Geodesic
Improved packings of \(n(n - 1)\) unit squares in a square
M. Z. Arslanov1 ; S. A. Mustafin ; Z. K. Shangitbayev
1Institute of information and computational technologies
The electronic journal of combinatorics, Tome 28 (2021) no. 4
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Let $s(n)$ be the side of the smallest square into which we can pack $n$ unit squares. The purpose of this paper is to prove that $s(n^2-n) for all $n\geq 12$. Besides, we show that $s(18^2-17) < 18, s(17^2-16) < 17,$ and $s(16^2-15) < 16.$
DOI : 10.37236/8586
Classification : 52C15, 05B40
Mots-clés : packings, square, unit squares

M. Z. Arslanov  1   ; S. A. Mustafin    ; Z. K. Shangitbayev 

1 Institute of information and computational technologies 
@article{10_37236_8586,
     author = {M. Z. Arslanov and S. A. Mustafin and Z. K. Shangitbayev},
     title = {Improved packings of \(n(n - 1)\) unit squares in a square},
     journal = {The electronic journal of combinatorics},
     year = {2021},
     volume = {28},
     number = {4},
     doi = {10.37236/8586},
     zbl = {1477.52025},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/8586/}
}
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M. Z. Arslanov; S. A. Mustafin; Z. K. Shangitbayev. Improved packings of \(n(n - 1)\) unit squares in a square. The electronic journal of combinatorics, Tome 28 (2021) no. 4. doi: 10.37236/8586

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