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Your data matches 14 different statistics following compositions of up to 3 maps.
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Matching statistic: St000944
Mp00287: Ordered set partitions —to composition⟶ Integer compositions
Mp00180: Integer compositions —to ribbon⟶ Skew partitions
Mp00183: Skew partitions —inner shape⟶ Integer partitions
St000944: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00180: Integer compositions —to ribbon⟶ Skew partitions
Mp00183: Skew partitions —inner shape⟶ Integer partitions
St000944: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[{1,2},{3}] => [2,1] => [[2,2],[1]]
=> [1]
=> 0
[{1,3},{2}] => [2,1] => [[2,2],[1]]
=> [1]
=> 0
[{2,3},{1}] => [2,1] => [[2,2],[1]]
=> [1]
=> 0
[{1},{2,3},{4}] => [1,2,1] => [[2,2,1],[1]]
=> [1]
=> 0
[{1},{2,4},{3}] => [1,2,1] => [[2,2,1],[1]]
=> [1]
=> 0
[{1},{3,4},{2}] => [1,2,1] => [[2,2,1],[1]]
=> [1]
=> 0
[{2},{1,3},{4}] => [1,2,1] => [[2,2,1],[1]]
=> [1]
=> 0
[{2},{1,4},{3}] => [1,2,1] => [[2,2,1],[1]]
=> [1]
=> 0
[{3},{1,2},{4}] => [1,2,1] => [[2,2,1],[1]]
=> [1]
=> 0
[{4},{1,2},{3}] => [1,2,1] => [[2,2,1],[1]]
=> [1]
=> 0
[{3},{1,4},{2}] => [1,2,1] => [[2,2,1],[1]]
=> [1]
=> 0
[{4},{1,3},{2}] => [1,2,1] => [[2,2,1],[1]]
=> [1]
=> 0
[{2},{3,4},{1}] => [1,2,1] => [[2,2,1],[1]]
=> [1]
=> 0
[{3},{2,4},{1}] => [1,2,1] => [[2,2,1],[1]]
=> [1]
=> 0
[{4},{2,3},{1}] => [1,2,1] => [[2,2,1],[1]]
=> [1]
=> 0
[{1,2},{3},{4}] => [2,1,1] => [[2,2,2],[1,1]]
=> [1,1]
=> 0
[{1,2},{4},{3}] => [2,1,1] => [[2,2,2],[1,1]]
=> [1,1]
=> 0
[{1,3},{2},{4}] => [2,1,1] => [[2,2,2],[1,1]]
=> [1,1]
=> 0
[{1,4},{2},{3}] => [2,1,1] => [[2,2,2],[1,1]]
=> [1,1]
=> 0
[{1,3},{4},{2}] => [2,1,1] => [[2,2,2],[1,1]]
=> [1,1]
=> 0
[{1,4},{3},{2}] => [2,1,1] => [[2,2,2],[1,1]]
=> [1,1]
=> 0
[{2,3},{1},{4}] => [2,1,1] => [[2,2,2],[1,1]]
=> [1,1]
=> 0
[{2,4},{1},{3}] => [2,1,1] => [[2,2,2],[1,1]]
=> [1,1]
=> 0
[{3,4},{1},{2}] => [2,1,1] => [[2,2,2],[1,1]]
=> [1,1]
=> 0
[{2,3},{4},{1}] => [2,1,1] => [[2,2,2],[1,1]]
=> [1,1]
=> 0
[{2,4},{3},{1}] => [2,1,1] => [[2,2,2],[1,1]]
=> [1,1]
=> 0
[{3,4},{2},{1}] => [2,1,1] => [[2,2,2],[1,1]]
=> [1,1]
=> 0
[{1,2},{3,4}] => [2,2] => [[3,2],[1]]
=> [1]
=> 0
[{1,3},{2,4}] => [2,2] => [[3,2],[1]]
=> [1]
=> 0
[{1,4},{2,3}] => [2,2] => [[3,2],[1]]
=> [1]
=> 0
[{2,3},{1,4}] => [2,2] => [[3,2],[1]]
=> [1]
=> 0
[{2,4},{1,3}] => [2,2] => [[3,2],[1]]
=> [1]
=> 0
[{3,4},{1,2}] => [2,2] => [[3,2],[1]]
=> [1]
=> 0
[{1,2,3},{4}] => [3,1] => [[3,3],[2]]
=> [2]
=> 0
[{1,2,4},{3}] => [3,1] => [[3,3],[2]]
=> [2]
=> 0
[{1,3,4},{2}] => [3,1] => [[3,3],[2]]
=> [2]
=> 0
[{2,3,4},{1}] => [3,1] => [[3,3],[2]]
=> [2]
=> 0
[{1},{2},{3,4},{5}] => [1,1,2,1] => [[2,2,1,1],[1]]
=> [1]
=> 0
[{1},{2},{3,5},{4}] => [1,1,2,1] => [[2,2,1,1],[1]]
=> [1]
=> 0
[{1},{2},{4,5},{3}] => [1,1,2,1] => [[2,2,1,1],[1]]
=> [1]
=> 0
[{1},{3},{2,4},{5}] => [1,1,2,1] => [[2,2,1,1],[1]]
=> [1]
=> 0
[{1},{3},{2,5},{4}] => [1,1,2,1] => [[2,2,1,1],[1]]
=> [1]
=> 0
[{1},{4},{2,3},{5}] => [1,1,2,1] => [[2,2,1,1],[1]]
=> [1]
=> 0
