A326902 Number of set-systems (without {}) covering n vertices that are closed under intersection.

1, 1, 3, 19, 319, 21881, 16417973, 1063459099837, 225402359008808647339

Offset

0,3

Comments

A set-system is a finite set of finite nonempty sets, so no two edges of a set-system that is closed under intersection can be disjoint.

Links

Table of n, a(n) for n=0..8.

Formula

Inverse binomial transform of A326901. - Andrew Howroyd, Aug 10 2019

Example

The a(0) = 1 through a(3) = 19 set-systems:
  {}  {{1}}  {{1,2}}      {{1,2,3}}
             {{1},{1,2}}  {{1},{1,2,3}}
             {{2},{1,2}}  {{2},{1,2,3}}
                          {{3},{1,2,3}}
                          {{1,2},{1,2,3}}
                          {{1,3},{1,2,3}}
                          {{2,3},{1,2,3}}
                          {{1},{1,2},{1,3}}
                          {{2},{1,2},{2,3}}
                          {{3},{1,3},{2,3}}
                          {{1},{1,2},{1,2,3}}
                          {{1},{1,3},{1,2,3}}
                          {{2},{1,2},{1,2,3}}
                          {{2},{2,3},{1,2,3}}
                          {{3},{1,3},{1,2,3}}
                          {{3},{2,3},{1,2,3}}
                          {{1},{1,2},{1,3},{1,2,3}}
                          {{2},{1,2},{2,3},{1,2,3}}
                          {{3},{1,3},{2,3},{1,2,3}}

Mathematica

Table[Length[Select[Subsets[Subsets[Range[n], {1, n}]], Union@@#==Range[n]&&SubsetQ[#, Intersection@@@Tuples[#, 2]]&]], {n, 0, 3}]

Crossrefs

The case closed under union and intersection is A006058.

The case with union instead of intersection is A102894.

The unlabeled version is A108800(n - 1).

The non-covering case is A326901.

The connected case is A326903.

Cf. A000798, A001930, A102895, A102898, A182507, A326866, A326876, A326878, A326882, A326900, A326901, A326904.

Sequence in context: A115705 A136171 A102586 * A346840 A132876 A357956

Adjacent sequences: A326899 A326900 A326901 * A326903 A326904 A326905

Keyword

nonn,more

Author

Gus Wiseman, Aug 04 2019

Extensions

a(5)-a(8) from Andrew Howroyd, Aug 10 2019

Status

approved