|
%I #6 Jun 30 2019 06:50:00
%S 1,2,16,512,49152,11534336,6039797760,6768868458496,15885743998107648,
%T 77083611222073409536,767126299049285413502976,
%U 15572324598183490228037091328,642316330843573124053884695740416,53681919993405760099480940765478125568
%N Number of digraphs with vertices {1..n} whose increasing edges are not crossing.
%C 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.
%C 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.
%F a(n) = 2^(n * (n + 1)/2) * A054726(n).
%t croXQ[eds_]:=MatchQ[eds,{___,{x_,y_},___,{z_,t_},___}/;x<z<y<t||z<x<t<y];
%t Table[Length[Select[Subsets[Tuples[Range[n],2]],!croXQ[#]&]],{n,0,4}]
%Y Simple graphs whose edges are non-crossing are A054726.
%Y Digraphs whose edges are not crossing are A326237.
%Y Digraphs whose increasing edges are crossing are A326252.
%Y Cf. A002416, A229865, A324170, A326209, A326250, A326251.
%K nonn
%O 0,2
%A _Gus Wiseman_, Jun 30 2019
|
