Morphisms fixing words associated with exchange of three intervals

Matrices of 3-iet preserving morphisms

We study matrices of morphisms preserving the family of words coding 3-interval exchange transformations. It is well known that matrices of morphisms preserving sturmian words (i.e. words coding 2-interval exchange transformations with the maximal possible factor complexity) form the monoid {M ∈ N | det M = ±1} = {M ∈ N | MEM = ±E}, where E = ( 0 1 −1 0 ). We prove that in case of exchange of t...

A note on 3iet preserving morphisms

An infinite word, which is aperiodic and codes the orbit of a transformation of the exchange of three intervals is called 3iet word. Such a word is thus a natural generalization of a sturmian word to a word over 3-letter alphabet. A morphism is said to be 3iet preserving if it maps any 3iet word to another 3iet word. It is known that the monoid of morphisms preserving sturmian words is finitely...

Morphisms preserving the set of words coding three interval exchange

Characterization of Substitution Invariant Words Coding Exchange of Three Intervals

We study infinite words coding an orbit under an exchange of three intervals which have full complexity C(n) = 2n + 1 for all n ∈ N (non-degenerate 3iet words). In terms of parameters of the interval exchange and the starting point of the orbit we characterize those 3iet words which are invariant under a primitive substitution. Thus, we generalize the result recently obtained for Sturmian words.

Sharp Characterizations of Squarefree Morphisms

Squarefree morphisms, i.e. morphisms that preserve squarefreeness of words, have been a subject of interest since the works of Thue [8]. They are a powerful tool to prove properties on squarefree words and are used in particular to prove the existence of infinite sequences without repetition. The study of squarefree words is connected with cluestions in algebra and game theory, and recentiy sev...