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
Partial words and a theorem of Fine and Wilf revisited
Theoretical Computer Science
Introduction to Algorithms
On Fine and Wilf's theorem for bidimensional words
Theoretical Computer Science
Periodicity, morphisms, and matrices
Theoretical Computer Science - Mathematical foundations of computer science
Graph connectivity, partial words, and a theorem of Fine and Wilf
Information and Computation
Periodicity properties on partial words
Information and Computation
On a Special Class of Primitive Words
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
Fine and Wilf words for any periods II
Theoretical Computer Science
On a special class of primitive words
Theoretical Computer Science
An Improved Bound for an Extension of Fine and Wilf’s Theorem and Its Optimality
Fundamenta Informaticae
Periods in partial words: an algorithm
IWOCA'11 Proceedings of the 22nd international conference on Combinatorial Algorithms
DLT'12 Proceedings of the 16th international conference on Developments in Language Theory
Periods in partial words: An algorithm
Journal of Discrete Algorithms
Fine and wilf's theorem and pseudo-repetitions
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
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The well known Fine and Wilf's theorem for words states that if a word has two periods and its length is at least as long as the sum of the two periods minus their greatest common divisor, then the word also has as period the greatest common divisor. We generalise this result for an arbitrary number of periods. Our bound is strictly better in some cases than previous generalisations. Moreover, we prove it optimal. We show also that any extrenal word is unique up to letter renaming and give an algorithm to compute both the bound and a corresponding extremal word.