Geodesic
Finite topologies and partitions
Journal of integer sequences, Tome 13 (2010) no. 3.

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Summary: Let $E$ be a set with $n$ elements, and let $T(n,k)$ be the number of all labeled topologies having $k$ open sets that can be defined on $E$. In this paper, we compute these numbers for $k \le 17$, and arbitrary $n$, as well as $t_{N0}(n,k)$, the number of all unlabeled non-$T_{0}$ topologies on $E$ with $k$ open sets, for $3 \le k \le 8$.
Classification : 05A15, 06A07, 06A99
Keywords: binary relation, enumeration, finite set, finite topology, partial order, posets 
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     author = {Benoumhani, Moussa and Kolli, Messaoud},
     title = {Finite topologies and partitions},
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     url = {http://geodesic.mathdoc.fr/item/JIS_2010__13_3_a1/}
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Benoumhani, Moussa; Kolli, Messaoud. Finite topologies and partitions. Journal of integer sequences, Tome 13 (2010) no. 3. http://geodesic.mathdoc.fr/item/JIS_2010__13_3_a1/