cp's OEIS Frontend

A326972 Number of unlabeled set-systems on n vertices whose dual is a (strict) antichain, also called unlabeled T_1 set-systems.

%I A326972 #8 Aug 12 2019 22:32:31
%S A326972 1,2,4,20,1232
%N A326972 Number of unlabeled set-systems on n vertices whose dual is a (strict) antichain, also called unlabeled T_1 set-systems.
%C A326972 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 of sets, none of which is a subset of any other.
%e A326972 Non-isomorphic representatives of the a(0) = 1 through a(3) = 20 set-systems:
%e A326972   {}  {}     {}               {}
%e A326972       {{1}}  {{1}}            {{1}}
%e A326972              {{1},{2}}        {{1},{2}}
%e A326972              {{1},{2},{1,2}}  {{1},{2},{3}}
%e A326972                               {{1},{2},{1,2}}
%e A326972                               {{1,2},{1,3},{2,3}}
%e A326972                               {{1},{2},{3},{2,3}}
%e A326972                               {{1},{2},{1,3},{2,3}}
%e A326972                               {{1},{2},{3},{1,2,3}}
%e A326972                               {{3},{1,2},{1,3},{2,3}}
%e A326972                               {{1},{2},{3},{1,3},{2,3}}
%e A326972                               {{1,2},{1,3},{2,3},{1,2,3}}
%e A326972                               {{1},{2},{3},{2,3},{1,2,3}}
%e A326972                               {{2},{3},{1,2},{1,3},{2,3}}
%e A326972                               {{1},{2},{1,3},{2,3},{1,2,3}}
%e A326972                               {{1},{2},{3},{1,2},{1,3},{2,3}}
%e A326972                               {{3},{1,2},{1,3},{2,3},{1,2,3}}
%e A326972                               {{1},{2},{3},{1,3},{2,3},{1,2,3}}
%e A326972                               {{2},{3},{1,2},{1,3},{2,3},{1,2,3}}
%e A326972                               {{1},{2},{3},{1,2},{1,3},{2,3},{1,2,3}}
%Y A326972 Unlabeled set-systems are A000612.
%Y A326972 Unlabeled set-systems whose dual is strict are A326946.
%Y A326972 The version with empty edges allowed is A326951.
%Y A326972 The labeled version is A326965.
%Y A326972 The version where the dual is not required to be strict is A326971.
%Y A326972 The covering version is A326974 (first differences).
%Y A326972 Cf. A059523, A319559, A319637, A326973, A326976, A326977, A326979.
%K A326972 nonn,more
%O A326972 0,2
%A A326972 _Gus Wiseman_, Aug 11 2019