Combinatorics of periods in strings

Abstract

We consider the set σ(n) of all period sets of strings of length n over a finite alphabet. We show that there is redundancy in period sets and introduce the notion of an irreducible period set. We prove that σ(n) is a lattice under set inclusion and does not satisfy the JordanDedekind condition.We propose the first enumeration algorithm for σ(n) and improve upon the previously known asymptotic lower bounds on the cardinality of σ(n) Finally, we provide a new recurrence to compute the number of strings sharing a given period set. © 2011 Springer-Verlag Berlin Heidelberg.