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.

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
Mots-clés : transcendental numbers, subword complexity, Rauzy graph 
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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. http://www.numdam.org/articles/10.1051/ita:2006034/

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