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We divide infinite sequences of subword complexity 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 be an integer. If the expansion in base 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.
@article{ITA_2006__40_3_459_0,
author = {K\"arki, Tomi},
title = {Transcendence of numbers with an expansion in a subclass of complexity 2n + 1},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
pages = {459--471},
publisher = {EDP-Sciences},
volume = {40},
number = {3},
year = {2006},
doi = {10.1051/ita:2006034},
mrnumber = {2269204},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/ita:2006034/}
}
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 - Informatique Théorique et Applications PY - 2006 SP - 459 EP - 471 VL - 40 IS - 3 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/ita:2006034/ DO - 10.1051/ita:2006034 LA - en ID - ITA_2006__40_3_459_0 ER -
%0 Journal Article %A Kärki, Tomi %T Transcendence of numbers with an expansion in a subclass of complexity 2n + 1 %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2006 %P 459-471 %V 40 %N 3 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/ita:2006034/ %R 10.1051/ita:2006034 %G en %F ITA_2006__40_3_459_0
Kärki, Tomi. Transcendence of numbers with an expansion in a subclass of complexity 2n + 1. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 40 (2006) no. 3, pp. 459-471. doi: 10.1051/ita:2006034
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