Geodesic
Bouquets of circles for lamination languages and complexities
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 48 (2014) no. 4, pp. 391-418

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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.

DOI : 10.1051/ita/2014016
Classification : 14Q05, 37B10, 37F20, 57R30, 68R15, 68Q45, 68R10
Keywords: curves, laminations on surfaces, symbolic dynamics, shifts, factor complexity, embedded graphs, train-tracks, Rauzy graphs, substitutions, spirals 
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     author = {Narbel, Philippe},
     title = {Bouquets of circles for lamination languages and complexities},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {391--418},
     publisher = {EDP-Sciences},
     volume = {48},
     number = {4},
     year = {2014},
     doi = {10.1051/ita/2014016},
     mrnumber = {3302494},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ita/2014016/}
}
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Narbel, Philippe. Bouquets of circles for lamination languages and complexities. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 48 (2014) no. 4, pp. 391-418. doi: 10.1051/ita/2014016

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