A319773 - OEIS

A319773

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

1, 1, 0, 1, 0, 0, 2, 1, 2, 4, 5

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OFFSET

0,7

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(10) = 5 set systems:

1: {{1}}

3: {{2},{1,2}}

6: {{3},{2,3},{1,2,3}}

{{1,2},{1,3},{2,3}}

7: {{1,3},{2,3},{1,2,3}}

8: {{2,4},{3,4},{1,2,3,4}}

{{3},{1,3},{2,3},{1,2,3}}

9: {{1,2,4},{1,3,4},{2,3,4}}