OFFSET
0,7
COMMENTS
An antichain is a set of sets, none of which is a subset of any other. It is covering if there are no isolated vertices.
The vertex-connectivity of a set-system is the minimum number of vertices that must be removed (along with any empty or duplicate edges) to obtain a non-connected set-system or singleton. Note that this means a single node has vertex-connectivity 0.
If empty edges are allowed, we have T(0,0) = 2.
EXAMPLE
Triangle begins:
1
1 0
1 1 0
2 1 2 0
6 4 4 6 0
23 29 37 37 54 0
Row n = 4 counts the following antichains:
{1}{234} {14}{234} {134}{234} {1234}
{12}{34} {13}{24}{34} {13}{14}{234} {12}{134}{234}
{1}{2}{34} {14}{24}{34} {12}{13}{24}{34} {124}{134}{234}
{1}{24}{34} {14}{23}{24}{34} {13}{14}{23}{24}{34} {12}{13}{14}{234}
{1}{2}{3}{4} {123}{124}{134}{234}
{1}{23}{24}{34} {12}{13}{14}{23}{24}{34}
CROSSREFS
KEYWORD
AUTHOR
Gus Wiseman, Sep 10 2019
STATUS
approved