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 k2 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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