Date of Award

Summer 2019

Document Type

Thesis Restricted

Degree Name

Master of Arts (MA)

Department

Mathematics

Committee Chairperson

Michael Fisher, Ph.D.

Committee Member

Scott Parsell, Ph.D.

Committee Member

James McLaughin, Ph.D.

Abstract

In the paper “Wythoff Partizan Subtraction”, Larsson et al. introduced a class of normal-play partizan games called Complementary Subtraction, and covered the tituar Wythoff Partizan Subtraction as a member of Complementary Subtraction. We investigate another member of this class, Pellian Partizan Subtraction. Whereas Wythoff Partizan Subtraction is based on the Beatty Sequence formed by the golden ratio and its complement, the sequences for Pellian Partizan Subtraction are formed by the square root of two. Since the topic is very specific, we first give a brief background in both Combinatorial Game Theory and Beatty Sequences. We then define the two subtraction sets for Pellian Partizan Subtraction, citing or proving a few important features of these sequences, before turning to the game itself. The Pellian Partizan Subtraction heaps of size one or two have simple forms; we partition the remaining heaps into four classes, and prove that three of them have a consistant reduced canonical form, while bounding the final class such that it does not impact the other three. We also provide an appendix of the Haskell code which we used for empirical discovery of the various properties throughout the paper.

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