E. Ackerman, G. Barequet, and R. Y. Pinter, On the Number of Rectangular Partitions, Proc. 15th ACM-SIAM Symp. on Discrete Algorithms, 2004.

E. Babson and E. Steingrímsson, Generalized permutation patterns and a classification of the Mahonian statistic, Séminaire Lotharingien de Combinatoire, 2000.

G. Baxter, On fixed points of the composite of commuting functions, Proceedings of the, pp.851-855, 1964.
DOI : 10.1090/S0002-9939-1964-0184217-8

N. Bonichon, M. Bousquet-mélou, and . Fusy, Baxter permutations and plane bipolar orientations, Electronic Notes in Discrete Mathematics, vol.31, pp.69-74, 2008.
DOI : 10.1016/j.endm.2008.06.011

URL : https://hal.archives-ouvertes.fr/hal-00355755

I. Chajda and V. Snásel, Congruences in 0rdered Sets, Mathematica Bohemica, vol.123, pp.95-100, 1998.

G. Duchamp, F. Hivert, and J. Thibon, NONCOMMUTATIVE SYMMETRIC FUNCTIONS VI: FREE QUASI-SYMMETRIC FUNCTIONS AND RELATED ALGEBRAS, International Journal of Algebra and Computation, vol.12, issue.05, pp.671-717, 2002.
DOI : 10.1142/S0218196702001139

URL : https://hal.archives-ouvertes.fr/hal-00622613

]. L. Foissy, Bidendriform bialgebras, trees, and free quasi-symmetric functions. arXiv:math/0505207v1 [math, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00004902

I. M. Gelfand, D. Krob, A. Lascoux, B. Leclerc, V. S. Retakh et al., Noncommutative symmetric functions I. arXiv:hep-th/9407124v1, 1994.

F. Hivert, J. Novelli, and J. Thibon, Un analogue du mono????de plaxique pour les arbres binaires de recherche, Comptes Rendus Mathematique, vol.335, issue.7, pp.577-580, 2002.
DOI : 10.1016/S1631-073X(02)02537-2

F. Hivert, J. Novelli, and J. Thibon, The algebra of binary search trees, Theoretical Computer Science, vol.339, issue.1, pp.129-165, 2005.
DOI : 10.1016/j.tcs.2005.01.012

URL : https://hal.archives-ouvertes.fr/hal-00622706

F. Hivert and J. Nzeutchap, Dual graded graphs in combinatorial Hopf algebras, 2007.

D. Knuth, The Art of Computer Programming, Generating All Trees, History of Combinatorial Generation, vol.4, 2006.

A. Lascoux and M. Schützenberger, Le mono¨?demono¨?de plaxique. Noncommutative Structures in Algebra and Geometric Combinatorics, pp.129-156, 1981.

S. Law and N. Reading, The Hopf algebra of diagonal rectangulations, Journal of Combinatorial Theory, Series A, vol.119, issue.3, 2010.
DOI : 10.1016/j.jcta.2011.09.006

J. Loday, Dialgebras, Dialgebras. Lecture Notes in Math, vol.1763, pp.7-66, 2001.
DOI : 10.1007/3-540-45328-8_2

URL : https://hal.archives-ouvertes.fr/hal-00139440

J. Loday and M. O. Ronco, Hopf Algebra of the Planar Binary Trees, Advances in Mathematics, vol.139, issue.2, pp.293-309, 1998.
DOI : 10.1006/aima.1998.1759

C. Malvenuto and C. Reutenauer, Duality between Quasi-Symmetrical Functions and the Solomon Descent Algebra, Journal of Algebra, vol.177, issue.3, pp.967-982, 1995.
DOI : 10.1006/jabr.1995.1336

J. Novelli, On the hypoplactic monoid, Discrete Mathematics, vol.217, issue.1-3, pp.315-336, 1998.
DOI : 10.1016/S0012-365X(99)00270-8

URL : https://hal.archives-ouvertes.fr/hal-00622670

S. Poirier and C. Reutenauer, Algèbres de Hopf de tableaux, Ann. Sci. Math. Québec, vol.19, pp.79-90, 1995.

N. Reading, Lattice congruences, fans and Hopf algebras, Journal of Combinatorial Theory, Series A, vol.110, issue.2, pp.237-273, 2005.
DOI : 10.1016/j.jcta.2004.11.001

URL : http://doi.org/10.1016/j.jcta.2004.11.001

M. Rey, Algebraic constructions on set partitions. Formal Power Series and Algebraic Combinatorics, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00622741

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

W. A. Stein, The Sage Development Team, Sage Mathematics Software, 2010.

X. Viennot, Up-down sequences of permutations, paths and canopy of binary trees, p.52, 2004.