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Izv. RAN. Ser. Mat., 2004, Volume 68, Issue 2, Pages 191–214 (Mi izv480)  

This article is cited in 7 scientific papers (total in 7 papers)

Partial words and the interaction property of periods

A. M. Shur, Yu. V. Gamzova


Abstract: A theorem of Fine and Wilf expresses the interaction property of periods, which is a basic property of periodic words. An arbitrary word with given periods $p$ and $q$ also has a “derived” period $\operatorname{gcd}(p,q)$ if the length of the word is greater than some critical value called the length of interaction. In this paper we consider a similar property for arbitrary periodic partial words and give a sharp linear bound for the length of interaction.

DOI: https://doi.org/10.4213/im480

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English version:
Izvestiya: Mathematics, 2004, 68:2, 405–428

Bibliographic databases:

UDC: 512.532.2+519.11
MSC: 68R15, 68Q45
Received: 08.01.2003

Citation: A. M. Shur, Yu. V. Gamzova, “Partial words and the interaction property of periods”, Izv. RAN. Ser. Mat., 68:2 (2004), 191–214; Izv. Math., 68:2 (2004), 405–428

Citation in format AMSBIB
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  • https://doi.org/10.4213/im480
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Yu. V. Gamzova, “Statisticheskie zakonomernosti vzaimodeistviya periodov chastichnykh slov”, Diskretn. analiz i issled. oper., ser. 1, ser. 1, 11:4 (2004), 20–35  mathnet  mathscinet  elib
    2. Halava V., Harju T., Kärki T., “The theorem of Fine and Wilf for relational periods”, Theor. Inform. Appl., 43:2 (2009), 209–220  crossref  mathscinet  zmath  isi  scopus
    3. Halava V., Harju T., Kärki T., Séébold P., “Overlap-freeness in infinite partial words”, Theoret. Comput. Sci., 410:8-10 (2009), 943–948  crossref  mathscinet  zmath  isi  scopus
    4. Idiatulina L.A., Shur A.M., “Periodic Partial Words and Random Bipartite Graphs”, Fundam. Inform., 132:1 (2014), 15–31  crossref  mathscinet  zmath  isi  scopus
    5. Blanchet-Sadri F., Cordier M., Kirsch R., “Border Correlations, Lattices, and the Subgraph Component Polynomial”, Eur. J. Comb., 68 (2018), 204–222  crossref  mathscinet  zmath  isi  scopus
    6. Kociumaka T., Radoszewski J., Rytter W., Walen T., “On Periodicity Lemma For Partial Words”, Language and Automata Theory and Applications (Lata 2018), Lecture Notes in Computer Science, 10792, eds. Klein S., MartinVide C., Shapira D., Springer International Publishing Ag, 2018, 232–244  crossref  mathscinet  zmath  isi  scopus
    7. Gourdel G., Kociumaka T., Radoszewski J., Rytter W., Shur A., Walen T., “String Periods in the Order-Preserving Model”, Inf. Comput., 270:SI (2020), 104463  crossref  isi
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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