C. [. Armstrong, H. Stump, and . Thomas, A uniform bijection between nonnesting and noncrossing partitions, Transactions of the American Mathematical Society, vol.365, issue.8, pp.4121-4151, 2013.
DOI : 10.1090/S0002-9947-2013-05729-7

E. Andries, A. Brouwer, and . Schrijver, On the period of an operator, defined on antichains, Math. Centr. report, vol.24, 1974.

J. Peter, . Cameron, and G. Dmitry, Fon-der-Flaass, Orbits of Antichains Revisited, European Journal of Combinatorics, vol.16, issue.6, pp.545-554, 1995.

[. Einstein and J. Propp, Combinatorial, piecewise-linear, and birational homomesy for products of two chains, arXiv:1310.5294v1 (preliminary version), 2013.

G. Dmitry, Fon-der-Flaass, Orbits of Antichains in Ranked Posets, European Journal of Combinatorics, vol.14, issue.1, pp.17-22, 1993.

D. Grinberg and T. Roby, Iterative properties of birational rowmotion, preprint. Citations refer to version 2.0 (arXiv:1402.6178v2 (not yet online, see MIT link))

]. D. Pan08 and . Panyushev, On orbits of antichains of positive roots, Europ. J. Combin, vol.30, issue.2, pp.586-594, 2009.

J. Propp and T. Roby, Homomesy in products of two chains
URL : https://hal.archives-ouvertes.fr/hal-01229696

R. Stanley, Two Poset Polytopes, Discrete & Computational Geometry, pp.9-23, 1986.

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

A. Yu and . Volkov, On the Periodicity Conjecture for Y-systems, Commun. Math. Phys, vol.276, pp.509-517, 2007.