A326971 - OEIS

A326971

Number of unlabeled set-systems on n vertices whose dual is a weak antichain.

1, 2, 5, 24, 1267

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

COMMENTS

A set-system is a finite set of finite nonempty sets. The dual of a set-system 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}}. A weak antichain is a multiset of sets, none of which is a proper subset of any other.

LINKS

Table of n, a(n) for n=0..4.

EXAMPLE

Non-isomorphic representatives of the a(0) = 1 through a(3) = 24 set-systems:

{} {} {} {}

{{1},{2}} {{1},{2}}

{{1},{2},{1,2}} {{1,2,3}}

{{1},{2,3}}

{{1},{2},{3}}

{{1},{2},{1,2}}

{{1,2},{1,3},{2,3}}

{{1},{2,3},{1,2,3}}

{{1},{2},{3},{2,3}}

{{1},{2},{1,3},{2,3}}

{{1},{2},{3},{1,2,3}}

{{3},{1,2},{1,3},{2,3}}

{{1},{2},{3},{1,3},{2,3}}

{{1,2},{1,3},{2,3},{1,2,3}}

{{1},{2},{3},{2,3},{1,2,3}}

{{2},{3},{1,2},{1,3},{2,3}}

{{1},{2},{1,3},{2,3},{1,2,3}}

{{1},{2},{3},{1,2},{1,3},{2,3}}

{{3},{1,2},{1,3},{2,3},{1,2,3}}

{{1},{2},{3},{1,3},{2,3},{1,2,3}}

{{2},{3},{1,2},{1,3},{2,3},{1,2,3}}

{{1},{2},{3},{1,2},{1,3},{2,3},{1,2,3}}

CROSSREFS

Unlabeled set-systems are A000612.

Unlabeled set-systems whose dual is strict are A326946.

The labeled version is A326968.

The version with empty edges allowed is A326969.

The T_0 case (with strict dual) is A326972.

The covering case is A326973 (first differences).

Cf. A319559, A326951, A326965, A326966, A326970, A326974, A326975, A326978.

Sequence in context: A076534 A095708 A120759 * A000895 A351895 A109306

Adjacent sequences: A326968 A326969 A326970 * A326972 A326973 A326974

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Aug 10 2019

STATUS

approved