cp's OEIS Frontend

A319773 Number of non-isomorphic intersecting set systems of weight n whose dual is also an intersecting set system.

%I A319773 #5 Sep 28 2018 15:23:24
%S A319773 1,1,0,1,0,0,2,1,2,4,5
%N A319773 Number of non-isomorphic intersecting set systems of weight n whose dual is also an intersecting set system.
%C A319773 The dual of a multiset partition has, for each vertex, one part consisting of the indices (or positions) of the parts containing that vertex, counted with multiplicity. For example, the dual of {{1,2},{2,2}} is {{1},{1,2,2}}.
%C A319773 The weight of a multiset partition is the sum of sizes of its parts. Weight is generally not the same as number of vertices.
%C A319773 A multiset partition is intersecting iff no two parts are disjoint. The dual of a multiset partition is intersecting iff every pair of distinct vertices appear together in some part.
%e A319773 Non-isomorphic representatives of the a(1) = 1 through a(10) = 5 set systems:
%e A319773 1:  {{1}}
%e A319773 3:  {{2},{1,2}}
%e A319773 6:  {{3},{2,3},{1,2,3}}
%e A319773     {{1,2},{1,3},{2,3}}
%e A319773 7:  {{1,3},{2,3},{1,2,3}}
%e A319773 8:  {{2,4},{3,4},{1,2,3,4}}
%e A319773     {{3},{1,3},{2,3},{1,2,3}}
%e A319773 9:  {{1,2,4},{1,3,4},{2,3,4}}
%e A319773     {{4},{2,4},{3,4},{1,2,3,4}}
%e A319773     {{1,2},{1,3},{1,4},{2,3,4}}
%e A319773     {{1,2},{1,3},{2,3},{1,2,3}}
%e A319773 10: {{4},{3,4},{2,3,4},{1,2,3,4}}
%e A319773     {{4},{1,2,4},{1,3,4},{2,3,4}}
%e A319773     {{1,2},{2,4},{1,3,4},{2,3,4}}
%e A319773     {{1,4},{2,4},{3,4},{1,2,3,4}}
%e A319773     {{2,3},{2,4},{3,4},{1,2,3,4}}
%Y A319773 Cf. A007716, A281116, A283877, A305854, A306006, A316980, A316983, A317757, A319616.
%Y A319773 Cf. A319752, A319765, A319766, A319767, A319768, A319769, A319774.
%K A319773 nonn,more
%O A319773 0,7
%A A319773 _Gus Wiseman_, Sep 27 2018