On Quasiperiodic Morphisms

Weakly and strongly quasiperiodic morphisms are tools introduced to study quasiperiodic words. Formally they map respectively at least one or any non-quasiperiodic word to a quasiperiodic word. Considering them both on finite and infinite words, we get four families of morphisms between which we study relations. We provide algorithms to decide whether a morphism is strongly quasiperiodic on finite words or on infinite words.Comment: 12 page

Determining Sets of Quasiperiods of Infinite Words

A word is quasiperiodic if it can be obtained by concatenations and overlaps of a smaller word, called a quasiperiod. Based on links between quasiperiods, right special factors and square factors, we introduce a method to determine the set of quasiperiods of a given right infinite word. Then we study the structure of the sets of quasiperiods of right infinite words and, using our method, we provide examples of right infinite words with extremal sets of quasiperiods (no quasiperiod is quasiperiodic, all quasiperiods except one are quasiperiodic, ...). Our method is also used to provide a short proof of a recent characterization of quasiperiods of the Fibonacci word. Finally we extend this result to a new characterization of standard Sturmian words using a property of their sets of quasiperiods

LIPIcs, Volume 274, ESA 2023, Complete Volume

LIPIcs, Volume 274, ESA 2023, Complete Volum