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A326946 Number of unlabeled T_0 set-systems on n vertices. 17

%I

%S 1,2,5,34,1919

%N Number of unlabeled T_0 set-systems on n vertices.

%C The dual of a multiset partition has, for each vertex, one block consisting of the indices (or positions) of the blocks containing that vertex. For example, the dual of {{1,2},{2,3}} is {{1},{1,2},{2}}. The T_0 condition means that the dual is strict (no repeated edges).

%F Partial sums of A319637.

%F a(n) = A326949(n)/2.

%e Non-isomorphic representatives of the a(0) = 1 through a(2) = 5 set-systems:

%e {} {} {}

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

%e {{1},{2}}

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

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

%t dual[eds_]:=Table[First/@Position[eds,x],{x,Union@@eds}];

%t Table[Length[Union[normclut/@Select[Subsets[Subsets[Range[n],{1,n}]],UnsameQ@@dual[#]&]]],{n,0,3}]

%Y The non-T_0 version is A000612.

%Y The antichain case is A245567.

%Y The covering case is A319637.

%Y The labeled version is A326940.

%Y The version with empty edges allowed is A326949.

%Y Cf. A003180, A055621, A059052, A059201, A316978, A319559, A319564, A326942.

%K nonn,more

%O 0,2

%A _Gus Wiseman_, Aug 08 2019

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Last modified March 29 21:29 EDT 2020. Contains 333117 sequences. (Running on oeis4.)