Sterling stirling play

In this paper we analyze a recently proposed impartial combinatorial ruleset that is played on a permutation of the set (left[ nright] ). 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[ nright] ) 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.