[{1},{5},{2,3},{4}] => [1,1,2,1] => [[2,2,1,1],[1]]
=> [1]
=> 0
[{1},{4},{2,5},{3}] => [1,1,2,1] => [[2,2,1,1],[1]]
=> [1]
=> 0
[{1},{5},{2,4},{3}] => [1,1,2,1] => [[2,2,1,1],[1]]
=> [1]
=> 0
[{1},{3},{4,5},{2}] => [1,1,2,1] => [[2,2,1,1],[1]]
=> [1]
=> 0
[{1},{4},{3,5},{2}] => [1,1,2,1] => [[2,2,1,1],[1]]
=> [1]
=> 0
[{1},{5},{3,4},{2}] => [1,1,2,1] => [[2,2,1,1],[1]]
=> [1]
=> 0
[{2},{1},{3,4},{5}] => [1,1,2,1] => [[2,2,1,1],[1]]
=> [1]
=> 0
Description
The 3-degree of an integer partition.
For an integer partition $\lambda$, this is given by the exponent of 3 in the Gram determinant of the integal Specht module of the symmetric group indexed by $\lambda$.
This stupid comment should not be accepted as an edit!
Matching statistic: St001330
Mp00287: Ordered set partitions —to composition⟶ Integer compositions
Mp00041: Integer compositions —conjugate⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St001330: Graphs ⟶ ℤResult quality: 25% ●values known / values provided: 43%●distinct values known / distinct values provided: 25%
Mp00041: Integer compositions —conjugate⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St001330: Graphs ⟶ ℤResult quality: 25% ●values known / values provided: 43%●distinct values known / distinct values provided: 25%
Values
[{1,2},{3}] => [2,1] => [2,1] => ([(0,2),(1,2)],3)
=> 2 = 0 + 2
[{1,3},{2}] => [2,1] => [2,1] => ([(0,2),(1,2)],3)
=> 2 = 0 + 2
[{2,3},{1}] => [2,1] => [2,1] => ([(0,2),(1,2)],3)
=> 2 = 0 + 2
[{1},{2,3},{4}] => [1,2,1] => [2,2] => ([(1,3),(2,3)],4)
=> 2 = 0 + 2
[{1},{2,4},{3}] => [1,2,1] => [2,2] => ([(1,3),(2,3)],4)
=> 2 = 0 + 2
[{1},{3,4},{2}] => [1,2,1] => [2,2] => ([(1,3),(2,3)],4)
=> 2 = 0 + 2
[{2},{1,3},{4}] => [1,2,1] => [2,2] => ([(1,3),(2,3)],4)
=> 2 = 0 + 2
[{2},{1,4},{3}] => [1,2,1] => [2,2] => ([(1,3),(2,3)],4)
=> 2 = 0 + 2
[{3},{1,2},{4}] => [1,2,1] => [2,2] => ([(1,3),(2,3)],4)
=> 2 = 0 + 2
[{4},{1,2},{3}] => [1,2,1] => [2,2] => ([(1,3),(2,3)],4)
=> 2 = 0 + 2
[{3},{1,4},{2}] => [1,2,1] => [2,2] => ([(1,3),(2,3)],4)
=> 2 = 0 + 2
[{4},{1,3},{2}] => [1,2,1] => [2,2] => ([(1,3),(2,3)],4)
=> 2 = 0 + 2
[{2},{3,4},{1}] => [1,2,1] => [2,2] => ([(1,3),(2,3)],4)
=> 2 = 0 + 2
[{3},{2,4},{1}] => [1,2,1] => [2,2] => ([(1,3),(2,3)],4)
=> 2 = 0 + 2
[{4},{2,3},{1}] => [1,2,1] => [2,2] => ([(1,3),(2,3)],4)
=> 2 = 0 + 2
[{1,2},{3},{4}] => [2,1,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 0 + 2
[{1,2},{4},{3}] => [2,1,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 0 + 2
[{1,3},{2},{4}] => [2,1,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 0 + 2
[{1,4},{2},{3}] => [2,1,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 0 + 2
[{1,3},{4},{2}] => [2,1,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 0 + 2
[{1,4},{3},{2}] => [2,1,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 0 + 2
[{2,3},{1},{4}] => [2,1,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 0 + 2
[{2,4},{1},{3}] => [2,1,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 0 + 2
[{3,4},{1},{2}] => [2,1,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 0 + 2
