New results on torus cube packings and tilings
Mathieu Dutour Sikirić, Yoshiaki Itoh · Proceedings of the Steklov Institute of Mathematics · 2015
We consider the sequential random packing of integral translates of cubes [0, N] n into the torus ℤ n /2Nℤ n . Two particular cases are of special interest: (1) N = 2, which corresponds to a discrete case of tilings, and (2) N = ∞, which corresponds to a case of continuous tilings. Both cases correspond to some special combinatorial structure, and we describe here new developments.