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Completing some Partial Latin Squares

✍ Scribed by Tristan Denley; Roland Häggkvist

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
112 KB
Volume
21
Category
Article
ISSN
0195-6698

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✦ Synopsis

We show that any partial 3r ×3r Latin square whose filled cells lie in two disjoint r ×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 × 2r square, for which there is a pairing of the columns so that in each row there is a filled cell in at most one of each matched pair of columns, can be completed if and only if there is some way to fill the cells of the top left 2r × 2r square.

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