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RAIRO - Theoretical Informatics and Applications (1)

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Transcendence of numbers with an expansion in a subclass of complexity 2n + 1
Tomi Kärki
Journal:

RAIRO - Theoretical Informatics and Applications / Volume 40 / Issue 3 / July 2006

Published online by Cambridge University Press:

18 October 2006, pp. 459-471

Print publication:

July 2006
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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.