A137814 - OEIS

%I #19 Aug 23 2023 10:59:36

%S 1,2,3,5,7,11,19,29,47,79,127,191,379

%N Smallest size of a topology that needs at least n points.

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

%H Swee Hong Chan and Igor Pak, <a href="https://arxiv.org/abs/2308.10214">Computational complexity of counting coincidences</a>, arXiv:2308.10214 [math.CO], 2023. See p. 10.

%H 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 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 There is no topology with less than 4 points having 7 open sets. However, there do exist topologies on 3 points that have 2, 3, 4, 5, 6 and 8 open sets.

%Y Cf. A137813 and A003064 (smallest number which needs an addition chain of at-least-length n).

%K nonn

%O 0,2

%A _Bridget Tenner_, Feb 11 2008

%E Name improved and a(0), a(1), a(12) added by _Achim Flammenkamp_, Oct 23 2016