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 A137813 Minimal number of points needed to make a topology having k open sets. 2

%I

%S 0,1,2,2,3,3,4,3,4,4,5,4,5,5,5,4,5,5,6,5,6,6,6,5,6,6,6,6,7,6,7,5,6,6,

%T 7,6,7,7,7,6,7,7,7,7,7,7,8,6,7,7,7,7,8,7,8,7,8,8,8,7,8,8,8,6,7,7,8,7,

%U 8,8,8,7,8,8,8,8,8,8,9,7,8,8,8,8,8,8,9,8,9,8,9,8,9,9,9,7,8,8,8,8,9,8,9,8,9

%N Minimal number of points needed to make a topology having k open sets.

%D M. ErnĂ© and K. Stege, Counting finite posets and topologies, Tech. Report 236, University of Hannover, 1990.

%H Achim Flammenkamp, <a href="/A137813/b137813.txt">Table of n, a(n) for n = 1..2790</a>

%H M. ErnĂ© and K. Stege, <a href="http://dx.doi.org/10.1007/BF00383446">Counting finite posets and topologies</a>, Order, September 1991, Volume 8, Issue 3, pp 247-265.

%H K. Ragnarsson and B. E. Tenner, <a href="http://dx.doi.org/10.1016/j.jcta.2009.05.002">Obtainable sizes of topologies on finite sets</a>, J. Combin. Theory Ser. A 117 (2010) 138-151.

%e A topology having 7 open sets can be made on 4 points. The open sets are: {}, {1}, {2}, {1,2}, {1,3}, {1,2,3}, {1,2,3,4}. No topology having 7 open sets can be made with fewer points.

%Y Cf. A137814.

%K nonn

%O 1,3

%A _Bridget Tenner_, Feb 11 2008

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