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 and be two multiplicatively independent Perron numbers. Then, a sequence x AN, where A is a finite alphabet, is both -substitutive and -substitutive if and only if x is ultimately periodic.

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Fabien Durand
• Keywords: CORR 2010, Education, Non-standard Numeration Systems, Seminal Theorem, So-called Substitutive Sequences