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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. RAIRO - Theoretical Informatics and Applications 40(3), 459-471, 2006.

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 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:

@ARTICLE{jKarki06a,
  title = {Transcendence of Numbers with an Expansion in a Subclass of Complexity 2n+1},
  author = {Kärki, Tomi},
  journal = {RAIRO - Theoretical Informatics and Applications},
  volume = {40},
  number = {3},
  publisher = {EDP Sciences},
  pages = {459-471},
  year = {2006},
  keywords = {transcendental numbers, subword complexity, Rauzy graph},
}

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

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