Latin Square
- An n×n arrangement where every row and every column contains exactly one occurrence of each symbol.
- Each row and column is a permutation of the symbol set.
- Used in fields like statistics and coding theory to control factors or construct codes.
Definition
Section titled “Definition”A Latin square is a square grid filled with symbols such that each row and each column contains exactly one of each symbol.
Explanation
Section titled “Explanation”In a Latin square, the entries are drawn from some set of symbols. Every row and every column is a permutation of that symbol set, meaning the symbols are rearranged but each symbol appears exactly once in each row and column. Latin squares can be constructed for any size and with any set of symbols.
Examples
Section titled “Examples”3x3 numeric example
Section titled “3x3 numeric example”| 1 | 2 | 3 |
|---|---|---|
| 2 | 3 | 1 |
| 3 | 1 | 2 |
4x4 letter example
Section titled “4x4 letter example”| A | B | C | D |
|---|---|---|---|
| B | D | A | C |
| C | A | D | B |
| D | C | B | A |
Use cases
Section titled “Use cases”- Statistics and design of experiments: controlling for the effects of nuisance variables.
- Coding theory: construction of error-correcting codes.
Related terms
Section titled “Related terms”- Permutation
- Symbols
- Statistics
- Design of experiments
- Nuisance variables
- Coding theory
- Error-correcting codes