]. D. Arm and . Armstrong, Generalized noncrossing partitions and combinatorics of Coxeter groups, 2009.

. D. Ast, C. Armstrong, H. Stump, and . Thomas, A uniform bijection between nonnesting and noncrossing partitions, Tran. Amer. Math. Soc, vol.365, issue.8, pp.4121-4151, 2013.

D. Bessis and V. Reiner, Cyclic Sieving of Noncrossing Partitions for Complex Reflection Groups, Annals of Combinatorics, vol.25, issue.3, pp.1-26, 2009.
DOI : 10.1007/s00026-011-0090-9

D. [. Cameron and . Fon-der-flaass, Orbits of antichains revisited, European Journal of Combinatorics, vol.16, issue.6, pp.545-554, 1995.
DOI : 10.1016/0195-6698(95)90036-5

J. [. Ceballos, C. Labbé, and . Stump, Subword complexes, cluster complexes, and generalized multiassociahedra, J. Algebraic Combin, pp.1-35, 2011.
DOI : 10.1007/s10801-013-0437-x
URL : http://arxiv.org/abs/1108.1776

P. [. Cellini and . Papi, Ad-nilpotent ideals of a Borel subalgebra II, Journal of Algebra, vol.258, issue.1, pp.112-12142, 1987.
DOI : 10.1016/S0021-8693(02)00532-X

M. Haiman, Dual equivalence with applications, including a conjecture of Proctor, Discrete Mathematics, vol.99, issue.1-3, pp.79-113, 1992.
DOI : 10.1016/0012-365X(92)90368-P

]. A. Mil and . Miller, Foulkes characters for complex reflection groups, 2013.

]. D. Pan and . Panyushev, On orbits of antichains of positive roots, Europ. J. Combin, vol.30, issue.2, pp.586-594, 2009.

]. R. Pro83 and . Proctor, Shifted plane partitions of trapezoidal shape, Proc. Amer, pp.553-559, 1983.

]. R. Pro84 and . Proctor, Bruhat lattices, plane partition generating functions, and minuscule representations, European Journal of Combinatorics, vol.5, issue.4, pp.331-350, 1984.

]. V. Rein and . Reiner, Non-crossing partitions for classical reflection groups, Discrete Mathematics, vol.177, issue.1, pp.195-222, 1997.

X. [. Rush and . Shi, On orbits of order ideals of minuscule posets, Journal of Algebraic Combinatorics, vol.24, issue.3, pp.1-25, 2011.
DOI : 10.1007/s10801-012-0380-2
URL : https://hal.archives-ouvertes.fr/hal-01229704

]. Shi and . Shi, Sign Types Corresponding to an Affine Weyl Group, Journal of the London Mathematical Society, vol.2, issue.1, pp.56-74, 1987.
DOI : 10.1112/jlms/s2-35.1.56

]. R. Stan84 and . Stanley, On the number of reduced decompositions of elements of Coxeter groups, Europ. J. Combin, vol.5, issue.4, pp.359-372, 1984.

]. R. Stan09 and . Stanley, Promotion and evacuation, Electron. J. Combin, vol.16, issue.2, p.9, 2009.

]. J. Stem and . Stembridge, On the fully commutative elements of Coxeter groups, J. Algebraic Combin, vol.5, issue.4, pp.353-385, 1996.

J. Striker and N. Williams, Promotion and rowmotion, European Journal of Combinatorics, vol.33, issue.8, pp.1919-1942, 2012.
DOI : 10.1016/j.ejc.2012.05.003
URL : https://hal.archives-ouvertes.fr/hal-01283167