cp's OEIS Frontend

A326974 Number of unlabeled set-systems covering n vertices where every vertex is the unique common element of some subset of the edges, also called unlabeled covering T_1 set-systems.

%I A326974 #10 Aug 12 2019 22:31:07
%S A326974 1,1,2,16,1212
%N A326974 Number of unlabeled set-systems covering n vertices where every vertex is the unique common element of some subset of the edges, also called unlabeled covering T_1 set-systems.
%C A326974 Alternatively, these are unlabeled set-systems covering n vertices whose dual is a (strict) antichain. A set-system is a finite set of finite nonempty sets. The dual of a set-system 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-system where no edge is a subset of any other.
%F A326974 a(n > 0) = A326972(n) - A326972(n - 1).
%e A326974 Non-isomorphic representatives of the a(0) = 1 through a(3) = 16 set-systems:
%e A326974   {}  {{1}}  {{1},{2}}        {{1},{2},{3}}
%e A326974              {{1},{2},{1,2}}  {{1,2},{1,3},{2,3}}
%e A326974                               {{1},{2},{3},{2,3}}
%e A326974                               {{1},{2},{1,3},{2,3}}
%e A326974                               {{1},{2},{3},{1,2,3}}
%e A326974                               {{3},{1,2},{1,3},{2,3}}
%e A326974                               {{1},{2},{3},{1,3},{2,3}}
%e A326974                               {{1,2},{1,3},{2,3},{1,2,3}}
%e A326974                               {{1},{2},{3},{2,3},{1,2,3}}
%e A326974                               {{2},{3},{1,2},{1,3},{2,3}}
%e A326974                               {{1},{2},{1,3},{2,3},{1,2,3}}
%e A326974                               {{1},{2},{3},{1,2},{1,3},{2,3}}
%e A326974                               {{3},{1,2},{1,3},{2,3},{1,2,3}}
%e A326974                               {{1},{2},{3},{1,3},{2,3},{1,2,3}}
%e A326974                               {{2},{3},{1,2},{1,3},{2,3},{1,2,3}}
%e A326974                               {{1},{2},{3},{1,2},{1,3},{2,3},{1,2,3}}
%Y A326974 Unlabeled covers are A055621.
%Y A326974 The same with T_0 instead of T_1 is A319637.
%Y A326974 The labeled version is A326961.
%Y A326974 The non-covering version is A326972 (partial sums).
%Y A326974 Unlabeled covering set-systems whose dual is a weak antichain are A326973.
%Y A326974 Cf. A000612, A059523, A319559, A326946, A326951, A326965, A326970, A326971, A326976, A326977, A326979.
%K A326974 nonn,more
%O A326974 0,3
%A A326974 _Gus Wiseman_, Aug 11 2019