Date Available
5-5-2021
Year of Publication
2021
Degree Name
Master of Science (MS)
Document Type
Master's Thesis
College
Engineering
Department/School/Program
Computer Science
First Advisor
Dr. Mirosław Truszczyński
Second Advisor
Dr. Richard Ehrenborg
Abstract
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)
https://doi.org/10.13023/etd.2021.117
Recommended Citation
Penn, Nelson, "Computational Utilities for the Game of Simplicial Nim" (2021). Theses and Dissertations--Computer Science. 104.
https://uknowledge.uky.edu/cs_etds/104
