Results

**1 - 2**of**2**### On Aperiodic Subtraction Games with Bounded Nim Sequence

"... Subtraction games are a class of impartial combinatorial games whose positions cor-respond to nonnegative integers and whose moves correspond to subtracting one of a fixed set of numbers from the current position. Though they are easy to define, sub-traction games have proven difficult to analyze. I ..."

Abstract
- Add to MetaCart

(Show Context)
Subtraction games are a class of impartial combinatorial games whose positions cor-respond to nonnegative integers and whose moves correspond to subtracting one of a fixed set of numbers from the current position. Though they are easy to define, sub-traction games have proven difficult to analyze. In particular, few general results about their Sprague-Grundy values are known. In this paper, we construct an example of a subtraction game whose sequence of Sprague-Grundy values is ternary and aperiodic, and we develop a theory that might lead to a generalization of our construction. 1