[{2,3},{4},{1}] => [2,1,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 0 + 2
[{2,4},{3},{1}] => [2,1,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 0 + 2
[{3,4},{2},{1}] => [2,1,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 0 + 2
[{1,2},{3,4}] => [2,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 0 + 2
[{1,3},{2,4}] => [2,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 0 + 2
[{1,4},{2,3}] => [2,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 0 + 2
[{2,3},{1,4}] => [2,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 0 + 2
[{2,4},{1,3}] => [2,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 0 + 2
[{3,4},{1,2}] => [2,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 0 + 2
[{1,2,3},{4}] => [3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 0 + 2
[{1,2,4},{3}] => [3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 0 + 2
[{1,3,4},{2}] => [3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 0 + 2
[{2,3,4},{1}] => [3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 0 + 2
[{1},{2},{3,4},{5}] => [1,1,2,1] => [2,3] => ([(2,4),(3,4)],5)
=> 2 = 0 + 2
[{1},{2},{3,5},{4}] => [1,1,2,1] => [2,3] => ([(2,4),(3,4)],5)
=> 2 = 0 + 2
[{1},{2},{4,5},{3}] => [1,1,2,1] => [2,3] => ([(2,4),(3,4)],5)
=> 2 = 0 + 2
[{1},{3},{2,4},{5}] => [1,1,2,1] => [2,3] => ([(2,4),(3,4)],5)
=> 2 = 0 + 2
[{1},{3},{2,5},{4}] => [1,1,2,1] => [2,3] => ([(2,4),(3,4)],5)
=> 2 = 0 + 2
[{1},{4},{2,3},{5}] => [1,1,2,1] => [2,3] => ([(2,4),(3,4)],5)
=> 2 = 0 + 2
[{1},{5},{2,3},{4}] => [1,1,2,1] => [2,3] => ([(2,4),(3,4)],5)
=> 2 = 0 + 2
[{1},{4},{2,5},{3}] => [1,1,2,1] => [2,3] => ([(2,4),(3,4)],5)
=> 2 = 0 + 2
[{1},{5},{2,4},{3}] => [1,1,2,1] => [2,3] => ([(2,4),(3,4)],5)
=> 2 = 0 + 2
[{1},{3},{4,5},{2}] => [1,1,2,1] => [2,3] => ([(2,4),(3,4)],5)
=> 2 = 0 + 2
[{1},{4},{3,5},{2}] => [1,1,2,1] => [2,3] => ([(2,4),(3,4)],5)
=> 2 = 0 + 2
[{1},{5},{3,4},{2}] => [1,1,2,1] => [2,3] => ([(2,4),(3,4)],5)
=> 2 = 0 + 2
[{2},{1},{3,4},{5}] => [1,1,2,1] => [2,3] => ([(2,4),(3,4)],5)
=> 2 = 0 + 2
[{2},{1},{3,5},{4}] => [1,1,2,1] => [2,3] => ([(2,4),(3,4)],5)
=> 2 = 0 + 2
[{2},{1},{4,5},{3}] => [1,1,2,1] => [2,3] => ([(2,4),(3,4)],5)
=> 2 = 0 + 2
[{3},{1},{2,4},{5}] => [1,1,2,1] => [2,3] => ([(2,4),(3,4)],5)
=> 2 = 0 + 2
[{3},{1},{2,5},{4}] => [1,1,2,1] => [2,3] => ([(2,4),(3,4)],5)
=> 2 = 0 + 2
[{4},{1},{2,3},{5}] => [1,1,2,1] => [2,3] => ([(2,4),(3,4)],5)
=> 2 = 0 + 2
[{5},{1},{2,3},{4}] => [1,1,2,1] => [2,3] => ([(2,4),(3,4)],5)
=> 2 = 0 + 2
[{4},{1},{2,5},{3}] => [1,1,2,1] => [2,3] => ([(2,4),(3,4)],5)
=> 2 = 0 + 2
[{5},{1},{2,4},{3}] => [1,1,2,1] => [2,3] => ([(2,4),(3,4)],5)
=> 2 = 0 + 2
[{3},{1},{4,5},{2}] => [1,1,2,1] => [2,3] => ([(2,4),(3,4)],5)
=> 2 = 0 + 2
[{4},{1},{3,5},{2}] => [1,1,2,1] => [2,3] => ([(2,4),(3,4)],5)
=> 2 = 0 + 2
[{1},{2,3},{4,5}] => [1,2,2] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 2
[{1},{2,4},{3,5}] => [1,2,2] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 2
[{1},{2,5},{3,4}] => [1,2,2] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 2
[{1},{3,4},{2,5}] => [1,2,2] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 2
