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Avoiding partial Latin squares and intricacy

✍ Scribed by Amanda G. Chetwynd; Susan J. Rhodes

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
768 KB
Volume
177
Category
Article
ISSN
0012-365X

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✦ Synopsis

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 ~>2 are avoidable and give some results on odd partial latin squares. We also use these results to show that the intricacy of avoiding partial latin squares is two and of avoiding more general arrays is at most three.

πŸ“œ SIMILAR VOLUMES

Completing some Partial Latin Squares
Completing some Partial Latin Squares
✍ Tristan Denley; Roland HΓ€ggkvist πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 112 KB

We show that any partial 3r Γ—3r Latin square whose filled cells lie in two disjoint r Γ—r sub-squares can be completed. We do this by proving the more general result that any partial 3r by 3r Latin square, with filled cells in the top left 2r Γ— 2r square, for which there is a pairing of the columns s