In this paper we consider the following problem: Given a partial n Γ n latin square P on symbols 1, 2 .... , n, is it possible to find an n x n latin square L on the same symbols which differs from P in every cell? In other words, is P avoidable? We show that all 2k Γ 2k partial latin squares for k
β¦ LIBER β¦
On avoiding odd partial Latin squares and r-multi Latin squares
β Scribed by Jaromy Scott Kuhl; Tristan Denley
- Book ID
- 108113690
- Publisher
- Elsevier Science
- Year
- 2006
- Tongue
- English
- Weight
- 189 KB
- Volume
- 306
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
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## Abstract A __k__βplex in a Latin square of order __n__ is a selection of __kn__ entries in which each row, column, and symbol is represented precisely __k__ times. A transversal of a Latin square corresponds to the case __k__β=β1. We show that for all even __n__β>β2 there exists a Latin square o