

A326960


Number of sets of subsets of {1..n} covering all n vertices whose dual is a (strict) antichain, also called covering T_1 sets of subsets.


9



2, 2, 4, 72, 38040, 4020463392, 18438434825136728352, 340282363593610211921722192165556850240, 115792089237316195072053288318104625954343609704705784618785209431974668731584
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,1


COMMENTS

Same as A059052 except with a(1) = 2 instead of 4.
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.
Alternatively, these are sets of subsets of {1..n} covering all n vertices where every vertex is the unique common element of some subset of the edges.


LINKS



FORMULA



EXAMPLE

The a(0) = 2 through a(2) = 4 sets of subsets:
{} {{1}} {{1},{2}}
{{}} {{},{1}} {{},{1},{2}}
{{1},{2},{1,2}}
{{},{1},{2},{1,2}}


MATHEMATICA

Table[Length[Select[Subsets[Subsets[Range[n]]], Length[Union[Select[Intersection@@@Rest[Subsets[#]], Length[#]==1&]]]==n&]], {n, 0, 3}]


CROSSREFS

Covering sets of subsets are A000371.
Covering T_0 sets of subsets are A326939.
The case without empty edges is A326961.
The noncovering version is A326967.


KEYWORD

nonn


AUTHOR



STATUS

approved



