JournalsjemsVol. 13, No. 6pp. 1799–1814

Cobham's theorem for substitutions

  • Fabien Durand

    Université de Picardie Jules Verne, Amiens, France
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Abstract

The seminal theorem of Cobham has given rise during the last 40 years to a lot of works about 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\alpha and β\beta be two multiplicatively independent Perron numbers. Then, a sequence xANx\in A^\mathbb{N}, where AA is a finite alphabet, is both α\alpha-substitutive and β\beta-substitutive if and only if xx is ultimately periodic.

Cite this article

Fabien Durand, Cobham's theorem for substitutions. J. Eur. Math. Soc. 13 (2011), no. 6, pp. 1799–1814

DOI 10.4171/JEMS/294