Geodesic
The number of antichains in multilayered ranked sets
Diskretnaya Matematika, Tome 1 (1989) no. 2, pp. 110-128 
A. A. Sapozhenko. The number of antichains in multilayered ranked sets. Diskretnaya Matematika, Tome 1 (1989) no. 2, pp. 110-128. http://geodesic.mathdoc.fr/item/DM_1989_1_2_a10/
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     author = {A. A. Sapozhenko},
     title = {The number of antichains in multilayered ranked sets},
     journal = {Diskretnaya Matematika},
     pages = {110--128},
     year = {1989},
     volume = {1},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_1989_1_2_a10/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We find the asymptotic behavior of the number of antichains in some multilayered partially ordered sets with a rank function given on them. As a consequence we obtain the asymptotic behavior of the number of monotone Boolean functions, the number of self-dual monotone Boolean functions, the number of monotone fuzzy $(0,1)$-functions, and the number of monotone Boolean functions that possess the property $\langle A^{(2)}\rangle$.