A. Cayley, On the Theory of the Analytical Forms called Trees, Phil. Mag, vol.13, pp.172-178, 1857.
DOI : 10.1017/CBO9780511703690.046

F. Chapoton, Alg??bres pr??-Lie et alg??bres de Hopf li??es ?? la renormalisation, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.332, issue.8, pp.681-684, 2001.
DOI : 10.1016/S0764-4442(01)01919-X

A. Connes and H. Moscovici, Hopf algebras, cyclic cohomology and the transverse index theory, Commun. Math. Phys, vol.198, pp.198-246, 1998.

H. Figueroa and J. , Combinatorial Hopf algebras in quantum field theory I Rev, Math. Phys, vol.17, p.881, 2005.

D. Foata and M. P. Schützenberger, Major Index and Inversion Number of Permutations, Mathematische Nachrichten, vol.20, issue.1, pp.143-159, 1970.
DOI : 10.1002/mana.19780830111

I. M. Gelfand, D. Krob, A. Lascoux, B. Leclerc, V. S. Retakh et al., Noncommutative Symmetrical Functions, Noncommutative symmetric functions, pp.218-348, 1995.
DOI : 10.1006/aima.1995.1032
URL : http://doi.org/10.1006/aima.1995.1032

F. Hivert and N. Thiéry, MuPAD-Combinat, an open-source package for research in algebraic combinatorics, Sém. Lothar. Combin, vol.51, p.70, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00622769

A. Lascoux, Symmetric functions and combinatorial operators on polynomials, CBMS Regional Conference Series in Mathematics, vol.99, issue.268, 2003.
DOI : 10.1090/cbms/099
URL : https://hal.archives-ouvertes.fr/hal-00622640

M. Lothaire, Algebraic combinatorics on words, 2002.
DOI : 10.1017/CBO9781107326019
URL : https://hal.archives-ouvertes.fr/hal-00620608

P. A. Macmahon, The indices of permutations and derivation therefore of functions of a single variable associated with the permutations of any assemblage of objects, Amer, J. Math, vol.35, pp.314-321, 1913.

D. P. Rawlings, Generalized Worpitzky Identities with Applications to Permutation Enumeration, European Journal of Combinatorics, vol.2, issue.1, pp.67-78, 1981.
DOI : 10.1016/S0195-6698(81)80023-6

M. Skandera, An Eulerian Partner for Inversions, Sém, Lothar. Combin, vol.46, 2001.

N. J. Sloane, The On-Line Encyclopedia of Integer Sequences
DOI : 10.1007/978-3-540-73086-6_12