Generating the Pseudo-Powers of a Word
Lila Kari, Manasi S. Kulkarni · Journal of automata, languages and combinatorics · 2014
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 $\theta$-catenation that gives rise to the notions of $\theta$-power (pseudo-power) and $\theta$-periodicity (pseudo-periodicity). We namely investigate the properties of $\theta$-catenation, its connection to the previously defined notion of $\theta$-primitive word, briefly explore closure properties of language families under $\theta$-catenation and language operations involving this operation, and propose Abelian catenation as the operation that generates Abelian powers of words.