[{1},{3,5},{2,4}] => [1,2,2] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 2
[{1},{4,5},{2,3}] => [1,2,2] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 2
[{2},{1,3},{4,5}] => [1,2,2] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 2
[{2},{1,4},{3,5}] => [1,2,2] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 2
[{2},{1,5},{3,4}] => [1,2,2] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 2
[{3},{1,2},{4,5}] => [1,2,2] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 2
[{4},{1,2},{3,5}] => [1,2,2] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 2
[{5},{1,2},{3,4}] => [1,2,2] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 2
[{3},{1,4},{2,5}] => [1,2,2] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 2
[{3},{1,5},{2,4}] => [1,2,2] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 2
[{4},{1,3},{2,5}] => [1,2,2] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 2
[{5},{1,3},{2,4}] => [1,2,2] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 2
[{4},{1,5},{2,3}] => [1,2,2] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 2
[{5},{1,4},{2,3}] => [1,2,2] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 2
[{2},{3,4},{1,5}] => [1,2,2] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 2
[{2},{3,5},{1,4}] => [1,2,2] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 2
[{2},{4,5},{1,3}] => [1,2,2] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 2
[{3},{2,4},{1,5}] => [1,2,2] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 2
[{3},{2,5},{1,4}] => [1,2,2] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 2
[{4},{2,3},{1,5}] => [1,2,2] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 2
[{5},{2,3},{1,4}] => [1,2,2] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 2
[{4},{2,5},{1,3}] => [1,2,2] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 2
[{5},{2,4},{1,3}] => [1,2,2] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 2
[{3},{4,5},{1,2}] => [1,2,2] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 2
[{4},{3,5},{1,2}] => [1,2,2] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 2
[{5},{3,4},{1,2}] => [1,2,2] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 2
[{1},{2,3,4},{5}] => [1,3,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 2
[{1},{2,3,5},{4}] => [1,3,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 2
[{1},{2,4,5},{3}] => [1,3,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 2
[{1},{3,4,5},{2}] => [1,3,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 2
[{2},{1,3,4},{5}] => [1,3,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 2
[{2},{1,3,5},{4}] => [1,3,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 2
[{2},{1,4,5},{3}] => [1,3,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 2
[{3},{1,2,4},{5}] => [1,3,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 2
[{3},{1,2,5},{4}] => [1,3,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 2
[{4},{1,2,3},{5}] => [1,3,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 2
Description
The hat guessing number of a graph.
