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Transcendence of numbers with an expansion in a subclass of complexity2n + 1

Published online by Cambridge University Press:  18 October 2006

Tomi Kärki
Tomi Kärki*
Affiliation:
Department of Mathematics and Turku Centre for Computer Science, University of Turku, 20014 Turku, Finland; [email protected]
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Abstract

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.

Keywords

Transcendental numberssubword complexityRauzy graph.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 40 , Issue 3: Word Avoidability Complexity And Morphisms (WACAM) , July 2006 , pp. 459 - 471
Copyright
© EDP Sciences, 2006

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