So Much More Than A Game: Using Group Theory and Linear Algebra to Determine Equivalent Sudoku Boards

Dolan, Elizabeth

So Much More Than A Game: Using Group Theory and Linear Algebra to Determine Equivalent Sudoku Boards

Persistent URL

https://dspace.allegheny.edu/handle/10456/56828

Author(s)

Dolan, Elizabeth

Date Issued

May 2, 2023

Abstract

The following comprehensive project analyzes the mathematics that shape and dictate the game of Sudoku, specifically the differences between equivalent and unique Sudoku boards. The introduction covers numerous concepts from group theory, focusing specifically on groups, homomorphisms, permutations, relations, and equivalence. There is also a brief introduction of matrices and determinants from linear algebra. These concepts are used throughout an in-depth analysis of Arcos's paper, ``Mini-Sudokus and Groups" as groups, symmetries, permutations, partitions, and relations are applied to 4x4 Sudoku boards. In the final chapter, research shifts to a linear algebra lens where matrix determinants are used to reach similar conclusions regarding equivalence as those discussed in chapter two.

Major

Mathematics

First Reader(s)

Dodge, Craig