On Sturmian substitutions closed under derivation

Invertible substitutions and Sturmian sequences

It is known on the one hand that a Sturmian sequence can be generated geometrically by the intersections of a straight line with the unit grid in the plane, and on the other hand that fixed points of invertible substitutions are Sturmian. We give a new characterization of invertible substitutions, which allows to determine the straight line which generates the fixed point of a given invertible ...

Bidimensional Sturmian Sequences and Substitutions

On Closed Sets of Relational Constraints and Classes of Functions Closed under Variable Substitutions

Pippenger’s Galois theory of finite functions and relational constraints is extended to the infinite case. The functions involved are functions of several variables on a set A and taking values in a possibly different set B, where any or both of A and B may be finite or infinite.

Open and Closed Prefixes of Sturmian Words

A word is closed if it contains a proper factor that occurs both as a prefix and as a suffix but does not have internal occurrences, otherwise it is open. We deal with the sequence of open and closed prefixes of Sturmian words and prove that this sequence characterizes every finite or infinite Sturmian word up to isomorphisms of the alphabet. We then characterize the combinatorial structure of ...

Languages under substitutions and balanced

= zu2(i + k) for all i E I,. If I = Z we call w a Z-word or a bi-infinite word. If I is finite we call x finite and its length Ixl is defined as The usual notation for a finite word of length n is x = xi ... zn where all xi E {a, &}. We write {a, b}* for the collection of finite words and {a, b~+ for the nonempty finite words. (The empty word will be denoted throughout by e). The concatena...