cp's OEIS Frontend

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

%I A137813 #32 Apr 20 2022 21:23:17
%S A137813 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 A137813 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 A137813 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 A137813 Minimal number of points needed to make a topology having n open sets.
%C A137813 Differs from A003313 first at a(71) = 8, where A003313(71) = 9, and then at indices n = 139, 141, 142, .... - _M. F. Hasler_, Apr 20 2022
%D A137813 M. Erné and K. Stege, Counting finite posets and topologies, Tech. Report 236, University of Hannover, 1990.
%H A137813 Achim Flammenkamp, <a href="/A137813/b137813.txt">Table of n, a(n) for n = 1..2790</a>
%H A137813 M. Erné 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 A137813 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 A137813 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 A137813 Cf. A137814.
%K A137813 nonn
%O A137813 1,3
%A A137813 _Bridget Tenner_, Feb 11 2008