A381472 Number of unlabeled set systems on n vertices which are closed under union of disjoint sets.

1, 2, 5, 22, 345, 152589

Offset: 0

Author

Andrew Howroyd, Mar 02 2025

Keywords

• nonn
• hard
• more

Comments

A set system is a finite set of finite nonempty sets.

a(n) is also the number of non-isomorphic sets of subsets of an n-set which are closed under union of disjoint sets and which include the empty set.

Examples

			Non-isomorphic representatives of the a(2) = 5 set-systems:
  {}
  {{1}}
  {{1,2}}
  {{1},{1,2}}
  {{1},{2},{1,2}}
The a(3) = 22 non-isomorphic set-systems include A193674(3) = 19 set-systems that are closed under union and 3 additional set-systems which do not include {1,2,3}:
  {{1,2},{1,3}}
  {{1},{1,2},{1,3}}
  {{1,2},{1,3},{2,3}}
		

Crossrefs

Cf. A000612 (set-systems), A193674 (closed under union of sets), A381471, A381575 (labeled case).