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A326209 Number of nesting labeled digraphs with vertices {1..n}. 17
0, 0, 4, 408, 64528 (list; graph; refs; listen; history; text; internal format)
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 edge-sets are:
{11,22}
{11,12,22}
{11,21,22}
{11,12,21,22}
LINKS
FORMULA
A002416(n) = a(n) + A326237(n).
EXAMPLE
The a(2) = 4 nesting digraph edge-sets:
{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
Non-nesting digraphs are A326237.
Nesting set partitions are A016098.
MM-numbers of nesting multiset partitions are A326256.
MM-numbers of unsortable multiset partitions are A326258.
Sequence in context: A259049 A280791 A198709 * A287965 A215647 A228242
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Jun 19 2019
STATUS
approved

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Last modified June 13 09:03 EDT 2024. Contains 373383 sequences. (Running on oeis4.)