A319634 Number of non-isomorphic antichain covers of n vertices by distinct sets whose dual is also an antichain of (not necessarily distinct) sets.

1, 1, 2, 4, 12, 87

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

Non-isomorphic representatives of the a(1) = 1 through a(4) = 12 antichain covers:
  {{1}}   {{1,2}}     {{1,2,3}}              {{1,2,3,4}}
         {{1},{2}}   {{1},{2,3}}            {{1},{2,3,4}}
                    {{1},{2},{3}}           {{1,2},{3,4}}
                 {{1,2},{1,3},{2,3}}       {{1},{2},{3,4}}
                                          {{1},{2},{3},{4}}
                                       {{1,2},{1,3,4},{2,3,4}}
                                       {{1},{2,3},{2,4},{3,4}}
                                      {{1,2},{1,3},{2,4},{3,4}}
                                     {{1,2},{1,3},{1,4},{2,3,4}}
                                   {{1,3},{1,4},{2,3},{2,4},{3,4}}
                                  {{1,2,3},{1,2,4},{1,3,4},{2,3,4}}
                                {{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: A353743 A217757 A053631 * A217041 A120618 A259048

Adjacent sequences: A319631 A319632 A319633 * A319635 A319636 A319637

Keyword

nonn,more

Author

Gus Wiseman, Sep 25 2018

Status

approved