Rock-Paper-Scissors Meets Borromean Rings

@article{Chamberland2015RockPaperScissorsMB,
  title={Rock-Paper-Scissors Meets Borromean Rings},
  author={Marc Chamberland and Eugene A. Herman},
  journal={The Mathematical Intelligencer},
  year={2015},
  volume={37},
  pages={20-25}
}
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… 
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wikipedia.org/wiki/Rock-paper-scissors-lizard-Spock Department of Mathematics and Statistics, Grinnell College, Grinnell, IA 50112, E-mail address: chamberl@math.grinnell
  • edu Department of Mathematics and Statistics