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Latin square
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orthogonal Latin squares
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Latin square

mathematics
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Quick Summary

orthogonal Latin squares
orthogonal Latin squares Figure 2: Two orthogonal Latin squares of order 4 and their superposition.

A Latin square is a square grid, typically k x k, filled with k distinct symbols. The key rule is that each symbol appears exactly once in each row and each column.12

Latin squares are used in experimental design, particularly in statistics, to help control for variables.1

Two Latin squares can be considered "orthogonal" if, when one is placed on top of the other, every possible pairing of symbols from the two squares occurs exactly once. The study of orthogonal Latin squares is a significant area within combinatorics, with ongoing mathematical research into their properties and existence for different orders.2

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2 Britannica Sources
  1. Latin square
  2. combinatorics - Orthogonal Latin squares

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