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Bouquets of circles for lamination languages and complexities

Published online by Cambridge University Press:  10 July 2014

Philippe Narbel
Philippe Narbel*
Affiliation:
LaBRI – UFR Math-Info, University of Bordeaux 1, 33405 Talence, France. . narbel@labri.fr
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Abstract

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 by using associated labeled embedded graphs, and which are subshifts. Here, we characterize the possible exact affine factor complexities of these languages through bouquets of circles, i.e. graphs made of one vertex, as representative coding graphs. We also show how to build families of laminations together with corresponding lamination languages covering all the possible exact affine complexities.

Keywords

Curveslaminations on surfacessymbolic dynamicsshiftsfactor complexityembedded graphstrain-tracksRauzy graphssubstitutionsspirals
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 48 , Issue 4: Special issue in the honor of the 14th "Journées Montoises d'Informatique Théorique" , October 2014 , pp. 391 - 418
Copyright
© EDP Sciences 2014

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