### 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 |
---|---|

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

*Electronic Journal of Combinatorics*,

*13*(1 R), 1-9.

}

*Electronic Journal of Combinatorics*, vol. 13, no. 1 R, pp. 1-9.

**Latin squares with forbidden entries.** / Cutler, Jonathan; Öhinan, Lars Daniel.

Research output: Contribution to journal › Article › Research › peer-review

TY - JOUR

T1 - Latin squares with forbidden entries

AU - Cutler, Jonathan

AU - Öhinan, Lars Daniel

PY - 2006/5/12

Y1 - 2006/5/12

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=33646720799&partnerID=8YFLogxK

M3 - Article

VL - 13

SP - 1

EP - 9

JO - Electronic Journal of Combinatorics

JF - Electronic Journal of Combinatorics

SN - 1077-8926

IS - 1 R

ER -