Sterling stirling play

Michael Fisher (), Richard J. Nowakowski () and Carlos Santos ()
Additional contact information
Michael Fisher: West Chester University
Richard J. Nowakowski: Dalhousie University
Carlos Santos: Center for Functional Analysis, Linear Structures and Applications

International Journal of Game Theory, 2018, vol. 47, issue 2, No 9, 557-576

Abstract: 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.

Keywords: Combinatorial game theory; Impartial games; Normal Play; Misère Play; Ordinal sum; Stirling numbers of the first kind (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s00182-017-0598-2

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