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The Erdos and Campbell-Staton conjectures about square packing

Iwan Praton
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Abstract

Put n open non-overlapping squares inside a unit square, and let f(n) denote the maximum possible value of the sum of the side lengths of the n squares. Campbell and Staton, building on a question of Erdos, conjectured that f(k^2+2c+1)=k+c/k, where c is any integer and k\geq |c|. We show that if this conjecture is true for one value of c, then it is true for all values of c.

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Iwan Praton. 2005-04-16. The Erdos and Campbell-Staton conjectures about square packing. https://arxiv.org/abs/math/0504341

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