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%I A326209 #14 Jun 21 2019 22:44:02
%S A326209 0,0,4,408,64528
%N A326209 Number of nesting labeled digraphs with vertices {1..n}.
%C A326209 Two edges (a,b), (c,d) are nesting if a < c and b > d or a > c and b < d.
%C A326209 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.
%C A326209 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:
%C A326209   {11,22}
%C A326209   {11,12,22}
%C A326209   {11,21,22}
%C A326209   {11,12,21,22}
%F A326209 A002416(n) = a(n) + A326237(n).
%e A326209 The a(2) = 4 nesting digraph edge-sets:
%e A326209   {12,21}
%e A326209   {11,12,21}
%e A326209   {12,21,22}
%e A326209   {11,12,21,22}
%t A326209 Table[Length[Select[Subsets[Tuples[Range[n],2]],!OrderedQ[Last/@#]&]],{n,4}]
%Y A326209 Non-nesting digraphs are A326237.
%Y A326209 Nesting set partitions are A016098.
%Y A326209 MM-numbers of nesting multiset partitions are A326256.
%Y A326209 MM-numbers of unsortable multiset partitions are A326258.
%Y A326209 Cf. A000108, A001519, A002416, A229865.
%Y A326209 Cf. A326210, A326211, A326243, A326246, A326248, A326250.
%K A326209 nonn,more
%O A326209 0,3
%A A326209 _Gus Wiseman_, Jun 19 2019

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