A327807 Triangle read by rows where T(n,k) is the number of unlabeled antichains of sets with n vertices and vertex-connectivity >= k.

1, 2, 0, 4, 1, 0, 9, 3, 2, 0, 29, 14, 10, 6, 0, 209, 157, 128, 91, 54, 0

Offset: 0

Author

Gus Wiseman, Sep 26 2019

Keywords

• nonn
• tabl
• more

Comments

An antichain is a set of sets, none of which is a subset of any other.

The vertex-connectivity of a set-system is the minimum number of vertices that must be removed (along with any resulting empty edges) to obtain a non-connected set-system or singleton. Note that this means a single node has vertex-connectivity 0.

Examples

			Triangle begins:
    1
    2   0
    4   1   0
    9   3   2   0
   29  14  10   6   0
  209 157 128  91  54   0
		

Crossrefs

Column k = 0 is A306505.

Column k = 1 is A261006 (clutters), if we assume A261006(0) = A261006(1) = 0.

Column k = 2 is A305028 (blobs), if we assume A305028(0) = A305028(2) = 0.

Except for the first column, same as A327358 (the covering case).

The labeled version is A327806.

Cf. A014466, A293606, A326704, A326950, A327062, A327334, A327350, A327351, A327805, A327808.