A Direct Construction of Nontransitive Dice Sets. Issue 11 (19th June 2017)

• Record Type: Journal Article
• Authors: Angel, Levi; Davis, Matt
• Is Part Of: Journal of combinatorial designs. Volume 25:Issue 11(2017:Nov.)
• Page Start: 523
• Page End: 529
• Publication Date: 2017-06-19
• Subjects: nontransitive dice; Combinatorial designs and configurations -- Periodicals; Configurations et schémas combinatoires -- Périodiques; 511.6
• DOI: 10.1002/jcd.21563
• Languages: English
• ISSNs: 1063-8539

Abstract

Abstract: In this paper, we give a direct construction for a set of dice realizing any given tournament T . The construction for a tournament with n vertices requires dice with n sides if n is odd, n + 1 sides if n is divisible by 4, and n − 1 sides if n ≡ 2 mod 4. This appears to be the most efficient general construction to date. Our construction relies only on a standard construction from graph theory.