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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. TUCS Technical Reports 654, Turku Centre for Computer Science, 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 two. 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.

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BibTeX entry:

@TECHREPORT{tKarki04a,
  title = {Transcendence of Numbers with an Expansion in a Subclass of Complexity 2n+1},
  author = {Kärki, Tomi},
  number = {654},
  series = {TUCS Technical Reports},
  publisher = {Turku Centre for Computer Science},
  year = {2004},
  keywords = {transcendental numbers, subword complexity, Rauzy graph},
  ISBN = {952-12-1488-0},
}

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

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