The Erdos and Campbell-Staton conjectures about square packing

Details The Erdos and Campbell-Staton conjectures about square packing The Erdos and Campbell-Staton conjectures about square packing

2005-04-16

arxiv.org/abs/math/0504341v1

Mathematics

Metric Geometry

2 pages

Scientific paper

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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