Abstract
We introduce the notion of a representation system: it can be viewed as a generalization of a numeration system in an integer base by means of which certain words on a finite alphabet can be represented. We show that under suitable hypotheses, concatenation of words is represented by a right-synchronized rational relation. We study languages which are represented by rational sets (this is the case, e. g., of the languages of binary overlap-free words, of partially abelian square-free words on three letters, and of a large class of PD0L languages). Several results on these languages are obtained, concerning density, prolongability, pattern-freeness.
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