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
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Aug 11 2019
STATUS
approved