A319633 Number of antichain covers of n vertices by distinct sets whose dual is also an antichain of (not necessarily distinct) sets.

1, 1, 2, 6, 40, 2309

Offset

0,3

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

The a(3) = 6 antichain covers:
   {{1,2,3}}
   {{3},{1,2}}
   {{2},{1,3}}
   {{1},{2,3}}
   {{1},{2},{3}}
   {{1,2},{1,3},{2,3}}

Crossrefs

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

Sequence in context: A051185 A118623 A000612 * A367365 A367603 A336281

Adjacent sequences: A319630 A319631 A319632 * A319634 A319635 A319636

Keyword

nonn,more

Author

Gus Wiseman, Sep 25 2018

Status

approved