Suppose that each vertex of a graph corresponds to a player, wearing a hat whose color is arbitrarily chosen from a set of $q$ possible colors. Each player can see the hat colors of his neighbors, but not his own hat color. All of the players are asked to guess their own hat colors simultaneously, according to a predetermined guessing strategy and the hat colors they see, where no communication between them is allowed. The hat guessing number $HG(G)$ of a graph $G$ is the largest integer $q$ such that there exists a guessing strategy guaranteeing at least one correct guess for any hat assignment of $q$ possible colors.
Because it suffices that a single player guesses correctly, the hat guessing number of a graph is the maximum of the hat guessing numbers of its connected components.
Matching statistic: St000454
Mp00287: Ordered set partitions —to composition⟶ Integer compositions
Mp00041: Integer compositions —conjugate⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000454: Graphs ⟶ ℤResult quality: 15% ●values known / values provided: 15%●distinct values known / distinct values provided: 50%
Mp00041: Integer compositions —conjugate⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000454: Graphs ⟶ ℤResult quality: 15% ●values known / values provided: 15%●distinct values known / distinct values provided: 50%
Values
[{1,2},{3}] => [2,1] => [2,1] => ([(0,2),(1,2)],3)
=> ? = 0 + 2
[{1,3},{2}] => [2,1] => [2,1] => ([(0,2),(1,2)],3)
=> ? = 0 + 2
[{2,3},{1}] => [2,1] => [2,1] => ([(0,2),(1,2)],3)
=> ? = 0 + 2
[{1},{2,3},{4}] => [1,2,1] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 2
[{1},{2,4},{3}] => [1,2,1] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 2
[{1},{3,4},{2}] => [1,2,1] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 2
[{2},{1,3},{4}] => [1,2,1] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 2
[{2},{1,4},{3}] => [1,2,1] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 2
[{3},{1,2},{4}] => [1,2,1] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 2
[{4},{1,2},{3}] => [1,2,1] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 2
[{3},{1,4},{2}] => [1,2,1] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 2
[{4},{1,3},{2}] => [1,2,1] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 2
[{2},{3,4},{1}] => [1,2,1] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 2
[{3},{2,4},{1}] => [1,2,1] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 2
[{4},{2,3},{1}] => [1,2,1] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 2
[{1,2},{3},{4}] => [2,1,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> ? = 0 + 2
[{1,2},{4},{3}] => [2,1,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> ? = 0 + 2
[{1,3},{2},{4}] => [2,1,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> ? = 0 + 2
[{1,4},{2},{3}] => [2,1,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> ? = 0 + 2
[{1,3},{4},{2}] => [2,1,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> ? = 0 + 2
[{1,4},{3},{2}] => [2,1,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> ? = 0 + 2
[{2,3},{1},{4}] => [2,1,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> ? = 0 + 2
[{2,4},{1},{3}] => [2,1,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> ? = 0 + 2
[{3,4},{1},{2}] => [2,1,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> ? = 0 + 2
[{2,3},{4},{1}] => [2,1,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> ? = 0 + 2
[{2,4},{3},{1}] => [2,1,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> ? = 0 + 2
[{3,4},{2},{1}] => [2,1,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> ? = 0 + 2
[{1,2},{3,4}] => [2,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 0 + 2
[{1,3},{2,4}] => [2,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 0 + 2
[{1,4},{2,3}] => [2,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 0 + 2
[{2,3},{1,4}] => [2,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 0 + 2
[{2,4},{1,3}] => [2,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 0 + 2
[{3,4},{1,2}] => [2,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 0 + 2
[{1,2,3},{4}] => [3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 0 + 2
[{1,2,4},{3}] => [3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 0 + 2
[{1,3,4},{2}] => [3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 0 + 2
[{2,3,4},{1}] => [3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 0 + 2
[{1},{2},{3,4},{5}] => [1,1,2,1] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 0 + 2
[{1},{2},{3,5},{4}] => [1,1,2,1] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 0 + 2
[{1},{2},{4,5},{3}] => [1,1,2,1] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 0 + 2
[{1},{3},{2,4},{5}] => [1,1,2,1] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 0 + 2
[{1},{3},{2,5},{4}] => [1,1,2,1] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 0 + 2
[{1},{4},{2,3},{5}] => [1,1,2,1] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 0 + 2
