Completing simple partial k-Latin squares
| Autor: | Nicholas Cavenagh, Giovanni Lo Faro, Antoinette Tripodi |
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| Jazyk: | English<br />Italian |
| Rok vydání: | 2018 |
| Předmět: | |
| Zdroj: | Atti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche, Matematiche e Naturali, Vol 96, Iss S2, p A4 (2018) |
| Druh dokumentu: | article |
| ISSN: | 0365-0359 1825-1242 |
| DOI: | 10.1478/AAPP.96S2A4 |
| Popis: | We study the completion problem for simple k-Latin rectangles, which are a special case of the generalized latin rectangles studied for which embedding theorems are given by Andersen and Hilton (1980) in “Generalized Latin rectangles II: Embedding”, Discrete Mathematics 31(3). Here an alternative proof of those theorems are given for k-Latin rectangles in the “simple” case. More precisely, generalizing two classic results on the completability of partial Latin squares, we prove the necessary and suffisucient conditions for a completion of a simple m x n k-Latin rectangle to a simple k-Latin square of order n and we show that if m ≤ n/2, any simple partial k-Latin square P of order m embeds in a simple k-Latin square L of order n. |
| Databáze: | Directory of Open Access Journals |
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