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We present two methods based on decimation for computing finite billiard words on any finite alphabet. The first method computes finite billiard words by iteration of some transformation on words. The number of iterations is explicitly bounded. The second one gives a direct formula for the billiard words. Some results remain true for infinite standard sturmian words, but cannot be used for computation as they only are limit results.
@article{ITA_2010__44_1_59_0,
author = {Borel, Jean-Pierre},
title = {How to build billiard words using decimations},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
pages = {59--77},
publisher = {EDP-Sciences},
volume = {44},
number = {1},
year = {2010},
doi = {10.1051/ita/2010005},
mrnumber = {2604935},
zbl = {1184.68369},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/ita/2010005/}
}
TY - JOUR AU - Borel, Jean-Pierre TI - How to build billiard words using decimations JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2010 SP - 59 EP - 77 VL - 44 IS - 1 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/ita/2010005/ DO - 10.1051/ita/2010005 LA - en ID - ITA_2010__44_1_59_0 ER -
%0 Journal Article %A Borel, Jean-Pierre %T How to build billiard words using decimations %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2010 %P 59-77 %V 44 %N 1 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/ita/2010005/ %R 10.1051/ita/2010005 %G en %F ITA_2010__44_1_59_0
Borel, Jean-Pierre. How to build billiard words using decimations. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 44 (2010) no. 1, pp. 59-77. doi: 10.1051/ita/2010005
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