Partial words and a theorem of Fine and Wilf
Theoretical Computer Science
Partial words and a theorem of Fine and Wilf revisited
Theoretical Computer Science
Finding approximate repetitions under Hamming distance
Theoretical Computer Science - Logic and complexity in computer science
Combinatorics of periods in strings
Journal of Combinatorial Theory Series A
Local periods and binary partial words: an algorithm
Theoretical Computer Science
Partial words and the critical factorization theorem
Journal of Combinatorial Theory Series A
Partial words and the critical factorization theorem revisited
Theoretical Computer Science
Periodicity properties on partial words
Information and Computation
Combinatorics on partial word correlations
Journal of Combinatorial Theory Series A
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Partial words are strings over a finite alphabet that may contain a number of "do not know" symbols. In this paper, we introduce the notions of binary and ternary correlations, which are binary and ternary vectors indicating the periods and weak periods of partial words. Extending a result of Guibas and Odlyzko, we characterize precisely which of these vectors represent the (weak) period sets of partial words and prove that all valid correlations may be taken over the binary alphabet. We show that the sets of all such vectors of a given length form distributive lattices under inclusion. We also show that there is a well defined minimal set of generators for any binary correlation of length n and demonstrate that these generating sets are the primitive subsets of {1, 2, ..., n - 1}. Finally, we investigate the number of correlations of length n.