Directive words of episturmian words: equivalences and normalization

Amy Glen; Florence Levé; Gwénaël Richomme

RAIRO - Theoretical Informatics and Applications (2008)

  • Volume: 43, Issue: 2, page 299-319
  • ISSN: 0988-3754

Abstract

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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.

How to cite

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Glen, Amy, Levé, Florence, and Richomme, Gwénaël. "Directive words of episturmian words: equivalences and normalization." RAIRO - Theoretical Informatics and Applications 43.2 (2008): 299-319. <http://eudml.org/doc/92918>.

@article{Glen2008,
abstract = { 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. },
author = {Glen, Amy, Levé, Florence, Richomme, Gwénaël},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Episturmian word; Sturmian word; Arnoux-Rauzy sequence; episturmian morphism; directive word.; episturmian word; sturmian word; directive word},
language = {eng},
month = {11},
number = {2},
pages = {299-319},
publisher = {EDP Sciences},
title = {Directive words of episturmian words: equivalences and normalization},
url = {http://eudml.org/doc/92918},
volume = {43},
year = {2008},
}

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
DA - 2008/11//
PB - EDP Sciences
VL - 43
IS - 2
SP - 299
EP - 319
AB - 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.
LA - eng
KW - Episturmian word; Sturmian word; Arnoux-Rauzy sequence; episturmian morphism; directive word.; episturmian word; sturmian word; directive word
UR - http://eudml.org/doc/92918
ER -

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