We proceed by induction on the length of u. When u = ?, the result holds with c = a, d = b and m = n. Assume Pal(u)c m d is a prefix of L u ,
The Ubiquitous Prouhet-Thue-Morse Sequence, Sequences and their applications, Proceedings of SETA'98, pp.1-16, 1999. ,
DOI : 10.1007/978-1-4471-0551-0_1
Repr??sentation g??om??trique de suites de complexit?? $2n+1$, Bulletin de la Société mathématique de France, vol.119, issue.2, pp.199-215, 1991. ,
DOI : 10.24033/bsmf.2164
URL : http://www.numdam.org/article/BSMF_1991__119_2_199_0.pdf
Combinatorics on Words: Christoffel Words and Repetitions in Words, 2008. ,
On different generalizations of episturmian words, Theoretical Computer Science, vol.393, issue.1-3, pp.23-36, 2008. ,
DOI : 10.1016/j.tcs.2007.10.043
On some problems related to palindromic closure. RAIRO-Theor, Inf. Appl, vol.42, pp.679-700, 2008. ,
Harmonic and gold Sturmian words, European Journal of Combinatorics, vol.25, issue.5, pp.685-705, 2004. ,
DOI : 10.1016/j.ejc.2003.10.007
URL : http://doi.org/10.1016/j.ejc.2003.10.007
On extremal properties of the Fibonacci word, RAIRO - Theoretical Informatics and Applications, vol.42, issue.4, pp.701-715, 2008. ,
DOI : 10.1051/ita:2008003
Substitution invariant cutting sequences, Journal de Th??orie des Nombres de Bordeaux, vol.5, issue.1, pp.123-137, 1993. ,
DOI : 10.5802/jtnb.83
The Index of Sturmian Sequences, European Journal of Combinatorics, vol.23, issue.1, pp.23-29, 2002. ,
DOI : 10.1006/eujc.2000.0496
Sturmian words: structure, combinatorics, and their arithmetics, Theoretical Computer Science, vol.183, issue.1, pp.45-82, 1997. ,
DOI : 10.1016/S0304-3975(96)00310-6
Pseudopalindrome closure operators in free monoids, Theoret. Comput. Sci, vol.362, issue.1-3, pp.45-82, 2006. ,
Episturmian words and some constructions of de Luca and Rauzy, Theoretical Computer Science, vol.255, issue.1-2, pp.539-553, 2001. ,
DOI : 10.1016/S0304-3975(99)00320-5
Determination of $[n heta ]$ by its sequence of differences, Bulletin canadien de math??matiques, vol.21, issue.4, pp.441-446, 1978. ,
DOI : 10.4153/CMB-1978-077-0
Episturmian words: a survey. RAIRO-Théor, Inform. and Appl, vol.43, pp.402-433, 2009. ,
Quasiperiodic and Lyndon episturmian words, Theoretical Computer Science, vol.409, issue.3, pp.578-600, 2008. ,
DOI : 10.1016/j.tcs.2008.09.056
URL : https://hal.archives-ouvertes.fr/hal-00599745
On the fixed points of the iterated pseudopalindromic closure operator, "WORDS'09 -7th International Conference on Words, 2009. ,
DOI : 10.1016/j.tcs.2010.03.018
URL : https://hal.archives-ouvertes.fr/hal-00391429
Episturmian morphisms and a Galois theorem on continued fractions, RAIRO - Theoretical Informatics and Applications, vol.39, issue.1, pp.207-215, 2005. ,
DOI : 10.1051/ita:2005012
Episturmian words and episturmian morphisms, Theoretical Computer Science, vol.276, issue.1-2, pp.281-313, 2002. ,
DOI : 10.1016/S0304-3975(01)00207-9
URL : http://doi.org/10.1016/s0304-3975(01)00207-9
Continued fractions. Translated by Peter Wynn, P. Noordhoff Ltd, 1963. ,
Self Generating Runs, Problem 5304, Amer. Math. Monthly, vol.72, p.674, 1965. ,
Algebraic Combinatorics on Words, volume 90 of Encyclopedia of Mathematics and its Applications, 2002. ,
Infinite words with linear subword complexity, Theoretical Computer Science, vol.65, issue.2, pp.221-242, 1989. ,
DOI : 10.1016/0304-3975(89)90046-7
URL : http://doi.org/10.1016/0304-3975(89)90046-7
Repetitions in the Fibonacci infinite word, RAIRO - Theoretical Informatics and Applications, vol.26, issue.3, pp.199-204, 1992. ,
DOI : 10.1051/ita/1992260301991
The structure of the set of cube-free $ Z$-words in a two-letter alphabet, Izvestiya: Mathematics, vol.64, issue.4, pp.847-861, 2000. ,
DOI : 10.1070/IM2000v064n04ABEH000301
Über die gegenseitige Lage gleicher Teile gewisser Zeichenreihen, Selected Mathematical Papers of Axel Thue, pp.1-67, 1912. ,
Sturmian words and words with a critical exponent, Theoretical Computer Science, vol.242, issue.1-2, pp.283-300, 2000. ,
DOI : 10.1016/S0304-3975(98)00227-8