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A321404
Number of non-isomorphic self-dual set multipartitions (multisets of sets) of weight n with no singletons.
4
1, 0, 0, 0, 1, 0, 1, 1, 3, 4, 6
OFFSET
0,9
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.
EXAMPLE
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}}
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Nov 15 2018
STATUS
approved