Geodesic
Efficient packing of unit squares in a square
The electronic journal of combinatorics, Tome 9 (2002)
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Let $s(N)$ denote the edge length of the smallest square in which one can pack $N$ unit squares. A duality method is introduced to prove that $s(6)=s(7)=3$. Let $n_r$ be the smallest integer $n$ such that $s(n^2+1)\le n+{1/r}$. We use an explicit construction to show that $n_r\le 27r^3/2+O(r^2)$, and also that $n_2\le43$.
DOI : 10.37236/1631
Classification : 05B40, 52C15
Mots-clés : packing, covering, arrangements of squares, unit squares 
@article{10_37236_1631,
     author = {Michael J Kearney and Peter Shiu},
     title = {Efficient packing of unit squares in a square},
     journal = {The electronic journal of combinatorics},
     year = {2002},
     volume = {9},
     doi = {10.37236/1631},
     zbl = {0993.05044},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1631/}
}
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%A Peter Shiu
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Michael J Kearney; Peter Shiu. Efficient packing of unit squares in a square. The electronic journal of combinatorics, Tome 9 (2002). doi: 10.37236/1631

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