Fine and Wilf's theorem and pseudo-repetitions

Abstract

The notion of repetition of factors in words is central to considerations on sequences. One of the recent generalizations regarding this concept was introduced by Czeizler et al. (2010) and investigates a restricted version of that notion in the context of DNA computing and bioinformatics. It considers a word to be a pseudo-repetition if it is the iterated concatenation of one of its prefixes and the image of this prefix through an involution. We present here a series of results in the fashion of the Fine and Wilf Theorem in a more general setting where we consider the periods of some word given by a prefix of it and images of that prefix through some arbitrary morphism or antimorphism. © 2012 Springer-Verlag.