]. Allouche and A. Glen, Extremal properties of (epi)Sturmian sequences and distribution modulo $1$, L???Enseignement Math??matique, vol.56, issue.3, 2009.
DOI : 10.4171/LEM/56-3-5

J. Allouche and J. Shallit, The Ubiquitous Prouhet-Thue-Morse Sequence, Sequences and Their Applications Proc. SETA'98, 1999.
DOI : 10.1007/978-1-4471-0551-0_1

J. Allouche and J. Shallit, Automatic sequences, 2003.
DOI : 10.1017/cbo9780511546563

E. Altman, B. Gaujal, and A. Hordijk, Balanced sequences and optimal routing, Journal of the ACM, vol.47, issue.4, p.752775, 2000.
DOI : 10.1145/347476.347482

URL : https://hal.archives-ouvertes.fr/hal-00005853

P. Arnoux and G. Rauzy, Repr??sentation g??om??trique de suites de complexit?? $2n+1$, Bulletin de la Société mathématique de France, vol.119, issue.2, p.199215, 1991.
DOI : 10.24033/bsmf.2164

URL : http://www.numdam.org/article/BSMF_1991__119_2_199_0.pdf

S. V. Avgustinovich, A. E. Frid, T. Kamae, and P. V. Salimov, Innite permutations of lowest maximal pattern complexity, 2009.

J. Barát and P. P. Varjú, Partitioning the positive integers to seven beatty sequences, Indag. Math. (N.S.), vol.14, issue.2, p.149161, 2003.

J. Berstel, Recent results in sturmian words, Developments in Language Theory, 1995.
URL : https://hal.archives-ouvertes.fr/hal-00619875

J. Berstel and D. Perrin, The origins of combinatorics on words, European Journal of Combinatorics, vol.28, issue.3
DOI : 10.1016/j.ejc.2005.07.019

URL : https://hal.archives-ouvertes.fr/hal-00619483

J. Berstel and P. Séébold, A characterization of Sturmian morphisms, In Mathematical Foundations of Computer Science Lecture Notes in Computer Science, vol.711, p.281290, 1993.
DOI : 10.1007/3-540-57182-5_20

URL : https://hal.archives-ouvertes.fr/hal-00619894

S. Brlek, Enumeration of factors in the Thue-Morse word, Discrete Applied Mathematics, vol.24, issue.1-3, p.8396, 1989.
DOI : 10.1016/0166-218X(92)90274-E

J. Cassaigne, S. Ferenczi, and L. Q. Zamboni, Imbalances in Arnoux-Rauzy sequences, Annales de l???institut Fourier, vol.50, issue.4, p.12651276, 2000.
DOI : 10.5802/aif.1792

E. M. Coven and G. A. Hedlund, Sequences with minimal block growth, Mathematical Systems Theory, vol.62, issue.2, p.138153, 1973.
DOI : 10.1007/BF01762232

J. Currie and N. Rampersad, Recurrent words with constant Abelian complexity, Advances in Applied Mathematics, vol.47, issue.1, 2009.
DOI : 10.1016/j.aam.2010.05.001

URL : http://doi.org/10.1016/j.aam.2010.05.001

X. Droubay, J. Justin, and G. Pirillo, Episturmian words and some constructions of de Luca and Rauzy, Theoretical Computer Science, vol.255, issue.1-2, p.539553, 2001.
DOI : 10.1016/S0304-3975(99)00320-5

X. Droubay and G. Pirillo, Palindromes and Sturmian words, Theoretical Computer Science, vol.223, issue.1-2, p.7385, 1999.
DOI : 10.1016/S0304-3975(97)00188-6

URL : http://doi.org/10.1016/s0304-3975(97)00188-6

L. Euler, On the expansion of the power of any polynomial (1+x+x 2 +x 3 +x 4 +etc) n, 2005.

D. G. Fon-der-flaass and A. E. Frid, On periodicity and low complexity of innite permutations, European J. Combin, vol.28, issue.8, p.21062114, 2007.

A. Glen and J. Justin, Episturmian words: a survey. RAIRO -Theor, Inform. Appl, vol.43, p.402433, 2009.

A. Glen, J. Justin, S. Widmer, and L. Q. Zamboni, Palindromic richness, European Journal of Combinatorics, vol.30, issue.2, p.510531, 2009.
DOI : 10.1016/j.ejc.2008.04.006

URL : https://hal.archives-ouvertes.fr/hal-00865934

R. Graham, Covering the positive integers by disjoint sets of the form {[n?? + ??]: n = 1, 2,???}, Journal of Combinatorial Theory, Series A, vol.15, issue.3, p.354358, 1973.
DOI : 10.1016/0097-3165(73)90084-8

P. Hubert, Propriétés combinatoires des suites dénies par le billard dans les triangles pavants, Theoret. Comput. Sci, vol.164, issue.12, p.165183, 1996.

