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Latin Squares, Partial Latin Squares and Their Generalized Quotients

✍ Scribed by Glebsky L. Yu; Carlos J. Rubio

Publisher
Springer Japan
Year
2005
Tongue
English
Weight
128 KB
Volume
21
Category
Article
ISSN
0911-0119

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πŸ“œ SIMILAR VOLUMES

Generalized latin square
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✍ A. Iranmanesh; A. R. Ashrafi πŸ“‚ Article πŸ“… 2006 πŸ› Springer-Verlag 🌐 English βš– 212 KB
Completing some Partial Latin Squares
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✍ 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

Avoiding partial Latin squares and intri
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✍ Amanda G. Chetwynd; Susan J. Rhodes πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 768 KB

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