Substitutions on two letters, cutting segments and their projections
Journal de Théorie des Nombres de Bordeaux, Volume 19 (2007) no. 2, pp. 523-545.

In this paper we study the structure of the projections of the finite cutting segments corresponding to unimodular substitutions over a two-letter alphabet. We show that such a projection is a block of letters if and only if the substitution is Sturmian. Applying the procedure of projecting the cutting segments corresponding to a Christoffel substitution twice results in the original substitution. This induces a duality on the set of Christoffel substitutions.

Dans cet article on considère la structure des projections des segments de coupure correspondant aux substitutions unimodulaires sur un alphabet binaire. On montre qu’une telle projection est un bloc de lettres si et seulement si la substitution est sturmienne. Une double application de ce procédé à une substitution de Christoffel donne la substitution originelle. On obtient ainsi une dualité sur l’ensemble des substitutions de Christoffel.

Received:
Published online:
DOI: 10.5802/jtnb.600
Sierk W. Rosema 1

1 Mathematical Institute Leiden University P.O. Box 9512, 2300 RA Leiden The Netherlands
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Sierk W. Rosema. Substitutions on two letters, cutting segments and their projections. Journal de Théorie des Nombres de Bordeaux, Volume 19 (2007) no. 2, pp. 523-545. doi : 10.5802/jtnb.600. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.600/

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