Generating the Pseudo-Powers of a Word

The notions of power of word, periodicity and primitivity are intrinsically connected to the operation of catenation, that dynamically generates word repetitions. When considering generalizations of the power of a word, other operations will be the ones that dynamically generate such pseudo-repetitions. In this paper we define and investigate the operation of θ-catenation that gives rise to the notions of θ-power (pseudopower) and θ-periodicity (pseudo-periodicity). We namely investigate the properties of θ-catenation, its connection to the previously defined notion of θ-primitive word, briefly explore closure properties of language families under θ-catenation and language operations involving this operation, and propose Abelian catenation as the operation that generates Abelian powers of words.