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Avoiding multiple entry arrays.

Chetwynd, Amanda G. and Rhodes, S. J. (1997) Avoiding multiple entry arrays. Journal of Graph Theory, 25 (4). pp. 257-266. ISSN 0364-9024

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Abstract

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 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

Item Type: Article
Journal or Publication Title: Journal of Graph Theory
Uncontrolled Keywords: latin • squares • restricted • colourings
Subjects: Q Science > QA Mathematics
Departments: Faculty of Science and Technology > Mathematics and Statistics
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ID Code: 20930
Deposited By: Prof Amanda Chetwynd
Deposited On: 04 Dec 2008 09:24
Refereed?: No
Published?: Published
Last Modified: 26 Jul 2012 15:42
Identification Number:
URI: http://eprints.lancs.ac.uk/id/eprint/20930

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