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Episturmian morphisms constitute a powerful tool to study episturmian words. Indeed, any episturmian word can be infinitely decomposed over the set of pure episturmian morphisms. Thus, an episturmian word can be defined by one of its morphic decompositions or, equivalently, by a certain directive word. Here we characterize pairs of words directing the same episturmian word. We also propose a way to uniquely define any episturmian word through a normalization of its directive words. As a consequence of these results, we characterize episturmian words having a unique directive word.
@article{ITA_2009__43_2_299_0,
author = {Glen, Amy and Lev\'e, Florence and Richomme, Gw\'ena\"el},
title = {Directive words of episturmian words : equivalences and normalization},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
pages = {299--319},
publisher = {EDP-Sciences},
volume = {43},
number = {2},
year = {2009},
doi = {10.1051/ita:2008029},
mrnumber = {2512261},
zbl = {1166.68034},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/ita:2008029/}
}
TY - JOUR AU - Glen, Amy AU - Levé, Florence AU - Richomme, Gwénaël TI - Directive words of episturmian words : equivalences and normalization JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2009 SP - 299 EP - 319 VL - 43 IS - 2 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/ita:2008029/ DO - 10.1051/ita:2008029 LA - en ID - ITA_2009__43_2_299_0 ER -
%0 Journal Article %A Glen, Amy %A Levé, Florence %A Richomme, Gwénaël %T Directive words of episturmian words : equivalences and normalization %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2009 %P 299-319 %V 43 %N 2 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/ita:2008029/ %R 10.1051/ita:2008029 %G en %F ITA_2009__43_2_299_0
Glen, Amy; Levé, Florence; Richomme, Gwénaël. Directive words of episturmian words : equivalences and normalization. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 43 (2009) no. 2, pp. 299-319. doi: 10.1051/ita:2008029
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