Complexity of Substitutive Sequences - Calculation of the Complexities of Substitutive Sequences Over a Binary Alphabet

Cobham's theorem for substitutions

The seminal theorem of Cobham has given rise during the last 40 years to a lot of works around non-standard numeration systems and has been extended to many contexts. In this paper, as a result of fifteen years of improvements, we obtain a complete and general version for the so-called substitutive sequences. Let α and β be two multiplicatively independent Perron numbers. Then, a sequence x ∈ A...

A characterization of substitutive sequences using return words

We prove that a sequence is primitive substitutive if and only if the set of its derived sequences is finite; we defined these sequences here.

Short Communication: The availability of sugar beet molasses as a substitutive medium for cultivation of Nannochloropsis sp. Hibberd, 1981 (Eustigmatophyta)

Short Communication: The availability of sugar beet molasses as a substitutive medium for cultivation of Nannochloropsis sp. Hibberd, 1981 (Eustigmatophyta)

Substitutive Arnoux-Rauzy sequences have pure discrete spectrum

We prove that the symbolic dynamical system generated by a purely substitutive Arnoux-Rauzy sequence is measurably conjugate to a toral translation. The proof is based on an explicit construction of a fundamental domain with fractal boundary (a Rauzy fractal) for this toral translation. Communicated by Pierre Liardet Dedicated to the memory of Gérard Rauzy