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

0,3

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.

Links

Table of n, a(n) for n=0..10.

Example

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.

Sequence in context: A275592 A319635 A179822 * A326083 A027959 A060730

Adjacent sequences: A319766 A319767 A319768 * A319770 A319771 A319772

Keyword

nonn,more

Author

Gus Wiseman, Sep 27 2018

Status

approved