[{1},{5},{2,3},{4}] => [1,1,2,1] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 0 + 2
[{1},{4},{2,5},{3}] => [1,1,2,1] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 0 + 2
[{1},{5},{2,4},{3}] => [1,1,2,1] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 0 + 2
[{1},{3},{4,5},{2}] => [1,1,2,1] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 0 + 2
[{1},{4},{3,5},{2}] => [1,1,2,1] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 0 + 2
[{1},{5},{3,4},{2}] => [1,1,2,1] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 0 + 2
[{2},{1},{3,4},{5}] => [1,1,2,1] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 0 + 2
[{1,2},{3},{4},{5}] => [2,1,1,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[{1,2},{3},{5},{4}] => [2,1,1,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[{1,2},{4},{3},{5}] => [2,1,1,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[{1,2},{5},{3},{4}] => [2,1,1,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[{1,2},{4},{5},{3}] => [2,1,1,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[{1,2},{5},{4},{3}] => [2,1,1,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[{1,3},{2},{4},{5}] => [2,1,1,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[{1,3},{2},{5},{4}] => [2,1,1,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[{1,4},{2},{3},{5}] => [2,1,1,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[{1,5},{2},{3},{4}] => [2,1,1,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[{1,4},{2},{5},{3}] => [2,1,1,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[{1,5},{2},{4},{3}] => [2,1,1,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[{1,3},{4},{2},{5}] => [2,1,1,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[{1,3},{5},{2},{4}] => [2,1,1,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[{1,4},{3},{2},{5}] => [2,1,1,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[{1,5},{3},{2},{4}] => [2,1,1,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[{1,4},{5},{2},{3}] => [2,1,1,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[{1,5},{4},{2},{3}] => [2,1,1,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[{1,3},{4},{5},{2}] => [2,1,1,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[{1,3},{5},{4},{2}] => [2,1,1,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[{1,4},{3},{5},{2}] => [2,1,1,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[{1,5},{3},{4},{2}] => [2,1,1,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[{1,4},{5},{3},{2}] => [2,1,1,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[{1,5},{4},{3},{2}] => [2,1,1,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[{2,3},{1},{4},{5}] => [2,1,1,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[{2,3},{1},{5},{4}] => [2,1,1,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[{2,4},{1},{3},{5}] => [2,1,1,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[{2,5},{1},{3},{4}] => [2,1,1,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[{2,4},{1},{5},{3}] => [2,1,1,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[{2,5},{1},{4},{3}] => [2,1,1,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[{3,4},{1},{2},{5}] => [2,1,1,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[{3,5},{1},{2},{4}] => [2,1,1,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[{4,5},{1},{2},{3}] => [2,1,1,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[{3,4},{1},{5},{2}] => [2,1,1,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[{3,5},{1},{4},{2}] => [2,1,1,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[{4,5},{1},{3},{2}] => [2,1,1,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[{2,3},{4},{1},{5}] => [2,1,1,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[{2,3},{5},{1},{4}] => [2,1,1,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[{2,4},{3},{1},{5}] => [2,1,1,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[{2,5},{3},{1},{4}] => [2,1,1,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[{2,4},{5},{1},{3}] => [2,1,1,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[{2,5},{4},{1},{3}] => [2,1,1,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[{3,4},{2},{1},{5}] => [2,1,1,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[{3,5},{2},{1},{4}] => [2,1,1,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[{4,5},{2},{1},{3}] => [2,1,1,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[{3,4},{5},{1},{2}] => [2,1,1,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[{3,5},{4},{1},{2}] => [2,1,1,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[{4,5},{3},{1},{2}] => [2,1,1,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[{2,3},{4},{5},{1}] => [2,1,1,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[{2,3},{5},{4},{1}] => [2,1,1,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
Description
The largest eigenvalue of a graph if it is integral.
