Overlapping factors in words

The concept of quasiperiodicity is a generalization of the notion of periodicity where in contrast to periodicity the quasiperiods of a quasiperiodic string may overlap. A lot of research has been concentrated around algorithms for the computation of quasiperiodicities in strings while not much is known about bounds on their maximum number of occurrences in words. We study the overlapping factors of a word as a means to provide more insight into quasiperiodic structures of words. We propose a linear time algorithm for the identification of all overlapping factors of a word, we investigate the appearance of overlapping factors in Fibonacci words and we provide some bounds on the maximum number of distinct overlapping factors in a word. ∗ Also at: Université Paris-Est, France. † Also at: Digital Ecosystems & Business Intelligence Institute, Curtin University, GPO Box U1987 Perth WA 6845, Australia 50 MANOLIS CHRISTODOULAKIS ET AL.