

A326209


Number of nesting labeled digraphs with vertices {1..n}.


17




OFFSET

0,3


COMMENTS

Two edges (a,b), (c,d) are nesting if a < c and b > d or a > c and b < d.
Also unsortable digraphs with vertices {1..n}, where a digraph is sortable if, when the edges are listed in lexicographic order, their targets are weakly increasing.
Also the number of 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 semicrossing digraph edgesets are:
{11,22}
{11,12,22}
{11,21,22}
{11,12,21,22}


LINKS



FORMULA



EXAMPLE

The a(2) = 4 nesting digraph edgesets:
{12,21}
{11,12,21}
{12,21,22}
{11,12,21,22}


MATHEMATICA

Table[Length[Select[Subsets[Tuples[Range[n], 2]], !OrderedQ[Last/@#]&]], {n, 4}]


CROSSREFS

Nesting set partitions are A016098.
MMnumbers of nesting multiset partitions are A326256.
MMnumbers of unsortable multiset partitions are A326258.


KEYWORD

nonn,more


AUTHOR



STATUS

approved