If a graph is $d$-regular, then its largest eigenvalue equals $d$. One can show that the largest eigenvalue always lies between the average degree and the maximal degree.
This statistic is undefined if the largest eigenvalue of the graph is not integral.
Matching statistic: St001645
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00287: Ordered set partitions —to composition⟶ Integer compositions
Mp00038: Integer compositions —reverse⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St001645: Graphs ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 25%
Mp00038: Integer compositions —reverse⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St001645: Graphs ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 25%
Values
[{1,2},{3}] => [2,1] => [1,2] => ([(1,2)],3)
=> ? = 0 + 6
[{1,3},{2}] => [2,1] => [1,2] => ([(1,2)],3)
=> ? = 0 + 6
[{2,3},{1}] => [2,1] => [1,2] => ([(1,2)],3)
=> ? = 0 + 6
[{1},{2,3},{4}] => [1,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 0 + 6
[{1},{2,4},{3}] => [1,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 0 + 6
[{1},{3,4},{2}] => [1,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 0 + 6
[{2},{1,3},{4}] => [1,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 0 + 6
[{2},{1,4},{3}] => [1,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 0 + 6
[{3},{1,2},{4}] => [1,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 0 + 6
[{4},{1,2},{3}] => [1,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 0 + 6
[{3},{1,4},{2}] => [1,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 0 + 6
[{4},{1,3},{2}] => [1,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 0 + 6
[{2},{3,4},{1}] => [1,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 0 + 6
[{3},{2,4},{1}] => [1,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 0 + 6
[{4},{2,3},{1}] => [1,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 0 + 6
[{1,2},{3},{4}] => [2,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
=> ? = 0 + 6
[{1,2},{4},{3}] => [2,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
=> ? = 0 + 6
[{1,3},{2},{4}] => [2,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
=> ? = 0 + 6
[{1,4},{2},{3}] => [2,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
=> ? = 0 + 6
[{1,3},{4},{2}] => [2,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
=> ? = 0 + 6
[{1,4},{3},{2}] => [2,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
=> ? = 0 + 6
[{2,3},{1},{4}] => [2,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
=> ? = 0 + 6
[{2,4},{1},{3}] => [2,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
=> ? = 0 + 6
[{3,4},{1},{2}] => [2,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
=> ? = 0 + 6
[{2,3},{4},{1}] => [2,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
=> ? = 0 + 6
[{2,4},{3},{1}] => [2,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
=> ? = 0 + 6
[{3,4},{2},{1}] => [2,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
=> ? = 0 + 6
[{1,2},{3,4}] => [2,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 6
[{1,3},{2,4}] => [2,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 6
[{1,4},{2,3}] => [2,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 6
[{2,3},{1,4}] => [2,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 6
[{2,4},{1,3}] => [2,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 6
[{3,4},{1,2}] => [2,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 6
[{1,2,3},{4}] => [3,1] => [1,3] => ([(2,3)],4)
=> ? = 0 + 6
[{1,2,4},{3}] => [3,1] => [1,3] => ([(2,3)],4)
=> ? = 0 + 6
[{1,3,4},{2}] => [3,1] => [1,3] => ([(2,3)],4)
=> ? = 0 + 6
[{2,3,4},{1}] => [3,1] => [1,3] => ([(2,3)],4)
=> ? = 0 + 6
[{1},{2},{3,4},{5}] => [1,1,2,1] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 6
[{1},{2},{3,5},{4}] => [1,1,2,1] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 6
[{1},{2},{4,5},{3}] => [1,1,2,1] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 6
[{1},{3},{2,4},{5}] => [1,1,2,1] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 6
