OFFSET
0,5
COMMENTS
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 dual of a multiset partition has empty intersection iff no part contains all the vertices.
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(2) = 1 through a(6) = 13 multiset partitions:
2: {{1},{2}}
3: {{1},{2},{3}}
4: {{1},{3},{2,3}}
{{1},{2},{3},{4}}
5: {{1},{2,4},{3,4}}
{{2},{1,3},{2,3}}
{{1},{2},{3},{2,3}}
{{1},{2},{4},{3,4}}
{{1},{2},{3},{4},{5}}
6: {{3},{1,4},{2,3,4}}
{{1,2},{1,3},{2,3}}
{{1,3},{2,4},{3,4}}
{{1},{2},{1,3},{2,3}}
{{1},{2},{3,5},{4,5}}
{{1},{3},{4},{2,3,4}}
{{1},{3},{2,4},{3,4}}
{{1},{4},{2,4},{3,4}}
{{2},{3},{1,3},{2,3}}
{{2},{4},{1,2},{3,4}}
{{1},{2},{3},{4},{3,4}}
{{1},{2},{3},{5},{4,5}}
{{1},{2},{3},{4},{5},{6}}
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Sep 27 2018
STATUS
approved