Bozóki, Sándor (2014) Nontransitive dice sets realizing the Paley tournaments for solving Schütte's tournament problem. MISKOLC MATHEMATICAL NOTES, 15 (1). pp. 3950. ISSN 17872405

Text
BozokiMiskolcMathNotes2014.pdf Download (339kB)  Preview 
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 1/2. 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.
Item Type:  Article 

Subjects:  Q Science / természettudomány > QA Mathematics / matematika Q Science / természettudomány > QA Mathematics / matematika > QA166QA166.245 Graphs theory / gráfelmélet Q Science / természettudomány > QA Mathematics / matematika > QA71 Number theory / számelmélet 
Depositing User:  Dr. Sándor Bozóki 
Date Deposited:  18 Sep 2017 14:31 
Last Modified:  18 Sep 2017 14:31 
URI:  http://real.mtak.hu/id/eprint/62873 
Actions (login required)
View Item 