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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; topeka@utu.fi
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Abstract

We divide infinite sequences of subword complexity 2n+1 intofour subclasses with respect to left and right special elementsand examine the structure of the subclasses with the help of Rauzygraphs. Let k ≥ 2 be an integer. If the expansion in base kof a number is an Arnoux-Rauzy word, then it belongs to Subclass Iand the number is known to be transcendental. We prove thetranscendence of numbers with expansions in the subclasses II andIII.

Keywords

Transcendental numberssubword complexityRauzy graph.

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