TITLE

NONTRANSITIVE DICE SETS REALIZING THE PALEY TOURNAMENTS FOR SOLVING SCHÃœTTE'S TOURNAMENT PROBLEM

AUTHOR(S)
BOZÓKI, S.
PUB. DATE
January 2014
SOURCE
Miskolc Mathematical Notes;2014, Vol. 15 Issue 1, p39
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
The problem of a multiple player dice tournament is discussed and solved in the paper. A die has a finite number of faces with real numbers written on each. Finite dice sets are proposed which have the following property, defined by Schütte for tournaments: for an arbitrary subset of k dice there is at least one die that beats each of the k with a probability greater than ½. It is shown that the proposed dice set realizes the Paley tournament, that is known to have the Schütte property (for a given k) if the number of vertices is large enough. The proof is based on Dirichlet's theorem, stating that the sum of quadratic nonresidues is strictly larger than the sum of quadratic residues.
ACCESSION #
97250471

 

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