Seyyed Ali Mohammadiyeh
Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317-53153, I. R. Iran
This talk introduces Latin squares—structured square arrays with unique symbols per row and column—and explores their mathematical significance and applications.
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Key Topics:
- Definition: An
n × n grid where each symbol appears once per row and column.
- Applications: Used in statistics, cryptography, game design (e.g., Sudoku), and combinatorics.
- Connection to Group Theory: Latin squares are related to quasigroups, which satisfy similar uniqueness properties.
Historical Insights:
- Leonhard Euler: Developed foundational work; coined the term using Latin symbols.
- Choi Seok-jeong: Discovered orthogonal Latin squares before Euler, and constructed a magic square using them.
Terminology:
- Order: Size of the square (e.g., 3×3).
- Growth: Number of Latin squares increases rapidly with size (e.g., 12 for n=3, billions for n=6).
- Sudoku: Described as a Latin square with added regional constraints.
Contact: alim@kashanu.ac.ir, max@std.kashanu.ac.ir, or my personal email maxbasecode@gmail.com