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International Journal of Game Theory

, Volume 47, Issue 2, pp 557–576 | Cite as

Sterling stirling play

  • Michael Fisher
  • Richard J. Nowakowski
  • Carlos Santos
Original Paper

Abstract

In this paper we analyze a recently proposed impartial combinatorial ruleset that is played on a permutation of the set \(\left[ n\right] \). 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 \(\left[ n\right] \) which are \(\mathcal {P}\)-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.

Keywords

Combinatorial game theory Impartial games Normal Play Misère Play Ordinal sum Stirling numbers of the first kind 

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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.West Chester UniversityWest ChesterUSA
  2. 2.Dalhousie UniversityHalifaxCanada
  3. 3.Center for Functional Analysis, Linear Structures and ApplicationsLisbonPortugal

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