dc.contributor.author Bauman, Shane en dc.date.accessioned 2006-08-22 14:21:32 (GMT) dc.date.available 2006-08-22 14:21:32 (GMT) dc.date.issued 2001 en dc.date.submitted 2001 en dc.identifier.uri http://hdl.handle.net/10012/1178 dc.description.abstract A balanced tournament design of order n, BTD(n), defined on a 2n-set V, is an arrangement of the all of the (2n2) distinct unordered pairs of elements of V into an n X (2n - 1) array such that (1) every element of V occurs exactly once in each column and (2) every element of V occurs at most twice in each row. We will show that there exists a BTD(n) for n a positive integer, n not equal to 2. For n = 2, a BTD (n) does not exist. If the BTD(n) has the additional property that it is possible to permute the columns of the array such that for every row, all the elements of V appear exactly once in the first n pairs of that row and exactly once in the last n pairs of that row then we call the design a partitioned balanced tournament design, PBTD(n). We will show that there exists a PBTD (n) for n a positive integer, n is greater than and equal to 5, except possibly for n an element of the set {9,11,15}. For n less than and equal to 4 a PBTD(n) does not exist. en dc.format application/pdf en dc.format.extent 438868 bytes dc.format.mimetype application/pdf dc.language.iso en en dc.publisher University of Waterloo en dc.rights Copyright: 2001, Bauman, Shane. All rights reserved. en dc.subject Mathematics en dc.subject combinatorial designs en dc.subject balanced tournament designs en dc.subject partitioned balanced tournament designs en dc.title The Existence of Balanced Tournament Designs and Partitioned Balanced Tournament Designs en dc.type Master Thesis en dc.pending false en uws-etd.degree.department Combinatorics and Optimization en uws-etd.degree Master of Mathematics en uws.typeOfResource Text en uws.peerReviewStatus Unreviewed en uws.scholarLevel Graduate en
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