Handbook of formal languages, vol. 1
Fine and Wilf's theorem for three periods and a generalization of Sturmian words
Theoretical Computer Science
Partial words and a theorem of Fine and Wilf
Theoretical Computer Science
Journal of Combinatorial Theory Series A
Partial words and a theorem of Fine and Wilf revisited
Theoretical Computer Science
Local periods and binary partial words: an algorithm
Theoretical Computer Science
Generalised fine and Wilf's theorem for arbitrary number of periods
Theoretical Computer Science - Combinatorics on words
Discrete Applied Mathematics
Testing primitivity on partial words
Discrete Applied Mathematics
Graph connectivity, partial words, and a theorem of Fine and Wilf
Information and Computation
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
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The concept of periodicity has played over the years a central role in the development of combinatorics on words and has been a highly valuable tool for the design and analysis of algorithms. Fine and Wilf's famous periodicity result, which is one of the most used and known results on words, has extensions to partial words, or sequences that may have a number of ''do not know'' symbols. These extensions fall into two categories: the ones that relate to strong periodicity and the ones that relate to weak periodicity. In this paper, we obtain consequences by generalizing, in particular, the combinatorial property that ''for any word u over {a, b}, ua or ub is primitive,'' which proves in some sense that there exist very many primitive partial words.