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Completing partial latin squares with prescribed diagonals

✍ Scribed by Martin Grüttmüller

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
302 KB
Volume
138
Category
Article
ISSN
0166-218X

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✦ Synopsis

This paper deals with completion of partial latin squares L = (lij) of order n with k cyclically generated diagonals (li+t;j+t = lij + t if lij is not empty; with calculations modulo n). There is special emphasis on cyclic completion. Here, we present results for k = 2; : : : ; 7 and odd n 6 21, and we describe the computational method used (hill climbing). Noncyclic completion is investigated in the cases k = 2; 3 or 4 and n 6 21.

📜 SIMILAR VOLUMES

Completing some Partial Latin Squares
Completing some Partial Latin Squares
✍ Tristan Denley; Roland Häggkvist 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 112 KB

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 s