In this paper I introduce some background for subtraction games and explore the Sprague-Grundy functions defined on them. I exhibit some subtraction games where the functions are guaranteed to be strictly periodic. I also exhibit a class of subtraction games which have bounded range, and show there are uncountably many of these.
College and Department
Physical and Mathematical Sciences; Mathematics
BYU ScholarsArchive Citation
Blackham, Bryce Emerson, "Subtraction Games: Range and Strict Periodicity" (2018). Theses and Dissertations. 6735.
Combinatorial Game Theory, Nim, Sprague-Grundy function, Periodicity, Subtraction Games