.bitstream archive/lib.dr.iastate.edu/rtd/15841/3289440.PDF|||Fri Jan 14 20:47:23 UTC 2022
dc.subject.disciplines Mathematics
dc.subject.keywords Mathematics;
dc.title Greco-Latin squares as bijections
dc.type article
dc.type.genre dissertation
dspace.entity.type Publication
relation.isOrgUnitOfPublication 82295b2b-0f85-4929-9659-075c93e82c48
thesis.degree.level dissertation
thesis.degree.name Doctor of Philosophy
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