3 research outputs found
Derivated sequences of complementary symmetric Rote sequences
Complementary symmetric Rote sequences are binary sequences which have factor
complexity for all integers and whose
languages are closed under the exchange of letters. These sequences are
intimately linked to Sturmian sequences. Using this connection we investigate
the return words and the derivated sequences to the prefixes of any
complementary symmetric Rote sequence which is associated with a
standard Sturmian sequence . We show that any non-empty prefix of
has three return words. We prove that any derivated sequence of
is coding of three interval exchange transformation and we
determine the parameters of this transformation. We also prove that
is primitive substitutive if and only if is primitive
substitutive. Moreover, if the sequence is a fixed point of a
primitive morphism, then all derivated sequences of are also fixed
by primitive morphisms. In that case we provide an algorithm for finding these
fixing morphisms
Rigidity and Substitutive Dendric Words
International audienceDendric words are infinite words that are defined in terms of extension graphs. These are bipartite graphs that describe the left and right extensions of factors. Dendric words are such that all their extension graphs are trees. They are also called tree words. This class of words includes classical families of words such as Sturmian words, codings of interval exchanges, or else, Arnoux-Rauzy words. We investigate here the properties of substitutive dendric words and prove some rigidity properties, that is, algebraic properties on the set of substitutions that fix a dendric word. We also prove that aperiodic minimal dendric subshifts (generated by dendric words) cannot have rational topological eigenvalues, and thus, cannot be generated by constant length substitutions