cp's OEIS Frontend

A327011 Number of unlabeled sets of subsets covering n vertices where every vertex is the unique common element of some subset of the edges, also called unlabeled covering T_1 sets of subsets.

%I A327011 #5 Aug 13 2019 13:20:37
%S A327011 2,2,4,32,2424
%N A327011 Number of unlabeled sets of subsets covering n vertices where every vertex is the unique common element of some subset of the edges, also called unlabeled covering T_1 sets of subsets.
%C A327011 Alternatively, these are unlabeled sets of subsets covering n vertices whose dual is a (strict) antichain. The dual of a set of subsets has, for each vertex, one edge consisting of the indices (or positions) of the edges containing that vertex. For example, the dual of {{1,2},{2,3}} is {{1},{1,2},{2}}. An antichain is a set of subsets where no edge is a subset of any other.
%F A327011 a(n) = A326974(n) / 2.
%F A327011 a(n > 0) = A326951(n) - A326951(n - 1).
%e A327011 Non-isomorphic representatives of the a(0) = 1 through a(2) = 4 sets of subsets:
%e A327011   {}    {{1}}     {{1},{2}}
%e A327011   {{}}  {{},{1}}  {{},{1},{2}}
%e A327011                   {{1},{2},{1,2}}
%e A327011                   {{},{1},{2},{1,2}}
%Y A327011 Unlabeled covering sets of subsets are A003181.
%Y A327011 The same with T_0 instead of T_1 is A326942.
%Y A327011 The non-covering version is A326951 (partial sums).
%Y A327011 The labeled version is A326960.
%Y A327011 The case without empty edges is A326974.
%Y A327011 Cf. A001146, A055621, A059523, A319637, A326961, A326972, A326973, A326976, A326977, A326979.
%K A327011 nonn,more
%O A327011 0,1
%A A327011 _Gus Wiseman_, Aug 13 2019