A326251 Number of digraphs with vertices {1..n} whose increasing edges are not crossing.

1, 2, 16, 512, 49152, 11534336, 6039797760, 6768868458496, 15885743998107648, 77083611222073409536, 767126299049285413502976, 15572324598183490228037091328, 642316330843573124053884695740416, 53681919993405760099480940765478125568

Offset

0,2

Comments

A directed edge (a,b) is increasing if a < b. Two edges (a,b), (c,d) are crossing if a < c < b < d or c < a < d < b.

Conjecture: Also the number of non-nesting digraphs with vertices {1..n} whose increasing edges are not crossing, where two edges (a,b), (c,d) are nesting if a < c < d < b or c < a < b < d.

Links

Table of n, a(n) for n=0..13.

Formula

a(n) = 2^(n * (n + 1)/2) * A054726(n).

Mathematica

croXQ[eds_]:=MatchQ[eds, {___, {x_, y_}, ___, {z_, t_}, ___}/; x<z<y<t||z<x<t<y];
Table[Length[Select[Subsets[Tuples[Range[n], 2]], !croXQ[#]&]], {n, 0, 4}]

Crossrefs

Simple graphs whose edges are non-crossing are A054726.

Digraphs whose edges are not crossing are A326237.

Digraphs whose increasing edges are crossing are A326252.

Cf. A002416, A229865, A324170, A326209, A326250, A326251.

Sequence in context: A265015 A267728 A063387 * A228979 A366514 A293150

Adjacent sequences: A326248 A326249 A326250 * A326252 A326253 A326254

Keyword

nonn

Author

Gus Wiseman, Jun 30 2019

Status

approved