A321406 - OEIS

A321406

Number of non-isomorphic self-dual set systems of weight n with no singletons.

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

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OFFSET

0,10

COMMENTS

Also the number of 0-1 symmetric matrices up to row and column permutations with sum of elements equal to n and no zero rows or columns, in which the rows are all different and none sums to 1.

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.

LINKS

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

EXAMPLE

Non-isomorphic representatives of the a(6) = 1 through a(10) = 4 set systems:

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

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

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

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

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

10: {{1,2},{2,4},{1,3,4},{2,3,4}}

10: {{1,3},{2,4},{1,3,4},{2,3,4}}