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

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