OFFSET
0,3
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}}.
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.
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(1) = 1 through a(4) = 15 multiset partitions:
1: {{1}}
2: {{1,1}}
{{1,2}}
{{1},{1}}
3: {{1,1,1}}
{{1,2,2}}
{{1,2,3}}
{{1},{1,1}}
{{2},{1,2}}
{{1},{1},{1}}
4: {{1,1,1,1}}
{{1,1,2,2}}
{{1,2,2,2}}
{{1,2,3,3}}
{{1,2,3,4}}
{{1},{1,1,1}}
{{1},{1,2,2}}
{{2},{1,2,2}}
{{3},{1,2,3}}
{{1,1},{1,1}}
{{1,2},{1,2}}
{{1,2},{2,2}}
{{1},{1},{1,1}}
{{2},{2},{1,2}}
{{1},{1},{1},{1}}
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Sep 27 2018
STATUS
approved