A327437 - OEIS

%I #4 Sep 11 2019 20:22:51

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

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

%C 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.

%C 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.

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

%e Non-isomorphic representatives of the a(1) = 1 through a(4) = 15 antichains:

%e   {}  {}         {}             {}

%e       {{1}}      {{1}}          {{1}}

%e       {{1},{2}}  {{1,2}}        {{1,2}}

%e                  {{1},{2}}      {{1},{2}}

%e                  {{1},{2,3}}    {{1,2,3}}

%e                  {{1},{2},{3}}  {{1},{2,3}}

%e                                 {{1,2},{1,3}}

%e                                 {{1},{2},{3}}

%e                                 {{1},{2,3,4}}

%e                                 {{1,2},{3,4}}

%e                                 {{1},{2},{3,4}}

%e                                 {{1},{2},{3},{4}}

%e                                 {{2},{1,3},{1,4}}

%e                                 {{1,2},{1,3},{2,3}}

%e                                 {{4},{1,2},{1,3},{2,3}}

%Y Column k = 0 of A327438.

%Y The labeled version is A327355.

%Y The covering case is A327426.

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

%K nonn,more

%O 0,3

%A _Gus Wiseman_, Sep 11 2019