Episturmian morphisms and a Galois theorem on continued fractions
RAIRO - Theoretical Informatics and Applications (2010)
- Volume: 39, Issue: 1, page 207-215
- ISSN: 0988-3754
Access Full Article
topAbstract
topHow to cite
topReferences
top- C. Allauzen, Une caractérisation simple des nombres de Sturm. J. Th. Nombres Bordeaux10 (1998) 237–241.
- P. Arnoux and G. Rauzy, Représentation géometrique de suites de complexité 2n + 1. Bull. Soc. Math. France119 (1991) 199–215.
- J. Berstel, Recent results on extensions of Sturmian words. Internat. J. Algebra Comput.12 (2002) 371–385.
- V. Berthé, Autour du système de numération d'Ostrowski. Bull. Belg. Math. Soc.8 (2001) 209–239.
- E. Cahen, Théorie des Nombres. Tome 2, Librairie Scient. A. Hermann, Paris (1924).
- A. Carpi and A. de Luca, Harmonic and Gold Sturmian Words, preprint, Dipart. di Mat. G. Castelnuovo, Università degli Studi di Roma La Sapienza, 22/2003 (2003).
- M.G. Castelli, F. Mignosi and A. Restivo, Fine and Wilf's theorem for three periods and a generalization of Sturmian words. Theor. Comput. Sci.218 (2001) 83–94.
- X. Droubay, J. Justin and G. Pirillo, Episturmian words and some constructions of de Luca and Rauzy. Theor. Comput. Sci.255 (2001) 539–553.
- E. Galois, Démonstration d'un théorème sur les fractions continues périodiques. Ann. Math. Pures Appl. de M. Gergonne19 (1829) 294–301.
- J. Justin, On a paper by Castelli, Mignosi, Restivo. Theor. Inform. Appl.34 (2000) 373–377.
- J. Justin and G. Pirillo, Episturmian words and episturmian morphisms. Theor. Comput. Sci.276 (2002) 281–313.
- J. Justin and G. Pirillo, Episturmian words: shifts, morphisms and numeration systems. Intern. J. Foundat. Comput. Sci.15 (2004) 329–348.
- M. Lothaire, Algebraic Combinatorics on Words, edited by M. Lothaire. Cambridge University Press. Encyclopedia of Mathematics90 (2002).
- F. Mignosi and L.Q. Zamboni, On the number of Arnoux-Rauzy words. Acta Arith.101 (2002) 121–129.
- M. Morse and G.A. Hedlund, Symbolic dynamics II: Sturmian trajectories. Amer. J. Math.62 (1940) 1–42.
- 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 and D. Perrin. Lect. Notes Comput. Sci.192 (1985) 165–171.
- R.N. Risley and L.Q. Zamboni, A generalization of Sturmian sequences, combinatorial structure and transcendence. Acta Arithmetica95 (2000) 167–184.
- N.N. Wozny and L.Q. Zamboni, Frequencies of factors in Arnoux-Rauzy sequences. Acta Arithmetica96 (2001) 261–278.
- L.Q. Zamboni, Une généralisation du théorème de Lagrange sur le développement en fraction continue. C. R. Acad. Sci. Paris I327 (1998) 527–530.