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The Existence of Balanced Tournament Designs and Partitioned Balanced Tournament Designs

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dc.contributor.authorBauman, Shaneen
dc.date.accessioned2006-08-22T14:21:32Z
dc.date.available2006-08-22T14:21:32Z
dc.date.issued2001en
dc.date.submitted2001en
dc.description.abstractA balanced tournament design of order <I>n</I>, BTD(<I>n</I>), defined on a 2<I>n</I>-set<I> V</i>, is an arrangement of the all of the (2<I>n</i>2) distinct unordered pairs of elements of <I>V</I> into an <I>n</I> X (2<I>n</i> - 1) array such that (1) every element of <I>V</i> occurs exactly once in each column and (2) every element of <I>V</I> occurs at most twice in each row. We will show that there exists a BTD(<i>n</i>) for <i>n</i> a positive integer, <i>n</i> not equal to 2. For <I>n</i> = 2, a BTD (<i>n</i>) does not exist. If the BTD(<i>n</i>) has the additional property that it is possible to permute the columns of the array such that for every row, all the elements of<I> V</I> appear exactly once in the first <i>n</i> pairs of that row and exactly once in the last <i>n</i> pairs of that row then we call the design a partitioned balanced tournament design, PBTD(<I>n</I>). We will show that there exists a PBTD (<I>n</I>) for <I>n</I> a positive integer, <I>n</I> is greater than and equal to 5, except possibly for <I>n</I> an element of the set {9,11,15}. For <I>n</I> less than and equal to 4 a PBTD(<I>n</I>) does not exist.en
dc.formatapplication/pdfen
dc.format.extent438868 bytes
dc.format.mimetypeapplication/pdf
dc.identifier.urihttp://hdl.handle.net/10012/1178
dc.language.isoenen
dc.pendingfalseen
dc.publisherUniversity of Waterlooen
dc.rightsCopyright: 2001, Bauman, Shane. All rights reserved.en
dc.subjectMathematicsen
dc.subjectcombinatorial designsen
dc.subjectbalanced tournament designsen
dc.subjectpartitioned balanced tournament designsen
dc.titleThe Existence of Balanced Tournament Designs and Partitioned Balanced Tournament Designsen
dc.typeMaster Thesisen
uws-etd.degreeMaster of Mathematicsen
uws-etd.degree.departmentCombinatorics and Optimizationen
uws.peerReviewStatusUnrevieweden
uws.scholarLevelGraduateen
uws.typeOfResourceTexten

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