A319640 - OEIS

A319640

Number of non-isomorphic antichain covers of n vertices by distinct sets whose dual is also an antichain of distinct sets.

1, 1, 1, 2, 7, 70

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OFFSET

0,4

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}}.

LINKS

Table of n, a(n) for n=0..5.

EXAMPLE

Non-isomorphic representatives of the a(1) = 1 through a(4) = 7 antichains:

1: {{1}}

2: {{1},{2}}

3: {{1},{2},{3}}

{{1,2},{1,3},{2,3}}

4: {{1},{2},{3},{4}}

{{1},{2,3},{2,4},{3,4}}

{{1,2},{1,3},{1,4},{2,3,4}}

{{1,2},{1,3},{2,4},{3,4}}

{{1,2,3},{1,2,4},{1,3,4},{2,3,4}}

{{1,3},{1,4},{2,3},{2,4},{3,4}}

{{1,2},{1,3},{1,4},{2,3},{2,4},{3,4}}

CROSSREFS

Cf. A006126, A007716, A049311, A059201, A283877, A293606, A316980, A316983, A318099, A319558, A319616-A319646, A300913.

Sequence in context: A217069 A323673 A366359 * A260566 A113866 A165978

Adjacent sequences: A319637 A319638 A319639 * A319641 A319642 A319643

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Sep 25 2018

STATUS

approved