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Atomic surfaces, tilings and coincidences II. Reducible case

Hiromi EiShunji ItoHui Rao — 2006

Annales de l’institut Fourier

The atomic surfaces of unimodular Pisot substitutions of irreducible type have been studied by many authors. In this article, we study the atomic surfaces of Pisot substitutions of reducible type. As an analogue of the irreducible case, we define the stepped-surface and the dual substitution over it. Using these notions, we give a simple proof to the fact that atomic surfaces form a self-similar tiling system. We show that the stepped-surface possesses the quasi-periodic property, which...

On substitution invariant Sturmian words: an application of Rauzy fractals

Valérie BerthéHiromi EiShunji ItoHui Rao — 2007

RAIRO - Theoretical Informatics and Applications

Sturmian words are infinite words that have exactly factors of length for every positive integer . A Sturmian word is also defined as a coding over a two-letter alphabet of the orbit of point under the action of the irrational rotation (mod 1). A substitution fixes a Sturmian word if and only if it is invertible. The main object of the present paper is to investigate Rauzy fractals associated with two-letter invertible substitutions. As an application, we give an alternative geometric...

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