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Putting dots in triangles

Blackburn, S.R. and Paterson, Maura B. and Stinson, D.R. (2011) Putting dots in triangles. Journal of Combinatorial Mathematics and Combinatorial Computing 78 , pp. 23-32. ISSN 0835-3026.

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Abstract

Given a right-angled triangle of squares in a grid whose horizontal and vertical sides are $n$ squares long, let N(n) denote the maximum number of dots that can be placed into the cells of the triangle such that each row, each column, and each diagonal parallel to the long side of the triangle contains at most one dot. It has been proven that $N(n) = \lfloor \frac{2n+1}{3} \rfloor$. In this note, we give a new proof of this result using linear programming techniques.

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: 29 Nov 2012 09:57
Last Modified: 17 Apr 2013 12:33
URI: http://eprints.bbk.ac.uk/id/eprint/5363

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