Sturm Numbers and Substitution Invariance of 3iet Words
نویسنده
چکیده
In this paper, we give a necessary condition for an infinite word defined by a nondegenerate interval exchange on three intervals (3iet word) to be invariant by a substitution: a natural parameter associated to this word must be a Sturm number. We deduce some algebraic consequences from this condition concerning the incidence matrix of the associated substitution. As a by-product of our proof, we give a combinatorial characterization of 3iet words.
منابع مشابه
Characterization of substitution invariant 3iet words
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.
متن کاملMorphisms fixing words associated with exchange of three intervals
We consider words coding exchange of three intervals with permutation (3,2,1), here called 3iet words. Recently, a characterization of substitution invariant 3iet words was provided. We study the opposite question: what are the morphisms fixing a 3iet word? We reveal a narrow connection of such morphisms and morphisms fixing Sturmian words using the new notion of amicability.
متن کاملCharacterization 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.
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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...
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We consider exchange of three intervals with permutation (3, 2, 1). The aim of this paper is to count the cardinality of the set 3iet(N) of all words of length N which appear as factors in infinite words coding such transformations. We use the strong relation of 3iet words and words coding exchange of two intervals, i.e., Sturmian words. The known asymptotic formula #2iet(N)/N ∼ 1 π 2 for the n...
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