So Much More Than A Game: Using Group Theory and Linear Algebra to Determine Equivalent Sudoku Boards
Project Author
Issue Date
2023-05-02
Authors
Dolan, Elizabeth
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First Reader
Dodge, Craig
Additional Readers
Werner, Caryn
Keywords
Sudoku , Group Theory , Linear Algebra , Equivalence
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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.
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Chair
Major
Mathematics
Department
Mathematics