How many squares can a string contain?
Journal of Combinatorial Theory Series A
Partial words and a theorem of Fine and Wilf
Theoretical Computer Science
Theoretical Computer Science
A simple proof that a word of length n has at most 2n distinct squares
Journal of Combinatorial Theory Series A
Testing primitivity on partial words
Discrete Applied Mathematics
SIAM Journal on Discrete Mathematics
A note on the number of squares in a word
Theoretical Computer Science
Graph connectivity, partial words, and a theorem of Fine and Wilf
Information and Computation
Algorithmic Combinatorics on Partial Words (Discrete Mathematics and Its Applications)
Algorithmic Combinatorics on Partial Words (Discrete Mathematics and Its Applications)
A new approach to the periodicity lemma on strings with holes
Theoretical Computer Science
Counting distinct squares in partial words
Acta Cybernetica
Periods in partial words: an algorithm
IWOCA'11 Proceedings of the 22nd international conference on Combinatorial Algorithms
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Partial words, or sequences over a finite alphabet that may have do-not-know symbols or holes, have been recently the subject of much investigation. Several interesting combinatorial properties have been studied such as the periodic behavior and the counting of distinct squares in partial words. In this paper, we extend the three-squares lemma on words to partial words with one hole. This result provides special information about the squares in a partial word with at most one hole, and puts restrictions on the positions at which periodic factors may occur, which is in contrast with the well known periodicity lemma of Fine and Wilf.