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A326971
Number of unlabeled set-systems on n vertices whose dual is a weak antichain.
10
1, 2, 5, 24, 1267
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.
EXAMPLE
Non-isomorphic representatives of the a(0) = 1 through a(3) = 24 set-systems:
{} {} {} {}
{{1}} {{1}} {{1}}
{{1,2}} {{1,2}}
{{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).
Sequence in context: A076534 A095708 A120759 * A000895 A351895 A109306
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Aug 10 2019
STATUS
approved