Geodesic
Transcendence of numbers with an expansion in a subclass of complexity 2n + 1
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 40 (2006) no. 3, pp. 459-471

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We divide infinite sequences of subword complexity 2n+1 into four subclasses with respect to left and right special elements and examine the structure of the subclasses with the help of Rauzy graphs. Let k≥2 be an integer. If the expansion in base k of a number is an Arnoux-Rauzy word, then it belongs to Subclass I and the number is known to be transcendental. We prove the transcendence of numbers with expansions in the subclasses II and III.

DOI : 10.1051/ita:2006034
Classification : 11J81, 68R15
Keywords: transcendental numbers, subword complexity, Rauzy graph 
Kärki, Tomi. Transcendence of numbers with an expansion in a subclass of complexity 2n + 1. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 40 (2006) no. 3, pp. 459-471. doi: 10.1051/ita:2006034
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     title = {Transcendence of numbers with an expansion in a subclass of complexity 2n + 1},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {459--471},
     year = {2006},
     publisher = {EDP-Sciences},
     volume = {40},
     number = {3},
     doi = {10.1051/ita:2006034},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ita:2006034/}
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