Combinatorics of Periods in Strings

We consider the set G n of all period sets of strings of length n over a finite alphabet. We show that there is redundan y in period sets and introdu e the notion of an irredu ible period set. We prove that G n is a latti e under set in lusion and does not satisfy the Jordan-- Dedekind ondition. We propose the first effi ient enumO[G;cF algorithm for G n and imdc]P upon the previously knownasymcL;P lower bounds on the ardinality of G n : Finally, we provide a new re urren e toomPOz thenumLz of strings sharing a given period set, and exhibit analgorithm tosamPL uniformc period sets through irredu ible period set