The Existence of Balanced Tournament Designs and Partitioned Balanced Tournament Designs

Mathematics;combinatorial designs;balanced tournament designs;partitioned balanced tournament designs

Bauman, Shane

University of Waterloo

关键词: Mathematics;    combinatorial designs;    balanced tournament designs;    partitioned balanced tournament designs;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/1178/1/sbbauman2001.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

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 nX (2n - 1) array such that (1) every element ofV 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.