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A326209
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Number of nesting labeled digraphs with vertices {1..n}.
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17
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OFFSET
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0,3
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COMMENTS
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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}
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LINKS
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FORMULA
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EXAMPLE
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The a(2) = 4 nesting digraph edge-sets:
{12,21}
{11,12,21}
{12,21,22}
{11,12,21,22}
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MATHEMATICA
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Table[Length[Select[Subsets[Tuples[Range[n], 2]], !OrderedQ[Last/@#]&]], {n, 4}]
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CROSSREFS
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Nesting set partitions are A016098.
MM-numbers of nesting multiset partitions are A326256.
MM-numbers of unsortable multiset partitions are A326258.
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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