# Graeco-Latin squares

Let $A=({a}_{ij})$ and $B=({b}_{ij})$ be two $n\times n$ matrices. We define their as the matrix whose $(i,j)$th entry is the pair $({a}_{ij},{b}_{ij})$.

A *Graeco-Latin square* is then the join of two Latin squares^{}.

The name comes from Euler’s use of Greek and Latin letters to differentiate the entries on each array.

An example of Graeco-Latin square:

$$\left(\begin{array}{cccc}\hfill a\alpha \hfill & \hfill b\beta \hfill & \hfill c\gamma \hfill & \hfill d\delta \hfill \\ \hfill d\gamma \hfill & \hfill c\delta \hfill & \hfill b\alpha \hfill & \hfill a\beta \hfill \\ \hfill b\delta \hfill & \hfill a\gamma \hfill & \hfill d\beta \hfill & \hfill c\alpha \hfill \\ \hfill c\beta \hfill & \hfill d\alpha \hfill & \hfill a\delta \hfill & \hfill b\gamma \hfill \end{array}\right)$$ |

Title | Graeco-Latin squares |
---|---|

Canonical name | GraecoLatinSquares |

Date of creation | 2013-03-22 12:14:36 |

Last modified on | 2013-03-22 12:14:36 |

Owner | Mathprof (13753) |

Last modified by | Mathprof (13753) |

Numerical id | 9 |

Author | Mathprof (13753) |

Entry type | Definition |

Classification | msc 05B15 |

Defines | join |