Avoiding multiple entry arrays

✍ Scribed by Chetwynd, Amanda G.

• Publisher: John Wiley and Sons
• Year: 1997
• Tongue: English
• Weight: 116 KB
• Volume: 25
• Category: Article
• ISSN: 0364-9024
• DOI: 10.1002/(sici)1097-0118(199708)25:4<257::aid-jgt3>3.0.co;2-j

✦ Synopsis

In this paper we consider the problem of avoiding arrays with more than one entry per cell. An n × n array on n symbols is said to be avoidable if an n × n latin square, on the same symbols, can be found which differs from the array in every cell. Our first result is for chessboard squares with at most two entries per black cell. We show that if k ≥ 1 and C is a 4k × 4k chessboard square on symbols 1, 2, . . . , 4k in which every black cell contains at most two symbols and every symbol appears at most once in every row and column, then C is avoidable. Our main result is for squares with at most two entries in any cell and answers a question of Hilton. If k > 3240 and F is a 4k × 4k array on 1, 2, . . . , 4k in which every cell contains at most two symbols and every symbol appears at most twice in every row and column, then F is avoidable.