Transcendence of numbers with an expansion in a subclass of complexity 2n + 1
Kärki, Tomi
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 40 (2006), p. 459-471 / Harvested from Numdam
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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.

Publié le : 2006-01-01
DOI : https://doi.org/10.1051/ita:2006034
Classification:  11J81,  68R15 
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     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},
     volume = {40},
     year = {2006},
     pages = {459-471},
     doi = {10.1051/ita:2006034},
     mrnumber = {2269204},
     zbl = {pre05123525},
     language = {en},
     url = {http://dml.mathdoc.fr/item/ITA_2006__40_3_459_0}
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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) pp. 459-471. doi : 10.1051/ita:2006034. http://gdmltest.u-ga.fr/item/ITA_2006__40_3_459_0/

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