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arXiv · 2411.07274

A note on the Erdős conjecture about square packing

Jineon Baek·Junnosuke Koizumi·Takahiro Ueoro
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Abstract

Let $f(n)$ denote the maximum total length of the sides of $n$ squares packed inside a unit square. Erdős conjectured that $f(k^2+1)=k$. We show that the conjecture is true if we assume that the sides of the squares are parallel to the sides of the unit square.

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Jineon Baek, Junnosuke Koizumi, Takahiro Ueoro. 2024-11-18. A note on the Erdős conjecture about square packing. https://arxiv.org/abs/2411.07274

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