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Honeycomb arrays

Blackburn, S.R. and Panoui, A. and Paterson, Maura B. and Stinson, D.R. (2010) Honeycomb arrays. Electronic Journal of Combinatorics 17 (R172), ISSN 1077-8926.

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Abstract

A honeycomb array is an analogue of a Costas array in the hexagonal grid; they were first studied by Golomb and Taylor in 1984. A recent result of Blackburn, Etzion, Martin and Paterson has shown that (in contrast to the situation for Costas arrays) there are only finitely many examples of honeycomb arrays, though their bound on the maximal size of a honeycomb array is too large to permit an exhaustive search over all possibilities. The present paper contains a theorem that significantly limits the number of possibilities for a honeycomb array (in particular, the theorem implies that the number of dots in a honeycomb array must be odd). Computer searches for honeycomb arrays are summarised, and two new examples of honeycomb arrays with 15 dots are given.

Item Type: Article
School or Research Centre: Birkbeck Schools and Research Centres > School of Business, Economics & Informatics > Economics, Mathematics and Statistics
Depositing User: Dr Maura B. Paterson
Date Deposited: 23 Nov 2012 16:46
Last Modified: 17 Apr 2013 12:33
URI: http://eprints.bbk.ac.uk/id/eprint/5360

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