# Multiplayer rock–paper–scissors

@article{Aten2019MultiplayerR, title={Multiplayer rock–paper–scissors}, author={Charlotte Aten}, journal={Algebra universalis}, year={2019}, volume={81}, pages={1-31} }

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 hypertournament algebras, count these algebras, study their automorphisms, and determine their congruence lattices. We produce a family of finite simple algebras.

#### References

SHOWING 1-10 OF 18 REFERENCES

Rock-Paper-Scissors Meets Borromean Rings

- Mathematics
- 2015

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… Expand

An application of dilworth's lattice of maximal antichains

- Computer Science, Mathematics
- Discret. Math.
- 1974

This paper outlines a proof of Dilworth's theorem, which states that under the natural ordering these antichains form a distributive lattice, and applies it to strengthen the results and shorten the proofs of [4]. Expand

A SURVEY OF ALGEBRA OF TOURNAMENTS

- 2004

The present paper surveys the history of algebraic represetations of complete directed graphs, known in graph theory as tournaments, or equivalently, relational structures with a trichotomous binary… Expand

The asymptotic numbers of regular tournaments, Eulerian digraphs and Eulerian oriented graphs

- Mathematics, Computer Science
- Comb.
- 1990

The saddle point method applied to appropriaten-dimensional integrals is used to solve the inequality of the following type: For α ≥ 1, β ≥ 1 using Eulerian oriented simple graphs. Expand

Universal Algebra: Fundamentals and Selected Topics

- Mathematics
- 2011

FUNDAMENTALS OF UNIVERSAL ALGEBRA Algebras Operations Examples More about subs, homs, and prods Generating subalgebras Congruences and quotient algebras Lattices Ordered sets Distributive and modular… Expand

Regular Hypertournaments and Arc-Pancyclicity

- Mathematics, Computer Science
- J. Graph Theory
- 2017

Several generalizations of regular tournaments are examined and the following generalization of Alspach's theorem concerning arc-pancyclicity is proved: Every Σ-regular k-hypertournament on n vertices, where 2≤k≤n−2, is arc- pancyclic. Expand

Game Theory and Exercises

- Mathematics
- 2016

1. How to build a game 2. Dominance 3. Nash equilibrium 4. Backward induction and repeated games 5. Trembles in a game 6. Solving a game differently Answers

The greatest common divisor of certain sets of binomial coefficients

- Mathematics
- 1985

Keywords: greatest common divisor ; binomial coefficient Reference CTN-ARTICLE-1985-001doi:10.1016/0022-314X(85)90013-7 Record created on 2008-12-12, modified on 2016-08-08

The On-Line Encyclopedia of Integer Sequences

- Mathematics, Computer Science
- Electron. J. Comb.
- 1994

The On-Line Encyclopedia of Integer Sequences (or OEIS) is a database of some 130000 number sequences which serves as a dictionary, to tell the user what is known about a particular sequence and is widely used. Expand

Multiplayer Rock-Paper-Scissors”. In: Algebras and Lattices in Hawai’i

- (cit. on p
- 2018