Year of Publication
Master of Science (MS)
Dr. Mirosław Truszczyński
Dr. Richard Ehrenborg
Simplicial nim games, a class of impartial games, have very interesting mathematical properties. Winning strategies on a simplicial nim game can be determined by the set of positions in the game whose Sprague-Grundy values are zero (also zero positions). In this work, I provide two major contributions to the study of simplicial nim games. First, I provide a modern and efficient implementation of the Sprague-Grundy function for an arbitrary simplicial complex, and discuss its performance and scope of viability. Secondly, I provide a method to find a simple mathematical expression to model that function if it exists. I show the effectiveness of this method on determining mathematical expressions that classify the set of zero positions on
several simplicial nim games.
Digital Object Identifier (DOI)
Penn, Nelson, "Computational Utilities for the Game of Simplicial Nim" (2021). Theses and Dissertations--Computer Science. 104.