### Abstract

Doyle (circa 1980) found a formula for the number of (Formula presented.) Latin rectangles (Formula presented.). This formula remained dormant until it was recently used for counting (Formula presented.) Latin rectangles, where (Formula presented.). We give a formal proof of Doyle’s formula for arbitrary k. We also improve a previous implementation of this formula, which we use to find (Formula presented.) when (Formula presented.) and (Formula presented.) , when (Formula presented.) and (Formula presented.) and when (Formula presented.) and (Formula presented.). Motivated by computational data for (Formula presented.) , some research problems and conjectures about the divisors of (Formula presented.) are presented.

Original language | English |
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Pages (from-to) | 1187-1202 |

Number of pages | 16 |

Journal | Graphs and Combinatorics |

Volume | 32 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1 May 2016 |

### Keywords

- Latin rectangle
- Latin square

## Cite this

*Graphs and Combinatorics*,

*32*(3), 1187-1202. https://doi.org/10.1007/s00373-015-1643-1