OFFSET
0,6
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 weight of a multiset partition is the sum of sizes of its parts. Weight is generally not the same as number of vertices.
A multiset partition is intersecting iff no two parts are disjoint. The dual of a multiset partition is intersecting iff every pair of distinct vertices appear together in some part.
EXAMPLE
Non-isomorphic representatives of the a(4) = 1 through a(6) = 20 multiset partitions:
4: {{1,3},{2,3}}
5: {{1,2},{2,3,3}}
{{1,3},{2,3,3}}
{{1,4},{2,3,4}}
{{3},{1,3},{2,3}}
6: {{1,2},{2,3,3,3}}
{{1,3},{2,2,3,3}}
{{1,3},{2,3,3,3}}
{{1,3},{2,3,4,4}}
{{1,4},{2,3,4,4}}
{{1,5},{2,3,4,5}}
{{1,1,2},{2,3,3}}
{{1,2,2},{2,3,3}}
{{1,2,3},{3,4,4}}
{{1,2,4},{3,4,4}}
{{1,2,5},{3,4,5}}
{{1,3,3},{2,3,3}}
{{1,3,4},{2,3,4}}
{{2},{1,2},{2,3,3}}
{{3},{1,3},{2,3,3}}
{{4},{1,4},{2,3,4}}
{{1,3},{2,3},{2,3}}
{{1,3},{2,3},{3,3}}
{{1,4},{2,4},{3,4}}
{{3},{3},{1,3},{2,3}}
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Sep 27 2018
STATUS
approved