Geodesic
Direct and elementary approach to enumerate topologies on a finite set
Journal of integer sequences, Tome 10 (2007) no. 3
Let $ \mathbb{E}$ be a set with $ n$ elements, and let $ \tau (n,k)$ be the set of all labelled topologies on $ \mathbb{E}$, having $ k$ open sets, and $ T(n,k)=\left\vert \tau (n,k)\right\vert $. In this paper, we use a direct approach to compute $ T(n,k)$ for all $ n\geq 4$ and $ k\geq 6\cdot 2^{n-4}$.
Classification : 05A15, 06A07, 06A99
Keywords: binary relation, enumeration, finite set, finite topology, partial order, posets 
@article{JIS_2007__10_3_a6,
     author = {Kolli,  Messaoud},
     title = {Direct and elementary approach to enumerate topologies on a finite set},
     journal = {Journal of integer sequences},
     year = {2007},
     volume = {10},
     number = {3},
     zbl = {1113.05007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2007__10_3_a6/}
}
TY  - JOUR
AU  - Kolli,  Messaoud
TI  - Direct and elementary approach to enumerate topologies on a finite set
JO  - Journal of integer sequences
PY  - 2007
VL  - 10
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/JIS_2007__10_3_a6/
LA  - en
ID  - JIS_2007__10_3_a6
ER  - 
%0 Journal Article
%A Kolli,  Messaoud
%T Direct and elementary approach to enumerate topologies on a finite set
%J Journal of integer sequences
%D 2007
%V 10
%N 3
%U http://geodesic.mathdoc.fr/item/JIS_2007__10_3_a6/
%G en
%F JIS_2007__10_3_a6
Kolli,  Messaoud. Direct and elementary approach to enumerate topologies on a finite set. Journal of integer sequences, Tome 10 (2007) no. 3. http://geodesic.mathdoc.fr/item/JIS_2007__10_3_a6/