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Transcendence of Numbers with an Expansion in a Subclass of Complexity 2n+1

Tomi Kärki, Transcendence of Numbers with an Expansion in a Subclass of Complexity 2n+1. In: Workshop on Word Avoidability, Complexity and Morphisms, 31-36, 2004.

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 be an integer at least 2. If the expansion in base k
of a number is 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.

BibTeX entry:

@INPROCEEDINGS{inpKarki04a,
  title = {Transcendence of Numbers with an Expansion in a Subclass of Complexity 2n+1},
  booktitle = {Workshop on Word Avoidability, Complexity and Morphisms},
  author = {Kärki, Tomi},
  pages = {31-36},
  year = {2004},
  keywords = {combinatorics on words, transcendental numbers, subword complexity, Rauzy graph},
}

Belongs to TUCS Research Unit(s): FUNDIM, Fundamentals of Computing and Discrete Mathematics

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