New results on torus cube packings and tilings
Mathieu Dutour Sikiri\'c, Yoshiaki Itoh

TL;DR
This paper explores new developments in the combinatorial structures of torus cube packings and tilings, focusing on discrete and continuous cases with integral translations, expanding understanding of their properties.
Contribution
It introduces new results on the structure and properties of torus cube packings and tilings for both discrete and continuous cases, connecting to prior combinatorial studies.
Findings
Analysis of the case N=2 related to discrete tilings
Investigation of the case N=∞ related to continuous tilings
Description of new combinatorial structures in torus packings
Abstract
We consider sequential random packing of integral translate of cubes into the torus . Two special cases are of special interest: (i) The case which corresponds to a discrete case of tilings (considered in \cite{cubetiling,book}) (ii) The case 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.
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Taxonomy
TopicsQuasicrystal Structures and Properties · Mathematical Dynamics and Fractals · Cellular Automata and Applications
