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
On spaced seeds for similarity search
Discrete Applied Mathematics
Partial words and the critical factorization theorem
Journal of Combinatorial Theory Series A
Designing seeds for similarity search in genomic DNA
Journal of Computer and System Sciences - Special issue on bioinformatics II
Algorithms on Strings
Optimal spaced seeds for faster approximate string matching
Journal of Computer and System Sciences
Partial words and the critical factorization theorem revisited
Theoretical Computer Science
Hardness of optimal spaced seed design
Journal of Computer and System Sciences
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
A universal algorithm for sequential data compression
IEEE Transactions on Information Theory
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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 consider the period and weak period sets of partial words of length n over a finite alphabet, and study the combinatorics of specific representations of them, called correlations, which are binary and ternary vectors of length n indicating the periods and weak periods. We characterize precisely which vectors represent the period and 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 suitably defined partial orderings. We 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}. We also investigate the number of partial word correlations of length n. Finally, we compute the population size, that is, the number of partial words sharing a given correlation, and obtain recurrences to compute it. Our results generalize those of Guibas, Odlyzko, Rivals and Rahmann.