, Subject word index, Progress in Growth Factor Research, vol.6, pp.ix-x, 1996.
From now on, assume that ||f || > #A and assume f ? P. By Lemma 6.12, all images of letters begin with the same letter, or, all images of letters end with the same letter. Assume that the first case holds (the second case is symmetric) and let ? be the first letter of images of letters. Let w ? E. By hypothesis f (w) ? E. As E ? Stab(L ? R) by Theorem 6.3, f (w) = L ? (w ? ) or f (w) = R ? (w ? ) for some letter ? and some word w ? . When f (w) = L ? (w ? ), we have ? = ? and we can find a morphism g such that f = L ? g. By Lemma 6.11, g preserves E. As f ? P, ||g|| < ||f || and by induction g ? S epi . So f ? S epi . Assume now that f (w) = R ? (w ? ). If all images of letters by f end with ?, then f = R ? g and, as in the case f = L ? g above, f ? S epi . If some image of a letter by f does not end with ?, as the image of letters is followed by ? in f (w) and by, Let ||f || = ??A |f (?)|. We prove by induction on ||f || that f ? S epi . Assume first that ||f || = #A. If f (A) ,
, FROM OUR READERS, Exchange, vol.10, issue.3, p.75, 1981.
Random product of substitutions with the same incidence matrix, Theoretical Computer Science, vol.543, pp.68-78, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-01113397
Numeration and discrete dynamical systems, Computing, vol.94, issue.2-4, pp.369-387, 2011. ,
Initial powers of Sturmian sequences, Acta Arithmetica, vol.122, issue.4, pp.315-347, 2006. ,
Combinatorics, Automata and Number Theory, of Encyclopedia of Mathematics and its Applications, vol.135, 2009. ,
Episturmian words and some constructions of de Luca and Rauzy, Theoretical Computer Science, vol.255, issue.1-2, pp.539-553, 2001. ,
Rank and symbolic complexity, Ergodic Theory and Dynamical Systems, vol.16, issue.4, pp.663-682, 1996. ,
Special factors and the combinatorics of suffix and factor automata, Theoretical Computer Science, vol.412, issue.29, pp.3604-3615, 2011. ,
Directive words of episturmian words: equivalences and normalization, RAIRO - Theoretical Informatics and Applications, vol.43, issue.2, pp.299-319, 2008. ,
URL : https://hal.archives-ouvertes.fr/hal-00599746
The stable set of a self-map, Advances in Applied Mathematics, vol.45, issue.3, pp.438-448, 2010. ,
Episturmian words and episturmian morphisms, Theoretical Computer Science, vol.276, issue.1-2, pp.281-313, 2002. ,
Contributionà la résolution de la conjecture S-adique, 2012. ,
Some improvements of the S-adic conjecture, Advances in Applied Mathematics, vol.48, issue.1, pp.79-98, 2012. ,
An S-adic characterization of minimal subshifts with first difference of complexity p(n+1)?p(n) ? 2, Discrete Math. Theor. Comput. Sci, vol.16, issue.1, pp.233-286, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-01179422
A COMBINATORIAL PROOF OF S-ADICITY FOR SEQUENCES WITH LINEAR COMPLEXITY, Integers, vol.13 ,
URL : https://hal.archives-ouvertes.fr/lirmm-00797658
Quasiperiodic Sturmian words and morphisms, Theoretical Computer Science, vol.372, issue.1, pp.15-25, 2007. ,
, of Encyclopedia of Mathematics and its Applications, vol.17, 1983.
Algebraic Combinatorics on Words, of Encyclopedia of Mathematics and its Applications, vol.90, 2002. ,
URL : https://hal.archives-ouvertes.fr/hal-00620608
Symbolic Dynamics II. Sturmian Trajectories, American Journal of Mathematics, vol.62, issue.1/4, p.1, 1940. ,
Substitutions in Dynamics, Arithmetics and Combinatorics, Substitutions in Dynamics, Arithmetics and Combinatorics, vol.1794, 2002. ,
Lyndon morphisms, Bulletin of the Belgian Mathematical Society - Simon Stevin, vol.10, issue.5, pp.761-785, 2003. ,
URL : https://hal.archives-ouvertes.fr/hal-00598219
Characterization of Infinite LSP Words and Endomorphisms Preserving the LSP Property, International Journal of Foundations of Computer Science, vol.30, issue.01, pp.171-196, 2019. ,
URL : https://hal.archives-ouvertes.fr/lirmm-01855460
Uber die gegenseitige Lage gleigher Teile gewisser Zeichenreihen, Kristiania Videnskapsselskapets Skrifter Klasse I. Mat.-naturv, vol.1, pp.1-67, 1912. ,