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Sterling stirling play

Author

Listed:
  • Michael Fisher

    (West Chester University)

  • Richard J. Nowakowski

    (Dalhousie University)

  • Carlos Santos

    (Center for Functional Analysis, Linear Structures and Applications)

Abstract

In this paper we analyze a recently proposed impartial combinatorial ruleset that is played on a permutation of the set $$\left[ n\right] $$ n . We call this ruleset Stirling Shave. A procedure utilizing the ordinal sum operation is given to determine the nim value of a given normal play position. Additionally, we enumerate the number of permutations of $$\left[ n\right] $$ n which are $$\mathcal {P}$$ P -positions. The formula given involves the Stirling numbers of the first-kind. We also give a complete analysis of the Misère version of Stirling Shave using Conway’s genus theory. An interesting by-product of this analysis is insight into how the ordinal sum operation behaves in Misère Play.

Suggested Citation

  • Michael Fisher & Richard J. Nowakowski & Carlos Santos, 2018. "Sterling stirling play," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(2), pages 557-576, May.
    • Handle: RePEc:spr:jogath:v:47:y:2018:i:2:d:10.1007_s00182-017-0598-2
    DOI: 10.1007/s00182-017-0598-2
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    References listed on IDEAS

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    1. Max Albert, 2008. "Introduction," Conferences on New Political Economy,in: Max Albert & Stefan Voigt & Dieter Schmidtchen (ed.), Conferences on New Political Economy, edition 1, volume 25, pages 1-9 Mohr Siebeck, Tübingen.
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