A321404 Number of non-isomorphic self-dual set multipartitions (multisets of sets) of weight n with no singletons.

1, 0, 0, 0, 1, 0, 1, 1, 3, 4, 6

Offset: 0

Author

Gus Wiseman, Nov 15 2018

Keywords

• nonn
• more

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 no row 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.

Examples

			Non-isomorphic representatives of the a(4) = 1 through a(10) = 6 set multipartitions:
   4: {{1,2},{1,2}}
   6: {{1,2},{1,3},{2,3}}
   7: {{1,3},{2,3},{1,2,3}}
   8: {{2,3},{1,2,3},{1,2,3}}
   8: {{1,2},{1,2},{3,4},{3,4}}
   8: {{1,2},{1,3},{2,4},{3,4}}
   9: {{1,2,3},{1,2,3},{1,2,3}}
   9: {{1,2},{1,2},{3,4},{2,3,4}}
   9: {{1,2},{1,3},{1,4},{2,3,4}}
   9: {{1,2},{1,4},{3,4},{2,3,4}}
  10: {{1,2},{1,2},{1,3,4},{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}}
  10: {{1,4},{2,4},{3,4},{1,2,3,4}}
  10: {{1,2},{1,2},{3,4},{3,5},{4,5}}
  10: {{1,2},{1,3},{2,4},{3,5},{4,5}}
		

Crossrefs

Cf. A007716, A049311, A135588, A138178, A283877, A302545, A316983.

Cf. A320797, A320798, A320811, A320812, A321403, A321404, A321405, A321406.