# Transcendence of numbers with an expansion in a subclass of complexity 2n + 1

RAIRO - Theoretical Informatics and Applications (2006)

- Volume: 40, Issue: 3, page 459-471
- ISSN: 0988-3754

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topKärki, Tomi. "Transcendence of numbers with an expansion in a subclass of complexity 2n + 1." RAIRO - Theoretical Informatics and Applications 40.3 (2006): 459-471. <http://eudml.org/doc/249703>.

@article{Kärki2006,

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.
},

author = {Kärki, Tomi},

journal = {RAIRO - Theoretical Informatics and Applications},

keywords = {Transcendental numbers; subword complexity; Rauzy graph.; transcendental numbers},

language = {eng},

month = {10},

number = {3},

pages = {459-471},

publisher = {EDP Sciences},

title = {Transcendence of numbers with an expansion in a subclass of complexity 2n + 1},

url = {http://eudml.org/doc/249703},

volume = {40},

year = {2006},

}

TY - JOUR

AU - Kärki, Tomi

TI - Transcendence of numbers with an expansion in a subclass of complexity 2n + 1

JO - RAIRO - Theoretical Informatics and Applications

DA - 2006/10//

PB - EDP Sciences

VL - 40

IS - 3

SP - 459

EP - 471

AB -
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.

LA - eng

KW - Transcendental numbers; subword complexity; Rauzy graph.; transcendental numbers

UR - http://eudml.org/doc/249703

ER -

## References

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