### Abstract

A Latin Square is a n x n table filled with integers from 1 to n where each number appears exactly once in each row and each column. A Latin Rectangle is a partially filled n x n table with r filled rows and n-r empty rows, such that each number appears at most once in each row and each column. The main result of this theory is that any Latin Rectangle can be completed to a Latin Square.

### License

BSD License

### Topics

- Mathematics/Combinatorics

### Session Latin_Square

- Latin_Square

### Depends on

- Hall’s Marriage Theorem

### Auto-related entries

- Prime Number Theorem with Remainder Term
- Pell’s Equation
- Treaps
- Descartes' Rule of Signs
- Category Theory

## Cite

×

Latin_Square-AFP

    @article{Latin_Square-AFP,
      author  = {Alexander Bentkamp},
      title   = {Latin Square},
      journal = {Archive of Formal Proofs},
      month   = {December},
      year    = {2015},
      note    = {\url{https://isa-afp.org/entries/Latin_Square.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

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