Geodesic
Perfect packing of $d$-cubes
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 853-864

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A packing of $d$-cubes into a $d$-box of the right area is called perfect packing. Since $\sum\limits_{i =1}^\infty {1/ i^{dt}}={\zeta(dt)}$, it can be asked for which $t$ can be found a perfect packing of the $d$-cubes of edge lengths $1$, $2^{-t}$, $3^{-t}$, $\ldots$ into a $d$-box of the right area. In this paper an algorithm will be presented which packs the $d$-cubes of edge lengths $1$, $2^{-t}$, $3^{-t}$, $\ldots$ into a $d$-box of area $\zeta(dt)$ for any $t$ on the interval $[d_0,{2^{d-1}/( d2^{d-1}-1)}]$, where $d_0$ depends on $d$ only.
Keywords: packing, $d$-cube, tiling. 
@article{SEMR_2020_17_a70,
     author = {A. Jo\'os},
     title = {Perfect packing of $d$-cubes},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {853--864},
     publisher = {mathdoc},
     volume = {17},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2020_17_a70/}
}
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A. Joós. Perfect packing of $d$-cubes. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 853-864. http://geodesic.mathdoc.fr/item/SEMR_2020_17_a70/