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

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, 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, 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

Offset

1,3

Comments

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

References

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

Links

Achim Flammenkamp, Table of n, a(n) for n = 1..2790

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

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.

Crossrefs

Cf. A137814.

Sequence in context: A259103 A334200 A128998 * A003313 A353058 A277608

Adjacent sequences: A137810 A137811 A137812 * A137814 A137815 A137816

Keyword

nonn

Author

Bridget Tenner, Feb 11 2008

Status

approved