The skeletion of an impartial game and the Nim-function of Moore's Nimk

Abstract

For any finite impartial two-player gameG of perfect information without chance moves, we define the skeletonS (G), another game of the same class, which economically represents the significant structure ofG. We then employ the skeleton of (k+1)-heap Nim k to discover a simple formula for its nim-function (also called “grundy function”).