A327011 Number of unlabeled sets of subsets covering n vertices where every vertex is the unique common element of some subset of the edges, also called unlabeled covering T_1 sets of subsets.

2, 2, 4, 32, 2424

Offset: 0

Author

Gus Wiseman, Aug 13 2019

Keywords

• nonn
• more

Comments

Alternatively, these are unlabeled sets of subsets covering n vertices whose dual is a (strict) antichain. The dual of a set of subsets has, for each vertex, one edge consisting of the indices (or positions) of the edges containing that vertex. For example, the dual of {{1,2},{2,3}} is {{1},{1,2},{2}}. An antichain is a set of subsets where no edge is a subset of any other.

Examples

			Non-isomorphic representatives of the a(0) = 1 through a(2) = 4 sets of subsets:
  {}    {{1}}     {{1},{2}}
  {{}}  {{},{1}}  {{},{1},{2}}
                  {{1},{2},{1,2}}
                  {{},{1},{2},{1,2}}
		

Crossrefs

Unlabeled covering sets of subsets are A003181.

The same with T_0 instead of T_1 is A326942.

The non-covering version is A326951 (partial sums).

The labeled version is A326960.

The case without empty edges is A326974.

Cf. A001146, A055621, A059523, A319637, A326961, A326972, A326973, A326976, A326977, A326979.

Formula

a(n) = A326974(n) / 2.

a(n > 0) = A326951(n) - A326951(n - 1).