OFFSET
0,7
COMMENTS
A multiset partition is intersecting if no two parts are disjoint. The weight of a multiset partition is the sum of sizes of its parts. 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 T_0 condition means the dual is strict.
EXAMPLE
Non-isomorphic representatives of the a(1) = 1 through a(8) = 7 multiset partitions:
1: {{1}}
3: {{2},{1,2}}
4: {{1,3},{2,3}}
5: {{3},{1,3},{2,3}}
6: {{3},{2,3},{1,2,3}}
{{1,2},{1,3},{2,3}}
{{1,4},{2,4},{3,4}}
7: {{4},{1,3,4},{2,3,4}}
{{1,3},{1,4},{2,3,4}}
{{1,3},{2,3},{1,2,3}}
{{1,4},{3,4},{2,3,4}}
{{4},{1,4},{2,4},{3,4}}
8: {{1,5},{2,4,5},{3,4,5}}
{{2,4},{3,4},{1,2,3,4}}
{{2,4},{1,2,5},{3,4,5}}
{{2,4},{1,3,4},{2,3,4}}
{{3},{1,3},{2,3},{1,2,3}}
{{4},{1,4},{3,4},{2,3,4}}
{{1,5},{2,5},{3,5},{4,5}}
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Sep 27 2018
STATUS
approved