no. 3
Transcendence of numbers with an expansion in a subclass of complexity 2n + 1
RAIRO. Theoretical Informatics and 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
Keywords: 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, Tome 40 (2006) no. 3, pp. 459-471. doi: 10.1051/ita:2006034

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