A327437 Number of unlabeled antichains of nonempty subsets of {1..n} that are either non-connected or non-covering (spanning edge-connectivity 0).

1, 1, 3, 6, 15, 52, 410, 32697

Offset

0,3

Comments

An antichain is a set of sets, none of which is a subset of any other. It is covering if there are no isolated vertices.

The spanning edge-connectivity of a set-system is the minimum number of edges that must be removed (without removing incident vertices) to obtain a set-system that is disconnected or covers fewer vertices.

Links

Table of n, a(n) for n=0..7.

Formula

a(n > 0) = A306505(n) - A261006(n).

Example

Non-isomorphic representatives of the a(1) = 1 through a(4) = 15 antichains:
  {}  {}         {}             {}
      {{1}}      {{1}}          {{1}}
      {{1},{2}}  {{1,2}}        {{1,2}}
                 {{1},{2}}      {{1},{2}}
                 {{1},{2,3}}    {{1,2,3}}
                 {{1},{2},{3}}  {{1},{2,3}}
                                {{1,2},{1,3}}
                                {{1},{2},{3}}
                                {{1},{2,3,4}}
                                {{1,2},{3,4}}
                                {{1},{2},{3,4}}
                                {{1},{2},{3},{4}}
                                {{2},{1,3},{1,4}}
                                {{1,2},{1,3},{2,3}}
                                {{4},{1,2},{1,3},{2,3}}

Crossrefs

Column k = 0 of A327438.

The labeled version is A327355.

The covering case is A327426.

Cf. A014466 A052446, A120338, A261005, A293606, A327201, A327236, A327352, A327353, A327354, A327438.

Sequence in context: A322851 A230950 A370888 * A267552 A241269 A102356

Adjacent sequences: A327434 A327435 A327436 * A327438 A327439 A327440

Keyword

nonn,more

Author

Gus Wiseman, Sep 11 2019

Status

approved