2018/06/29 by Ethan Akin, Akin, Ethan
Engineering · Mathematics · #05C20 #05C25 #05C38 #05C45 #05C76 #Advanced Topology and Set Theory #Combinatorics (math.CO) #Dynamical Systems (math.DS) #FOS: Mathematics #Limits and Structures in Graph Theory #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1806.11241
openalex publication_date 2018/06/29 · openalex created_date 2020/09/01 · openalex updated_date 2026/07/28
The classic Rock-Paper-Scissors game of size 3 and its extension, Rock-Paper-Scissors-Lizard-Spock, are modeled by directed graphs called tournaments. They can be further extended to any odd size. The extended games are regular tournaments where each strategy beats and is beaten by exactly half of the alternatives. We survey the properties of regular tournaments, which we will call games. In the process we describe a number of constructions for such games. These include games on groups of odd order and the associated games on coset spaces. We obtain a new lower bound for the number of games of size 2n+1.