Directed graphs with an odd number of vertices n, where each vertex has both (n − 1)/2 incoming and outgoing edges, have a rich structure. We were lead to their study by both the Borromean rings and the game rockpaper-scissors. An interesting interplay between groups, graphs, topological links, and matrices reveals the structure of these objects, and for larger values of n, extensive computation produces some surprises. Perhaps most surprising is how few of the larger graphs have any symmetry… Expand

Acta crystallographica. Section A, Foundations and advances

2021

TLDR

An extended family of structures related to the classical `Borromean rings', in which no two rings are directly linked are described, which may serve as templates for the designed synthesis of Borromean polycatenanes.Expand

We study a class of algebras we regard as generalized rock–paper–scissors games. We determine when such algebras can exist, show that these algebras generate the varieties generated by… Expand

Summary We show that the extension of Rock-Paper-Scissors to include Lizard and Spock is the unique such five move fair game up to isomorphism. We also categorize all analogous six move fair games.

Otto Neugebauer’s early academic career was marked by a series of transitions. His interests shifted from physics to mathematics, and finally to the history of ancient mathematics and exact sciences.… Expand

wikipedia.org/wiki/Rock-paper-scissors-lizard-Spock Department of Mathematics and Statistics, Grinnell College, Grinnell, IA 50112, E-mail address: chamberl@math.grinnell