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A319622 Number of non-isomorphic connected weight-n antichains of distinct sets whose dual is also an antichain of (not necessarily distinct) sets. 0
1, 1, 1, 1, 1, 1, 2, 1, 3, 2, 7 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

COMMENTS

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.

LINKS

Table of n, a(n) for n=0..10.

EXAMPLE

Non-isomorphic representatives of the a(1) = 1 through a(10) = 7 antichains:

1:  {{1}}

2:  {{1,2}}

3:  {{1,2,3}}

4:  {{1,2,3,4}}

5:  {{1,2,3,4,5}}

6:  {{1,2,3,4,5,6}}

    {{1,2},{1,3},{2,3}}

7:  {{1,2,3,4,5,6,7}}

8:  {{1,2,3,4,5,6,7,8}}

    {{1,2},{1,3,4},{2,3,4}}

    {{1,2},{1,3},{2,4},{3,4}}

9:  {{1,2,3,4,5,6,7,8,9}}

    {{1,2},{1,3},{1,4},{2,3,4}}

10: {{1,2,3,4,5,6,7,8,9,10}}

    {{1,2},{1,3,4,5},{2,3,4,5}}

    {{1,2,3},{1,4,5},{2,3,4,5}}

    {{1,2},{1,3},{2,4,5},{3,4,5}}

    {{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}}

CROSSREFS

Cf. A006126, A007716, A007718, A056156, A059201, A283877, A316980, A316983, A318099, A319557, A319565, A319616-A319646, A300913.

Sequence in context: A022477 A238944 A144238 * A082833 A101709 A005247

Adjacent sequences:  A319619 A319620 A319621 * A319623 A319624 A319625

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Sep 25 2018

STATUS

approved

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Last modified May 12 07:28 EDT 2021. Contains 343821 sequences. (Running on oeis4.)