Hostname: page-component-546b4f848f-sw5dq Total loading time: 0 Render date: 2023-05-31T17:37:57.468Z Has data issue: false Feature Flags: { "useRatesEcommerce": true } hasContentIssue false
  • English

The theorem of Fine and Wilf for relational periods

Published online by Cambridge University Press:  05 June 2008

Vesa Halava ,
Tero Harju  and
Tomi Kärki
Vesa Halava
Affiliation:
Department of Mathematics and Turku Centre for Computer Science, University of Turku, FIN-20014 Turku, Finland; vehalava@utu.fi; harju@utu.fi; topeka@utu.fi
Tero Harju
Affiliation:
Department of Mathematics and Turku Centre for Computer Science, University of Turku, FIN-20014 Turku, Finland; vehalava@utu.fi; harju@utu.fi; topeka@utu.fi
Tomi Kärki
Affiliation:
Department of Mathematics and Turku Centre for Computer Science, University of Turku, FIN-20014 Turku, Finland; vehalava@utu.fi; harju@utu.fi; topeka@utu.fi
Get access

Abstract

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.

Keywords

Periodpartial wordcompatibilityFineWilf.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 43 , Issue 2 , April 2009 , pp. 209 - 220
Copyright
© EDP Sciences, 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Berstel, J. and Boasson, L., Partial words and a theorem of Fine and Wilf. Theoret. Comput. Sci. 218 (1999) 135–141. CrossRef
Blanchet-Sadri, F., A periodicity result of partial words with one hole. Comput. Math. Appl. 46 (2003) 813–820. CrossRef
Blanchet-Sadri, F., Periodicity on partial words. Comput. Math. Appl. 47 (2004) 71–82. CrossRef
Blanchet-Sadri, F., Codes, orderings, and partial words. Theoret. Comput. Sci. 329 (2004) 177–202. CrossRef
Blanchet-Sadri, F. and Chriscoe, A., Local periods and binary partial words: an algorithm. Theoret. Comput. Sci. 314 (2004) 189–216. CrossRef
Blanchet-Sadri, F. and Duncan, S., Partial words and the critical factorization theorem. J. Combin. Theory Ser. A 109 (2005) 221–245. CrossRef
Blanchet-Sadri, F. and Hegstrom, R.A., Partial words and a theorem of Fine and Wilf revisited. Theoret. Comput. Sci. 270 (2002) 401–419. CrossRef
Fine, N.J. and Wilf, H.S., Uniqueness theorem for periodic functions. Proc. Amer. Math. Soc. 16 (1965) 109–114. CrossRef
Halava, V., Harju, T. and Kärki, T., Relational codes of words. Theoret. Comput. Sci. 389 (2007) 237–249. CrossRef
Halava, V., Harju, T. and Kärki, T., Defect theorems with compatibility relation. Semigroup Forum 76 (2008) 1–24. CrossRef
Leupold, P., Partial words for DNA coding. Lect. Notes Comput. Sci. 3384 (2005) 224–234. CrossRef
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.
Shur, A.M. and Gamzova, Yu.V., Partial words and the interaction property of periods. Izv. Math. 68 (2004) 405–428. CrossRef