A note on the Erdős conjecture about square packing
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913579685380096 |
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| author | Baek, Jineon Koizumi, Junnosuke Ueoro, Takahiro |
| author_facet | Baek, Jineon Koizumi, Junnosuke Ueoro, Takahiro |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_07274 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on the Erdős conjecture about square packing Baek, Jineon Koizumi, Junnosuke Ueoro, Takahiro Combinatorics Metric Geometry 52C15, 52C10 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. |
| title | A note on the Erdős conjecture about square packing |
| topic | Combinatorics Metric Geometry 52C15, 52C10 |
| url | https://arxiv.org/abs/2411.07274 |