login
Number of set-systems with {} that are closed under intersection and cover n vertices.
13

%I #9 Aug 11 2019 12:23:39

%S 1,1,5,71,4223,2725521,151914530499,28175294344381108057

%N Number of set-systems with {} that are closed under intersection and cover n vertices.

%F Inverse binomial transform of A102895. - _Andrew Howroyd_, Aug 10 2019

%e The a(2) = 5 set-systems:

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

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

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

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

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

%t Table[Length[Select[Subsets[Subsets[Range[n]]],MemberQ[#,{}]&&Union@@#==Range[n]&&SubsetQ[#,Intersection@@@Tuples[#,2]]&]],{n,0,3}]

%Y The case also closed under union is A000798.

%Y The connected case (i.e., with maximum) is A102894.

%Y The same for union instead of intersection is (also) A102894.

%Y The non-covering case is A102895.

%Y The BII-numbers of these set-systems (without the empty set) are A326880.

%Y The unlabeled case is A326883.

%Y Cf. A003465, A014466, A102896, A102897, A193674, A193675, A306445, A307249, A326878.

%K nonn,more

%O 0,3

%A _Gus Wiseman_, Jul 30 2019

%E a(5)-a(7) from _Andrew Howroyd_, Aug 10 2019