A321402 -id:A321402 - cp's OEIS frontend

A321401 Number of non-isomorphic strict self-dual multiset partitions of weight n.

1, 1, 2, 4, 7, 14, 29, 57, 117, 240, 498

Offset: 0

Gus Wiseman, Nov 09 2018

Also the number of nonnegative integer 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 (or columns) are all different.

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}}.

			Non-isomorphic representatives of the a(1) = 1 through a(5) = 14 multiset partitions:
  {{1}}  {{1,1}}    {{1,1,1}}      {{1,1,1,1}}        {{1,1,1,1,1}}
         {{1},{2}}  {{1},{2,2}}    {{1,1},{2,2}}      {{1,1},{1,2,2}}
                    {{2},{1,2}}    {{1},{2,2,2}}      {{1,1},{2,2,2}}
                    {{1},{2},{3}}  {{2},{1,2,2}}      {{1,2},{1,2,2}}
                                   {{1},{2},{3,3}}    {{1},{2,2,2,2}}
                                   {{1},{3},{2,3}}    {{2},{1,2,2,2}}
                                   {{1},{2},{3},{4}}  {{1},{2,2},{3,3}}
                                                      {{1},{2},{3,3,3}}
                                                      {{1},{3},{2,3,3}}
                                                      {{2},{1,2},{3,3}}
                                                      {{2},{1,3},{2,3}}
                                                      {{1},{2},{3},{4,4}}
                                                      {{1},{2},{4},{3,4}}
                                                      {{1},{2},{3},{4},{5}}

Cf. A000219, A007716, A045778, A059201, A316980, A316983, A319560, A319616.

Cf. A320796, A320797, A321402, A321405, A321406, A321407.

A321406 Number of non-isomorphic self-dual set systems of weight n with no singletons.

Original entry on oeis.org

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

Offset: 0

Gus Wiseman, Nov 15 2018

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.

			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}}

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

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

cp's OEIS Frontend

A321401 Number of non-isomorphic strict self-dual multiset partitions of weight n.

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