A319638 -id:A319638 - cp's OEIS frontend

A319625 Number of non-isomorphic connected weight-n antichains of distinct sets whose dual is also an antichain of distinct sets.

1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 3

Offset: 0

Gus Wiseman, Sep 25 2018

The dual of a multiset partition has, for each vertex, one block consisting of the indices (or positions) of the blocks 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.

			Non-isomorphic representatives of the a(1) = 1 through a(10) = 3 antichains:
               {{1}}
        {{1,2},{1,3},{2,3}}
     {{1,2},{1,3},{2,4},{3,4}}
    {{1,2},{1,3},{1,4},{2,3,4}}
   {{1,3},{2,4},{1,2,5},{3,4,5}}
  {{1,2},{1,3},{2,4},{3,5},{4,5}}
  {{1,3},{1,4},{2,3},{2,4},{3,4}}

Cf. A006126, A007716, A007718, A056156, A059201, A283877, A316980, A316983, A318099, A319557, A319558, A319565, A319616-A319646.

Euler transform is A319638.

cp's OEIS Frontend

A319625 Number of non-isomorphic connected weight-n antichains of distinct sets whose dual is also an antichain of distinct sets.

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