Abstract
Abstract
Dendric shifts are defined by combinatorial restrictions of the extensions of the words in their languages. This family generalizes well-known families of shifts such as Sturmian shifts, Arnoux–Rauzy shifts and codings of interval exchange transformations. It is known that any minimal dendric shift has a primitive
$\mathcal {S}$
-adic representation where the morphisms in
$\mathcal {S}$
are positive tame automorphisms of the free group generated by the alphabet. In this paper, we investigate those
$\mathcal {S}$
-adic representations, heading towards an
$\mathcal {S}$
-adic characterization of this family. We obtain such a characterization in the ternary case, involving a directed graph with two vertices.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,General Mathematics
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