Geodesic
Antichains of multisets
Journal of integer sequences, Tome 7 (2004) no. 1
The problem of enumeration of $m$-antichains of $k$-bounded multisets on an $n$-set is considered. A formula for calculating the cardinality of the corresponding family in terms of graph theory is obtained. A more general case of multi-antichains is also considered. As an illustration the corresponding explicit formulas are given for the case when $1\le m \le 4$, $k \ge1$ and $n \ge 0$.
Classification : 68R05, 68R10, 05A10, 05A15, 11B73, 11B83
Keywords: exact enumeration, antichain, multiset, digraph, bipartite graph, monotone coloring of a digraph, monotone Boolean function 
@article{JIS_2004__7_1_a5,
     author = {Kilibarda,  Goran and Jovovi\'c,  Vladeta},
     title = {Antichains of multisets},
     journal = {Journal of integer sequences},
     year = {2004},
     volume = {7},
     number = {1},
     zbl = {1071.06001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2004__7_1_a5/}
}
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%A Jovović,  Vladeta
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Kilibarda,  Goran; Jovović,  Vladeta. Antichains of multisets. Journal of integer sequences, Tome 7 (2004) no. 1. http://geodesic.mathdoc.fr/item/JIS_2004__7_1_a5/