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Multiplayer rock–paper–scissors

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Abstract

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.

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References

  1. Aten, C.: Multiplayer rock–paper–scissors. In: Adaricheva, K., DeMeo, W., Hyndman, J. (eds) Algebras and Lattices in Hawai’i, pp. 12–19 (2018). https://www.lulu.com/commerce/index.php?fBuyContent=22805798. ISBN 9781387772483

  2. Bergman, C.: Universal Algebra: Fundamentals and Selected Topics. Chapman and Hall/CRC, Boca Raton (2011)

    Book  Google Scholar 

  3. Chamberland, M., Herman, E.A.: Rock–paper–scissors meets Borromean rings. Math. Intell. 37, 20–25 (2015)

    Article  MathSciNet  Google Scholar 

  4. Crvenković, S., Dolinka, I., Marković, P.: A survey of algebra of tournaments. Novi Sad J. Math. 29, 95–130 (1999)

    MathSciNet  MATH  Google Scholar 

  5. Freese, R.: An application of Dilworth’s lattice of maximal antichains. Discrete Math. 7, 107–109 (1974)

    Article  MathSciNet  Google Scholar 

  6. Joris, H., Oestreicher, C., Steinig, J.: The greatest common divisor of certain sets of binomial coefficients. J. Number Theory 21, 101–119 (1985)

    Article  MathSciNet  Google Scholar 

  7. McKay, B.D.: The asymptotic numbers of regular tournaments, Eulerian digraphs and Eulerian oriented graphs. Combinatorica 10, 367–377 (1990)

    Article  MathSciNet  Google Scholar 

  8. Rock Paper Scissors Spock Lizard. http://www.samkass.com/theories/RPSSL.html. Accessed 16 Jan 2018

  9. Surmacs, M.: Regular hypertournaments and arc-pancyclicity. J. Graph Theory 84, 176–190 (2016)

    Article  MathSciNet  Google Scholar 

  10. The On-Line Encyclopedia of Integer Sequences: A007079. https://oeis.org/A007079

  11. Umbhauer, G.: Game Theory and Exercises. Routledge Advanced Texts in Economics and Finance, 1st edn. Routledge, Abingdon (2016)

    MATH  Google Scholar 

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Acknowledgements

Thanks to Jonathan Pakianathan and Clifford Bergman for their helpful comments. Thanks to Scott Kirila for pointing out the result of Joris, Oestreicher, and Steinig we use in Section 2. A short version of this paper appeared in the proceedings of the 2018 Algebras and Lattices in Hawai’i conference  [1].

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  1. Mathematics Department, University of Rochester, Rochester, 14627, USA

    Charlotte Aten

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  1. Charlotte Aten
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Correspondence to Charlotte Aten.

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Communicated by W. DeMeo.

Dedicated to Ralph Freese, Bill Lampe, and J.B. Nation.

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This research was supported in part by the people of the Yosemite Valley.

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Aten, C. Multiplayer rock–paper–scissors. Algebra Univers. 81, 40 (2020). https://doi.org/10.1007/s00012-020-00667-5

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  • DOI: https://doi.org/10.1007/s00012-020-00667-5

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