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

Author

Bridget Tenner, Feb 11 2008

Keywords

• nonn

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

Examples

			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.
		

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.

Crossrefs

Cf. A137814.