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
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top- J.-P. Allouche and J. Shallit, Automatic sequences: Theory, Applications, Generalizations. Cambridge University Press (2003).
- P. Arnoux and G. Rauzy, Représentation géométrique de suites de complexités . Bull. Soc. Math. France119 (1991) 199–215.
- J. Berstel, Sturmian and episturmian words (a survey of some recent results), in Proceedings of CAI 2007. Lect. Notes Comput. Sci., Vol. 4728. Springer-Verlag (2007).
- V. Berthé, C. Holton and L.Q. Zamboni, Initial powers of Sturmian sequences. Acta Arith.122 (2006) 315–347.
- X. Droubay, J. Justin and G. Pirillo, Episturmian words and some constructions of de Luca and Rauzy. Theoret. Comput. Sci.255 (2001) 539–553.
- S. Ferenczi, Complexity of sequences and dynamical systems. Discrete Math.206 (1999) 145–154.
- A. Glen, On Sturmian and episturmian words, and related topics. Ph.D. thesis, The University of Adelaide, Australia (2006).
- A. Glen, A characterization of fine words over a finite alphabet. Theoret. Comput. Sci.391 (2008) 51–60.
- A. Glen and J. Justin, Episturmian words: a survey. RAIRO-Theor. Inf. Appl. (submitted). e-print arxiv:0801.1655 (2007).
- A. Glen, J. Justin and G. Pirillo, Characterizations of finite and infinite episturmian words via lexicographic orderings. Eur. J. Combin.29 (2008) 45–58.
- A. Glen, F. Levé and G. Richomme, Quasiperiodic and Lyndon episturmian words. Theoret. Comput. Sci. DOI: . DOI10.1016/j.tcs.2008.09.056
- E. Godelle, Représentation par des transvections des groupes d'artin-tits. Group Geom. Dyn.1 (2007) 111–133.
- J. Justin and G. Pirillo, Episturmian words and episturmian morphisms. Theoret. Comput. Sci.276 (2002) 281–313.
- J. Justin and G. Pirillo, On a characteristic property of Arnoux-Rauzy sequences. RAIRO-Theor. Inf. Appl.36 (2003) 385–388.
- J. Justin and G. Pirillo, Episturmian words: shifts, morphisms and numeration systems. Int. J. Found. Comput. Sci.15 (2004) 329–348.
- F. Levé and G. Richomme, Quasiperiodic infinite words: some answers. Bull. Eur. Assoc. Theor. Comput. Sci.84 (2004) 128–138.
- F. Levé and G. Richomme, Quasiperiodic episturmian words, in Proceedings of the 6th International Conference on Words, Marseille, France (2007).
- F. Levé and G. Richomme, Quasiperiodic Sturmian words and morphisms. Theoret. Comput. Sci.372 (2007) 15–25.
- M. Lothaire, Combinatorics on Words, Encyclopedia of Mathematics and its Applications, Vol. 17. Addison-Wesley (1983).
- M. Lothaire, Algebraic Combinatorics on Words, Encyclopedia of Mathematics and its Applications, Vol. 90, Cambridge University Press (2002).
- M. Morse and G. Hedlund, Symbolic Dynamics II. Sturmian trajectories. Amer. J. Math.61 (1940) 1–42.
- G. Paquin and L. Vuillon, A characterization of balanced episturmian sequences. Electron. J. Combin.14 (2007) 33.
- N. Pytheas Fogg, Substitutions in dynamics, arithmetics and combinatorics. Lect. Notes Math., Vol. 1794. Springer (2002).
- G. Rauzy, Nombres algébriques et substitutions. Bull. Soc. Math. France110 (1982) 147–178.
- G. Rauzy, Mots infinis en arithmétique, in Automata on Infinite words, edited by M. Nivat, D. Perrin. Lect. Notes Comput. Sci., Vol. 192. Springer-Verlag, Berlin (1985).
- G. Richomme, Conjugacy and episturmian morphisms. Theoret. Comput. Sci.302 (2003) 1–34.
- G. Richomme, Lyndon morphisms. Bull. Belg. Math. Soc. Simon Stevin10 (2003) 761–785.
- G. Richomme, Conjugacy of morphisms and Lyndon decomposition of standard Sturmian words. Theoret. Comput. Sci.380 (2007) 393–400.
- G. Richomme, A local balance property of episturmian words, in Proc. DLT '07. Lect. Notes Comput. Sci., Vol. 4588. Springer, Berlin (2007) 371–381.
- R. Risley and L. Zamboni, A generalization of Sturmian sequences: combinatorial structure and transcendence. Acta Arith.95 (2000) 167–184.
- P. Séébold, Fibonacci morphisms and Sturmian words. Theoret. Comput. Sci.88 (1991) 365–384.
- Z.-X. Wen and Y. Zhang, Some remarks on invertible substitutions on three letter alphabet. Chinese Sci. Bull.44 (1999) 1755–1760.