A326945 Number of T_0 sets of subsets of {1..n} that are closed under intersection.

2, 4, 12, 96, 4404, 2725942, 151906396568, 28175293281055562650

Offset

0,1

Comments

The dual of a multiset partition has, for each vertex, one block consisting of the indices (or positions) of the blocks containing that vertex. For example, the dual of {{1,2},{2,3}} is {{1},{1,2},{2}}. The T_0 condition means that the dual is strict (no repeated edges).

Links

Table of n, a(n) for n=0..7.

Formula

Binomial transform of A326943.

Example

The a(0) = 2 through a(2) = 12 sets of subsets:
  {}    {}        {}
  {{}}  {{}}      {{}}
        {{1}}     {{1}}
        {{},{1}}  {{2}}
                  {{},{1}}
                  {{},{2}}
                  {{1},{1,2}}
                  {{2},{1,2}}
                  {{},{1},{2}}
                  {{},{1},{1,2}}
                  {{},{2},{1,2}}
                  {{},{1},{2},{1,2}}

Mathematica

Table[Length[Select[Subsets[Subsets[Range[n]]], UnsameQ@@dual[#]&&SubsetQ[#, Intersection@@@Tuples[#, 2]]&]], {n, 0, 3}]

Crossrefs

The non-T_0 version is A102897.

The version not closed under intersection is A326941.

The covering case is A326943.

The case without empty edges is A326959.

Cf. A003180, A182507, A316978, A319564, A326906, A326939, A326940, A326944, A326947.

Sequence in context: A120618 A259048 A228809 * A309718 A230814 A325502

Adjacent sequences: A326942 A326943 A326944 * A326946 A326947 A326948

Keyword

nonn,more

Author

Gus Wiseman, Aug 08 2019

Extensions

a(5)-a(7) from Andrew Howroyd, Aug 14 2019

Status

approved