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R´ef´erences

[1] F. Brenti, A class of q-symmetric functions arising from plethysm, J. Combin. Theory Ser. A 91 (2000), 137–170.

[2] C. Brouder, A. Frabetti, C. Krattenthaler, Non-commutative Hopf algebra of formal diffeomor- phisms, Adv. Math. 200 (2006), 479–524.

[3] S. Chaiken and D. J. Kleitman, Matrix tree theorems, J. Comb. Theory A 24 (1978), 377–381.

[4] W. Chu, A new combinatorial interpretation of the generalized Catalan number, Discrete Ma- thematics 65 (1987), 91–94.

[5] R.M. Corless, G.H. Gonnet, D.E.G. Hare, D.J. Jeffrey, D.E. Knuth,On the Lambert W func- tion, Adv. Comput. Math. 5 (1996), no. 4, 329–359.

[6] G. Duchamp, F. Hivert, and J.-Y. Thibon, Noncommutative symmetric functions VI : free quasi-symmetric functions and related algebras, Internat. J. Alg. Comput. 12 (2002), 671–717.

[7] L. Euler, De serie Lambertine plurimisque eius insignibus proprietatibus, Acta Academiae Scientiarum Imperialis Petropolitanae, Volume 1779 : II, pp. 29-51. Opera Omnia Series 1, Volume 6, pp.350-369.

[8] L. Foissy, J.-C. Novelli and J.-Y. Thibon, Polynomial realizations of some combinatorial Hopf algebras, J. Noncommut. Geom. 8 (2014), 141–162.

[9] L. Foissy and J. Unterberger, Ordered forests, permutations and iterated integrals, Internat.

Math. Res. Notices 2013 (2013), 846–885. arXiv :1004.5208.

[10] I.M. Gelfand, D. Krob, A. Lascoux, B. Leclerc, V. S. Retakh, J.-Y. Thibon, Noncommutative symmetric functions, Adv. in Math. 112 (1995), 218–348.

[11] I. Gessel, Noncommutative generalization and q-analog of the Lagrange inversion formula, Trans. Amer. Math. Soc. 257 (1980), no. 2, 455–482.

[12] T. L. Graham, D. E. Knuth, O. Patashnik, Concrete Mathematics. Addison-Wesley, Reading, Mass., 1989 ; 2nd Ed. 1994.

[13] M. Haiman, Conjectures on the quotient ring by diagonal invariants, J. Algebraic Combin. 3 (1994), 17–36.

[14] F. Hirzebruch, Topological methods in algebraic geometry, Springer (1978).

[15] G. Kreweras and P. Moszkowski, Tree codes that preserve increases and degree sequences.

Discrete Math. 87 (1991), no. 3, 291–296.

[16] D. Krob, B. Leclerc, J.-Y. Thibon, Noncommutative symmetric functions II : Transformations of alphabets, Intern. J. Alg. Comput. 7 (1997), 181–264.

[17] D. Krob, J.-Y. Thibon, Noncommutative symmetric functions IV : Quantum linear groups and Hecke algebras atq= 0, J. Alg. Comb. 6 (1997), 339–376.

[18] A. G. Konheim, B. Weiss, An occupancy discipline and applications, SIAM J. Appl. Math. 14 (1966), 1266–1274.

[19] J. P. S. Kung, C. Yan, Gon˘carov polynomials and parking functions, J. Combin. Theory A 102 (2003), 16–37.

[20] A. Lascoux, Symmetric functions and combinatorial operators on polynomials, CBMS Regional Conference Series in Mathematics 99, American Math. Soc., Providence, RI, 2003 ; xii+268 pp.

[21] C. Lenart, Lagrange inversion and Schur functions, J. Algebraic Combin. 11 (2000), 1, 69–78.

[22] S.-S. Ma, Counting permutations by numbers of excedances, fixed poins and cycles, Bull. Aust.

Math. Soc. 85 (2012), 415–421

[23] I.G. Macdonald, Symmetric functions and Hall polynomials, 2nd ed., Oxford University Press, 1995.

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38

[24] F. Hivert, J.-C. Novelli, and J.-Y. Thibon, Commutative combinatorial Hopf algebras, J.

Algebraic Combin.28(2008), no. 1, 65–95.

[25] E. Jabotinsky,Representation of functions by matrices. Application to Faber polynomials, Proc.

Amer. Math. Soc.4 (1953), 546–553.

[26] D.E. Knuth, B. Pittel, A recurrence rela ted to trees, Proceedings of the American Mathematical Society 105 (1989),335–349.

[27] J.-L. Lagrange, Nouvelle m´ethode pour r´esoudre les ´equations litt´erales par le moyen des s´eries, Histoire de l’Acad´emie Royale des Sciences et Belles-Lettres de Berlin (1770) 251–326.

[28] F. Menous, J.-C. Novelli, J.-Y. Thibon Combinatorics of Poincar´e’s and Schroeder’s equation, in Resurgence, Physics and Numbers, (F. Fauvet, D. Manchon, S. Marmi and D. Sauzin Eds.), CRM Series 20, Edizioni della Normale, Pisa, 2017,

[29] J.-C. Novelli, J.-Y. Thibon, and N.M. Thi´ery, Alg`ebres de Hopf de graphes, C. R. Acad. Sci., Paris, S´er. A, 339, vol. 9, (2004), 607–610.

[30] J.-C. Novelli and J.-Y. Thibon, Noncommutative symmetric functions and Lagrange inversion, Adv. Appl. Math. 40 (2008), 8–35.

[31] J.-C. Novelli and J.-Y. Thibon, On composition polynomials, J. Combinatorial Theory A 152 (2017), 1–9.

[32] J.-C. Novelli and J.-Y. Thibon, Duplicial algebras and Lagrange inversion (with J.-C. No- velli), in Algebraic Combinatorics, Resurgence, Moulds and Applications (CARMA), vol.1, (F.

Chapoton, F. Fauvet, C. Malvenuto, J.-Y. Thibon eds.) IRMA Lectures in Mathematics and Theoretical Physics 31, European Mathematica Society, 2020.

[33] I. Pak, A. Postnikov, V. S. Retakh, Noncommutative Lagrange Theorem and Inversion Poly- nomials, preprint, 1995, available at http ://www-math.mit.edu/pak/research.html.

[34] G. N. Raney, Functional composition patterns and power series reversion, Trans. Amer. Math.

Soc. 94 (1960), 441–451.

[35] L. Schl¨afli, Bemerkungen ¨uber die Lambertische Reihe. Archiv der Mathematik und Physik 10, 332-340 (1847). Verzeichnis Graf, Nr. 16.

[36] R.P. Stanley,Catalan Numbers, Cambridge University Press, 2015.

[37] R. P. Stanley, J. Pitman, A Polytope Related to Empirical Distributions, Plane Trees, Parking Functions, and the Associahedron, Discrete Comput. Geom. 27 (2002), 603–634.

[38] R. P. Stanley, Enumerative combinatorics, vol. 2, Cambridge University Press, 1999.

[39] V. Strehl, Identities of Rothe-Abel-Schl¨afli-Hurwitz-type. Discrete Math. 99 (1992), no. 1-3, 321–340.

[40] The On-Line Encyclopedia of Integer Sequences, published electronically at http ://oeis.org, 2010.

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