Geodesic
The number of antichains in multilayered ranked sets
Diskretnaya Matematika, Tome 1 (1989) no. 2, pp. 149-169

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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 $\langle A^{(2)}\rangle$. 
@article{DM_1989_1_2_a10,
     author = {A. A. Sapozhenko},
     title = {The number of antichains in multilayered ranked sets},
     journal = {Diskretnaya Matematika},
     pages = {149--169},
     publisher = {mathdoc},
     volume = {1},
     number = {2},
     year = {1989},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_1989_1_2_a10/}
}
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A. A. Sapozhenko. The number of antichains in multilayered ranked sets. Diskretnaya Matematika, Tome 1 (1989) no. 2, pp. 149-169. http://geodesic.mathdoc.fr/item/DM_1989_1_2_a10/