OFFSET
0,2
COMMENTS
These are digraphs with the property that, if the edges are listed in lexicographic order, the sequence of targets is weakly increasing. For example, the digraph with lexicographically ordered edge set {(1,2),(2,1),(3,1),(3,2)} is nesting because the targets are (2,1,1,2), a sequence that is not weakly increasing.
Also the number of non-semicrossing digraphs with vertices {1..n}, where two edges (a,b), (c,d) are semicrossing if a < c and b < d or a > c and b > d. For example, the a(2) = 4 non-semicrossing digraph edge-sets are:
{}
{11}
{12}
{21}
{22}
{11,12}
{11,21}
{12,21}
{12,22}
{21,22}
{11,12,21}
{12,21,22}
Apparently a duplicate of A152254. - R. J. Mathar, Jul 12 2019
EXAMPLE
The a(2) = 12 non-nesting digraph edge-sets:
{}
{11}
{12}
{21}
{22}
{11,12}
{11,21}
{11,22}
{12,22}
{21,22}
{11,12,22}
{11,21,22}
MATHEMATICA
Table[Length[Select[Subsets[Tuples[Range[n], 2]], OrderedQ[Last/@#]&]], {n, 4}]
CROSSREFS
KEYWORD
nonn,more,changed
AUTHOR
Gus Wiseman, Jun 19 2019
STATUS
approved