A319767 Number of non-isomorphic intersecting set systems spanning n vertices whose dual is also an intersecting set system.

1, 1, 1, 5, 73

Offset

0,4

Comments

The dual of a multiset partition has, for each vertex, one part consisting of the indices (or positions) of the parts containing that vertex, counted with multiplicity. For example, the dual of {{1,2},{2,2}} is {{1},{1,2,2}}.

A multiset partition is intersecting iff no two parts are disjoint. The dual of a multiset partition is intersecting iff every pair of distinct vertices appear together in some part.

The weight of a multiset partition is the sum of sizes of its parts. Weight is generally not the same as number of vertices.

Links

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

Example

Non-isomorphic representatives of the a(1) = 1 through a(3) = 5 multiset partitions:
1: {{1}}
2: {{2},{1,2}}
3: {{3},{2,3},{1,2,3}}
   {{1,2},{1,3},{2,3}}
   {{1,3},{2,3},{1,2,3}}
   {{3},{1,3},{2,3},{1,2,3}}
   {{1,2},{1,3},{2,3},{1,2,3}}

Crossrefs

Cf. A007716, A281116, A283877, A305854, A306006, A316980, A316983, A317757, A319616.

Cf. A319752, A319765, A319766, A319768, A319769, A319773, A319774.

Sequence in context: A362679 A307932 A136637 * A341670 A138623 A206280

Adjacent sequences: A319764 A319765 A319766 * A319768 A319769 A319770

Keyword

nonn,more

Author

Gus Wiseman, Sep 27 2018

Status

approved