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A Direct Construction of Nontransitive Dice Sets
Author(s) -
Angel Levi,
Davis Matt
Publication year - 2017
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.21563
Subject(s) - dice , tournament , mathematics , combinatorics , graph , discrete mathematics , statistics
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.
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