A319769 Number of non-isomorphic intersecting set multipartitions (multisets of sets) of weight n whose dual is also an intersecting set multipartition.

1, 1, 2, 3, 5, 7, 12, 16, 26, 38, 61

Offset: 0

Author

Gus Wiseman, Sep 27 2018

Keywords

• nonn
• more

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}}.

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

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.

Examples

			Non-isomorphic representatives of the a(1) = 1 through a(5) = 7 set multipartitions:
1: {{1}}
2: {{1,2}}
   {{1},{1}}
3: {{1,2,3}}
   {{2},{1,2}}
   {{1},{1},{1}}
4: {{1,2,3,4}}
   {{3},{1,2,3}}
   {{1,2},{1,2}}
   {{2},{2},{1,2}}
   {{1},{1},{1},{1}}
5: {{1,2,3,4,5}}
   {{4},{1,2,3,4}}
   {{2,3},{1,2,3}}
   {{2},{1,2},{1,2}}
   {{3},{3},{1,2,3}}
   {{2},{2},{2},{1,2}}
   {{1},{1},{1},{1},{1}}
		

Crossrefs

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

Cf. A319752, A319765, A319766, A319767, A319768, A319773, A319774.