On the expansion of three-element subtraction sets
We study the periodicity of nim-sequences for subtraction games having subtraction sets with three elements. In particular, we give solutions in several cases, and we describe how these subtraction sets can be augmented by additional numbers without changing the nim-sequence. The paper concludes with a conjecture on ultimately bipartite subtraction games.
subtraction sets periodicity nim-sequence subtraction games bipartite subtraction games combinatorial games expansion set