A note on 3iet preserving morphisms
نویسندگان
چکیده
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 generated. On the contrary, in this note we prove that the monoid of 3iet preserving morphisms is not finitely generated, that is, there are infinitely many 3iet preserving morphisms, which cannot be written as a non-trivial decomposition of other 3iet preserving morphisms.
منابع مشابه
Morphisms 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 کاملA Note on Spectrum Preserving Additive Maps on C*-Algebras
Mathieu and Ruddy proved that if be a unital spectral isometry from a unital C*-algebra Aonto a unital type I C*-algebra B whose primitive ideal space is Hausdorff and totallydisconnected, then is Jordan isomorphism. The aim of this note is to show that if be asurjective spectrum preserving additive map, then is a Jordan isomorphism without the extraassumption totally disconnected.
متن کاملThe witness set of coexistence of quantum effects and its preservers
One of unsolved problems in quantum measurement theory is to characterize coexistence of quantum effects. In this paper, applying positive operator matrix theory, we give a mathematical characterization of the witness set of coexistence of quantum effects and obtain a series of properties of coexistence. We also devote to characterizing bijective morphisms on quantum effects leaving the witness...
متن کاملClassification of coset-preserving skew-morphisms of finite cyclic groups
The concept of a coset-preserving skew-morphism is a generalization of the widely studied t-balanced skew-morphisms of regular Cayley maps which are in turn generalizations of group automorphisms. In case of abelian groups, all skew-morphisms of regular Cayley maps are roots of coset-preserving skew-morphisms, and therefore, classification of cosetpreserving skew-morphisms of finite abelian gro...
متن کاملSturm Numbers and Substitution Invariance of 3iet Words
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, ...
متن کامل