A. Björner and M. L. Wachs, Permutation statistics and linear extensions of posets, Journal of Combinatorial Theory, Series A, vol.58, issue.1, pp.85-114, 1991.
DOI : 10.1016/0097-3165(91)90075-R

F. Chapoton, Alg??bres de Hopf des permutah??dres, associah??dres et hypercubes, Advances in Mathematics, vol.150, issue.2, pp.264-275, 2000.
DOI : 10.1006/aima.1999.1868

G. Châtel and V. Pilaud, Cambrian Hopf algebras, Advances in Mathematics, vol.311, pp.598-633, 2017.
DOI : 10.1016/j.aim.2017.02.027

G. Châtel, V. Pilaud, and V. Pons, The weak order on integer posets, 2017.

A. Dermenjian, C. Hohlweg, and V. Pilaud, The facial weak order and its lattice quotients, Transactions of the American Mathematical Society, vol.370, issue.2, pp.1469-1507, 2018.
DOI : 10.1090/tran/7307

I. M. Gelfand, D. Krob, A. Lascoux, B. Leclerc, V. S. Retakh et al., Noncommutative Symmetrical Functions, Advances in Mathematics, vol.112, issue.2, pp.218-348, 1995.
DOI : 10.1006/aima.1995.1032

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

J. Loday, Realization of the Stasheff polytope, Archiv der Mathematik, vol.83, issue.3, pp.267-278, 2004.
DOI : 10.1007/s00013-004-1026-y
URL : https://hal.archives-ouvertes.fr/hal-00139415

D. Krob, M. Latapy, J. Novelli, H. Phan, and S. Schwer, Pseudo-Permutations I: First Combinatorial and Lattice Properties, 13th International Conference on Formal Power Series and Algebraic Combinatorics, 2001.

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-symmetric functions and the Solomon descent algebra, J. Algebra, vol.1773, pp.967-982, 1995.

P. Palacios and M. O. Ronco, Weak Bruhat order on the set of faces of the permutohedron and the associahedron, Journal of Algebra, vol.299, issue.2, pp.648-678, 2006.
DOI : 10.1016/j.jalgebra.2005.09.042

V. Pilaud and V. Pons, Permutrees, Algebraic Combinatorics, vol.1, issue.2, pp.173-224, 2018.
DOI : 10.4153/CJM-1961-015-3
URL : https://hal.archives-ouvertes.fr/hal-01575092

V. Pilaud and V. Pons, The Hopf algebra of integer binary relations, 2018.

N. Reading, Cambrian lattices, Advances in Mathematics, vol.205, issue.2, pp.313-353, 2006.
DOI : 10.1016/j.aim.2005.07.010

N. Reading, Lattice Congruences of the Weak Order, Order, vol.110, issue.2, pp.315-344, 2004.
DOI : 10.1007/978-3-662-02772-1