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2 results

  • Bouquets of circles for lamination languages andcomplexities

  • Philippe Narbel
  • Journal:
    RAIRO - Theoretical Informatics and Applications / Volume 48 / Issue 4 / October 2014
    Published online by Cambridge University Press:
    10 July 2014, pp. 391-418
    Print publication:
    October 2014

  • Laminations are classic sets of disjoint and non-self-crossing curves on surfaces.Lamination languages are languages of two-way infinite words which code laminations byusing associated labeled embedded graphs, and which are subshifts. Here, we characterizethe possible exact affine factor complexities of these languages through bouquets ofcircles, i.e. graphs made of one vertex, as representative coding graphs.We also show how to build families of laminations together with corresponding laminationlanguages covering all the possible exact affine complexities.

  • Binary words avoiding the pattern AABBCABBA

  • Pascal Ochem
  • Journal:
    RAIRO - Theoretical Informatics and Applications / Volume 44 / Issue 1 / January 2010
    Published online by Cambridge University Press:
    11 February 2010, pp. 151-158
    Print publication:
    January 2010

  • We show that there are three types of infinite words over the two-letteralphabet {0,1} that avoid the pattern AABBCABBA. These types, P, E 0, and E 1,differ by the factor complexity and the asymptotic frequency of the letter 0.Type P has polynomial factor complexity and letter frequency $\frac{1}{2}$ .Type E 0 has exponential factor complexity and the frequency of the letter 0 is at least0.45622 and at most 0.48684. Type E 1 is obtained from type E 0 by exchanging 0 and 1.