J. Justin and G. Pirillo, Episturmian words and episturmian morphisms, Theoretical Computer Science, vol.276, issue.1-2, p.281313, 2002.
DOI : 10.1016/S0304-3975(01)00207-9

T. Kamae and L. Q. Zamboni, Maximal pattern complexity for discrete systems, Ergodic Theory and Dynamical Systems, vol.22, issue.04, p.12011214, 2002.
DOI : 10.1017/S0143385702000585

T. Kamae and L. Q. Zamboni, Sequence entropy and the maximal pattern complexity of innite words. Ergodic Theory Dynam, Systems, vol.22, p.11911199, 2002.

M. Lothaire, Combinatorics on Words, of Encyclopedia of Mathematics and its Applications, 1983.
DOI : 10.1017/CBO9780511566097

URL : https://hal.archives-ouvertes.fr/hal-00620607

M. Lothaire, Algebraic Combinatorics on Words, volume 90 of Encyclopedia of Mathematics and its Applications, 2002.

M. Lothaire, Applied Combinatorics on Words, volume 105 of Encyclopedia of Mathematics and its Applications, 2005.

A. De-luca, Sturmian words: structure, combinatorics, and their arithmetics, Theoretical Computer Science, vol.183, issue.1, p.4582, 1997.
DOI : 10.1016/S0304-3975(96)00310-6

]. A. De-luca and S. Varricchio, Some combinatorial properties of the Thue???Morse sequence and a problem in semigroups, Theoretical Computer Science, vol.63, issue.3, p.333348, 1989.
DOI : 10.1016/0304-3975(89)90013-3

M. A. Makarov, On permutations generated by innite binary words, Sib. Èlektron. Mat. Izv, vol.3, issue.304311, 2006.

M. A. Makarov, On the permutations generated by Sturmian words, Siberian Mathematical Journal, vol.380, issue.3, p.674680, 2009.
DOI : 10.1007/s11202-009-0076-6

M. A. Makarov, On the innite permutation generated by the period doubling word

M. Morse, Recurrent geodesics on a surface of negative curvature, Transactions of the American Mathematical Society, vol.22, issue.1, p.84100, 1921.
DOI : 10.1090/S0002-9947-1921-1501161-8

M. Morse and G. A. Hedlund, Symbolic Dynamics, American Journal of Mathematics, vol.60, issue.4, p.815866, 1938.
DOI : 10.2307/2371264

M. Morse and G. A. Hedlund, Symbolic Dynamics II. Sturmian Trajectories, American Journal of Mathematics, vol.62, issue.1/4, p.142, 1940.
DOI : 10.2307/2371431

G. Paquin and L. Vuillon, A characterization of balanced episturmian sequences, Electron. J. Combin, vol.14, issue.1, p.33, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00387310

G. Richomme, K. Saari, and L. Q. Zamboni, Abelian complexity of minimal subshifts, Journal of the London Mathematical Society, vol.83, issue.1
DOI : 10.1112/jlms/jdq063

URL : https://hal.archives-ouvertes.fr/lirmm-00598086

G. Richomme, K. Saari, and L. Q. Zamboni, Balance and Abelian complexity of the Tribonacci word, Advances in Applied Mathematics, vol.45, issue.2, p.212231, 2010.
DOI : 10.1016/j.aam.2010.01.006

URL : https://hal.archives-ouvertes.fr/hal-00599750

C. F. Sainte-marie, Solution to question nr, 48. L'intermédiaire des Mathématiciens, p.107110, 1894.

A. Thue, Über unendliche Zeichenreihen. Norske vid, Selsk. Skr. Mat. Nat. Kl, vol.7, p.122, 1906.

A. Thue, Über die gegenseitige lage gleicher Teile gewisser Zeichenreihen. Norske vid, Selsk. Skr. Mat. Nat. Kl, vol.1, p.167, 1912.

R. Tijdeman, Exact covers of balanced sequences and Fraenkel's conjecture, Algebraic Number Theory and Diophantine Analysis, p.467483, 1998.
DOI : 10.1515/9783110801958.467

J. Tromp and J. Shallit, Subword complexity of a generalized Thue-Morse word, Information Processing Letters, vol.54, issue.6, p.313316, 1995.
DOI : 10.1016/0020-0190(95)00074-M

T. Van-aardenne-ehrenfest and N. G. De-bruijn, Circuits and Trees in Oriented Linear Graphs, Bull. Belg. Math. Soc. Simon Stevin, vol.28, p.203217, 1951.
DOI : 10.1007/978-0-8176-4842-8_12

L. Vuillon, Balanced words, Bull. Belg. Math. Soc. Simon Stevin, vol.10, issue.5, p.787805, 2003.

S. Widmer, Permutation complexity of the Thue???Morse word, Advances in Applied Mathematics, vol.47, issue.2
DOI : 10.1016/j.aam.2010.08.002