A137814 Smallest size of a topology that needs at least n points.

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

Offset

0,2

References

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

Links

Table of n, a(n) for n=0..12.

Swee Hong Chan and Igor Pak, Computational complexity of counting coincidences, arXiv:2308.10214 [math.CO], 2023. See p. 10.

M. Erné and K. Stege, Counting finite posets and topologies, Order, September 1991, Volume 8, Issue 3, pp 247-265.

K. Ragnarsson and B. E. Tenner, Obtainable sizes of topologies on finite sets, J. Combin. Theory Ser. A 117 (2010) 138-151.

Example

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.

Crossrefs

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

Sequence in context: A115617 A003064 A057429 * A065726 A215161 A227907

Adjacent sequences: A137811 A137812 A137813 * A137815 A137816 A137817

Keyword

nonn

Author

Bridget Tenner, Feb 11 2008

Extensions

Name improved and a(0), a(1), a(12) added by Achim Flammenkamp, Oct 23 2016

Status

approved