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}}

CROSSREFS

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Nov 15 2018

STATUS

approved