J. Berstel and L. Boasson. Partial words and a theorem of Fine and Wilf. Theoret. Comput. Sci., 218:135--141, 1999. Home/Search Document Details and Download
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Overlap-Free Symmetric D0L words - Frid (2001) (1 citation) (Correct)
....morphism, and if all symbols occurring in j(0) are distinct, then the fixed point w = w(j) is overlap free. The remaining part of the paper is devoted to the proof of this result. 2 Proof of Theorem 2 Let us start with introducing some more notions and citing a result by Berstel and Boasson [4] which we shall need later. A partial word is a word on the alphabet S[f g, where the symbol = 2 S is called the hole . Each hole means an unknown symbol of S. A (partial) word u = u 1 : u n , where u i are symbols, is called (locally) p periodic if u i = u i p for all i 2 f1; n ....
....an unknown symbol of S. A (partial) word u = u 1 : u n , where u i are symbols, is called (locally) p periodic if u i = u i p for all i 2 f1; n pg such that u i 6= and u i p 6= The following result is a generalization of the classical Fine and Wilf s theorem [9, 6] Theorem 3 ([4]) Let u be a partial word of length n which is p periodic and q periodic. If u contains only one hole, and if n p q, then u is gcd(p;q) periodic. Now let us start the proof of Theorem 2 and first consider the easiest case: Lemma 1 If the symmetric morphism j is defined by j(0) 0c 2c : m ....
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J. Berstel and L. Boasson. Partial words and a theorem of Fine and Wilf. Theoret. Comput. Sci. 218 (1999), no. 1, 135--141.
Combinatorics on Words - A Tutorial - Berstel, Karhumäki (2003) (5 citations) Self-citation (Berstel) (Correct)
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J. Berstel and L. Boasson, Partial words and a theorem of Fine and Wilf, WORDS (Rouen, 1997), Theoret. Comput. Sci. 218, 135-141, 1999.
Periodicity and Repetition in Combinatorics on Words - Wang (2004) (Correct)
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J. Berstel and L. Boasson. Partial words and a theorem of Fine and Wilf. Theoret. Comput. Sci., 218:135--141, 1999.
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