### Abstract

An n × n array is avoidable if there exists a Latin square which differs from the array in every cell. The main aim of this paper is to present a generalization of a result of Chetwynd and Rhodes involving avoiding arrays with multiple entries in each cell. They proved a result regarding arrays with at most two entries in each cell, and we generalize their method to obtain a similar result for arrays with arbitrarily many entries per cell. In particular, we prove that if m ∞ N there exists an N = N(m) such that if F is an N × N array with at most m entries in each cell, then F is avoidable.

Original language | English |
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Pages (from-to) | 1-9 |

Number of pages | 9 |

Journal | Electronic Journal of Combinatorics |

Volume | 13 |

Issue number | 1 R |

State | Published - 12 May 2006 |

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## Cite this

Cutler, J., & Öhinan, L. D. (2006). Latin squares with forbidden entries.

*Electronic Journal of Combinatorics*,*13*(1 R), 1-9.