no. 2
The theorem of Fine and Wilf for relational periods
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 43 (2009) no. 2, pp. 209-220.

We consider relational periods, where the relation is a compatibility relation on words induced by a relation on letters. We prove a variant of the theorem of Fine and Wilf for a (pure) period and a relational period.

DOI : 10.1051/ita:2008025
Classification : 68R15
Mots clés : period, partial word, compatibility, Fine, Wilf 
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     author = {Halava, Vesa and Harju, Tero and K\"arki, Tomi},
     title = {The theorem of {Fine} and {Wilf} for relational periods},
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Halava, Vesa; Harju, Tero; Kärki, Tomi. The theorem of Fine and Wilf for relational periods. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 43 (2009) no. 2, pp. 209-220. doi : 10.1051/ita:2008025. http://www.numdam.org/articles/10.1051/ita:2008025/

[1] J. Berstel and L. Boasson, Partial words and a theorem of Fine and Wilf. Theoret. Comput. Sci. 218 (1999) 135-141. | MR | Zbl

[2] F. Blanchet-Sadri, A periodicity result of partial words with one hole. Comput. Math. Appl. 46 (2003) 813-820. | MR | Zbl

[3] F. Blanchet-Sadri, Periodicity on partial words. Comput. Math. Appl. 47 (2004) 71-82. | MR | Zbl

[4] F. Blanchet-Sadri, Codes, orderings, and partial words. Theoret. Comput. Sci. 329 (2004) 177-202. | MR | Zbl

[5] F. Blanchet-Sadri and A. Chriscoe, Local periods and binary partial words: an algorithm. Theoret. Comput. Sci. 314 (2004) 189-216. | MR | Zbl

[6] F. Blanchet-Sadri and S. Duncan, Partial words and the critical factorization theorem. J. Combin. Theory Ser. A 109 (2005) 221-245. | MR | Zbl

[7] F. Blanchet-Sadri and R.A. Hegstrom, Partial words and a theorem of Fine and Wilf revisited. Theoret. Comput. Sci. 270 (2002) 401-419. | MR | Zbl

[8] N.J. Fine and H.S. Wilf, Uniqueness theorem for periodic functions. Proc. Amer. Math. Soc. 16 (1965) 109-114. | MR | Zbl

[9] V. Halava, T. Harju and T. Kärki, Relational codes of words. Theoret. Comput. Sci. 389 (2007) 237-249. | MR | Zbl

[10] V. Halava, T. Harju and T. Kärki, Defect theorems with compatibility relation. Semigroup Forum 76 (2008) 1-24. | MR | Zbl

[11] P. Leupold, Partial words for DNA coding. Lect. Notes Comput. Sci. 3384 (2005) 224-234. | MR | Zbl

[12] A.M. Shur and Y.V. Gamzova, Periods' interaction property for partial words, in Proceedings of Words'03, edited by T. Harju and J. Karhumäki. TUCS General Publication 27 (2003) 75-82. | MR | Zbl

[13] A.M. Shur and Yu.V. Gamzova, Partial words and the interaction property of periods. Izv. Math. 68 (2004) 405-428. | MR | Zbl

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