The Period of the subtraction games

TL;DR

This paper uses the PTFN algorithm to analyze the periodicity of subtraction games, offering a new approach that is more suitable than traditional Sprague-Grundy Theory and providing four new conclusions.

Contribution

Introduces the PTFN algorithm as a new method for analyzing the period of subtraction games, surpassing traditional approaches.

Findings

Four new conclusions about the period of subtraction games

PTFN algorithm proves more suitable than Sprague-Grundy Theory

Provides a new direction for studying subtraction game periods

Abstract

Subtraction games is a class of impartial combinatorial games, They with finite subtraction sets are known to have periodic nim-sequences. So people try to find the regular of the games. But for specific of Sprague-Grundy Theory, it is too difficult to find, they obtained some conclusions just by simple observing. This paper used PTFN algorithm to analyze the period of the Subtraction games. It is more suitable than Sprague-Grundy Theory, and this paper obtained four conclusions by PTFN algorithm . This algorithm provide a new direction to study the subtraction games' period.