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.
Mots clés : period, partial word, compatibility, Fine, Wilf
@article{ITA_2009__43_2_209_0, author = {Halava, Vesa and Harju, Tero and K\"arki, Tomi}, title = {The theorem of {Fine} and {Wilf} for relational periods}, journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications}, pages = {209--220}, publisher = {EDP-Sciences}, volume = {43}, number = {2}, year = {2009}, doi = {10.1051/ita:2008025}, mrnumber = {2512255}, zbl = {1166.68035}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/ita:2008025/} }
TY - JOUR AU - Halava, Vesa AU - Harju, Tero AU - Kärki, Tomi TI - The theorem of Fine and Wilf for relational periods JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2009 SP - 209 EP - 220 VL - 43 IS - 2 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ita:2008025/ DO - 10.1051/ita:2008025 LA - en ID - ITA_2009__43_2_209_0 ER -
%0 Journal Article %A Halava, Vesa %A Harju, Tero %A Kärki, Tomi %T The theorem of Fine and Wilf for relational periods %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2009 %P 209-220 %V 43 %N 2 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ita:2008025/ %R 10.1051/ita:2008025 %G en %F ITA_2009__43_2_209_0
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://archive.numdam.org/articles/10.1051/ita:2008025/
[1] Partial words and a theorem of Fine and Wilf. Theoret. Comput. Sci. 218 (1999) 135-141. | MR | Zbl
and ,[2] A periodicity result of partial words with one hole. Comput. Math. Appl. 46 (2003) 813-820. | MR | Zbl
,[3] Periodicity on partial words. Comput. Math. Appl. 47 (2004) 71-82. | MR | Zbl
,[4] Codes, orderings, and partial words. Theoret. Comput. Sci. 329 (2004) 177-202. | MR | Zbl
,[5] Local periods and binary partial words: an algorithm. Theoret. Comput. Sci. 314 (2004) 189-216. | MR | Zbl
and ,[6] Partial words and the critical factorization theorem. J. Combin. Theory Ser. A 109 (2005) 221-245. | MR | Zbl
and ,[7] Partial words and a theorem of Fine and Wilf revisited. Theoret. Comput. Sci. 270 (2002) 401-419. | MR | Zbl
and ,[8] Uniqueness theorem for periodic functions. Proc. Amer. Math. Soc. 16 (1965) 109-114. | MR | Zbl
and ,[9] Relational codes of words. Theoret. Comput. Sci. 389 (2007) 237-249. | MR | Zbl
, and ,[10] Defect theorems with compatibility relation. Semigroup Forum 76 (2008) 1-24. | MR | Zbl
, and ,[11] Partial words for DNA coding. Lect. Notes Comput. Sci. 3384 (2005) 224-234. | MR | Zbl
,[12] 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
and ,[13] Partial words and the interaction property of periods. Izv. Math. 68 (2004) 405-428. | MR | Zbl
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