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

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}}
  10: {{1,4},{2,4},{3,4},{1,2,3,4}}
  10: {{1,2},{1,3},{2,4},{3,5},{4,5}}

Crossrefs

Cf. A000219, A007716, A045778, A049311, A135588, A138178, A283877, A302545, A316980, A316983.

Cf. A320796, A320797, A321401, A321402, A321403, A321405.

Sequence in context: A216979 A334822 A082871 * A166926 A266296 A028573

Adjacent sequences: A321403 A321404 A321405 * A321407 A321408 A321409

Keyword

nonn,more

Author

Gus Wiseman, Nov 15 2018

Status

approved