English

The Erdos and Campbell-Staton conjectures about square packing

Metric Geometry 2007-05-23 v1

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.

Keywords

Cite

@article{arxiv.math/0504341,
  title  = {The Erdos and Campbell-Staton conjectures about square packing},
  author = {Iwan Praton},
  journal= {arXiv preprint arXiv:math/0504341},
  year   = {2007}
}

Comments

2 pages

R2 v1 2026-07-22T17:18:13.441Z