Putting Dots in Triangles

Details Putting Dots in Triangles Putting Dots in Triangles

2009-10-22

arxiv.org/abs/0910.4325v3

Computer Science

Discrete Mathematics

10 pages Minor rephrasing: final version to submit to journal.

Scientific paper

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.

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