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A326973
Number of unlabeled set-systems covering n vertices whose dual is a weak antichain.
13
1, 1, 3, 19, 1243
OFFSET
0,3
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) = 19 set-systems:
{} {{1}} {{1,2}} {{1,2,3}}
{{1},{2}} {{1},{2,3}}
{{1},{2},{1,2}} {{1},{2},{3}}
{{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 covering set-systems are A055621.
The labeled version is A326970.
The non-covering case is A326971 (partial sums).
The case that is also T_0 is the T_1 case A326974.
Sequence in context: A114301 A258669 A192340 * A248704 A098796 A365579
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Aug 11 2019
STATUS
approved