New results on torus cube packings and tilings

Abstract

We consider sequential random packing of integral translate of cubes $[0,N{]}^n$ into the torus $Z^n/2N{Z}^n$. Two special cases are of special interest: (i) The case $N=2$ which corresponds to a discrete case of tilings (considered in \cite{cubetiling,book}) (ii) The case $N=\infty$ corresponds to a case of continuous tilings (considered in \cite{combincubepack,book}) Both cases correspond to some special combinatorial structure and we describe here new developments.

5 pages, conference paper