, Volume 20, Issue 2, pp 265-279

Nonperiodicity implies unique composition for self-similar translationally finite Tilings

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Abstract

Let T be a translationally finite self-similar tiling of R d . We prove that if T is nonperiodic, then it has the unique composition property. More generally, T has the unique composition property modulo the group of its translation symmetries.

This research was partially supported by NSF.