Combinatorics of Periods in Strings
نویسندگان
چکیده
We consider the set Γ (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 Γ (n) is a lattice under set inclusion and does not satisfy the JordanDedekind condition. We propose the first enumeration algorithm for Γ (n) and improve upon the previously known asymptotic lower bounds on the cardinality of Γ (n). Finally, we provide a new recurrence to compute the number of strings sharing a given period set.
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