[{1},{3},{2,5},{4}] => [1,1,2,1] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 6
[{1},{4},{2,3},{5}] => [1,1,2,1] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 6
[{1},{5},{2,3},{4}] => [1,1,2,1] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 6
[{1},{4},{2,5},{3}] => [1,1,2,1] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 6
[{1},{5},{2,4},{3}] => [1,1,2,1] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 6
[{1},{3},{4,5},{2}] => [1,1,2,1] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 6
[{1},{4},{3,5},{2}] => [1,1,2,1] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 6
[{1},{5},{3,4},{2}] => [1,1,2,1] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 6
[{2},{1},{3,4},{5}] => [1,1,2,1] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 6
[{1},{2},{3},{4,5},{6}] => [1,1,1,2,1] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 0 + 6
[{1},{2},{3},{4,6},{5}] => [1,1,1,2,1] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 0 + 6
[{1},{2},{3},{5,6},{4}] => [1,1,1,2,1] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 0 + 6
[{1},{2},{4},{3,5},{6}] => [1,1,1,2,1] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 0 + 6
[{1},{2},{4},{3,6},{5}] => [1,1,1,2,1] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 0 + 6
[{1},{2},{5},{3,4},{6}] => [1,1,1,2,1] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 0 + 6
[{1},{2},{6},{3,4},{5}] => [1,1,1,2,1] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 0 + 6
[{1},{2},{5},{3,6},{4}] => [1,1,1,2,1] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 0 + 6
[{1},{2},{6},{3,5},{4}] => [1,1,1,2,1] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 0 + 6
[{1},{2},{4},{5,6},{3}] => [1,1,1,2,1] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 0 + 6
[{1},{2},{5},{4,6},{3}] => [1,1,1,2,1] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 0 + 6
[{1},{2},{6},{4,5},{3}] => [1,1,1,2,1] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 0 + 6
[{1},{3},{2},{4,5},{6}] => [1,1,1,2,1] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 0 + 6
[{1},{3},{2},{4,6},{5}] => [1,1,1,2,1] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 0 + 6
[{1},{3},{2},{5,6},{4}] => [1,1,1,2,1] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 0 + 6
[{1},{4},{2},{3,5},{6}] => [1,1,1,2,1] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 0 + 6
[{1},{4},{2},{3,6},{5}] => [1,1,1,2,1] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 0 + 6
[{1},{5},{2},{3,4},{6}] => [1,1,1,2,1] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 0 + 6
[{1},{6},{2},{3,4},{5}] => [1,1,1,2,1] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 0 + 6
[{1},{5},{2},{3,6},{4}] => [1,1,1,2,1] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 0 + 6
[{1},{6},{2},{3,5},{4}] => [1,1,1,2,1] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 0 + 6
[{1},{4},{2},{5,6},{3}] => [1,1,1,2,1] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 0 + 6
[{1},{5},{2},{4,6},{3}] => [1,1,1,2,1] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 0 + 6
[{1},{6},{2},{4,5},{3}] => [1,1,1,2,1] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 0 + 6
[{1},{3},{4},{2,5},{6}] => [1,1,1,2,1] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 0 + 6
[{1},{3},{4},{2,6},{5}] => [1,1,1,2,1] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 0 + 6
[{1},{3},{5},{2,4},{6}] => [1,1,1,2,1] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 0 + 6
[{1},{3},{6},{2,4},{5}] => [1,1,1,2,1] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 0 + 6
[{1},{3},{5},{2,6},{4}] => [1,1,1,2,1] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 0 + 6
[{1},{3},{6},{2,5},{4}] => [1,1,1,2,1] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 0 + 6
[{1},{4},{3},{2,5},{6}] => [1,1,1,2,1] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 0 + 6
[{1},{4},{3},{2,6},{5}] => [1,1,1,2,1] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 0 + 6
[{1},{5},{3},{2,4},{6}] => [1,1,1,2,1] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 0 + 6
[{1},{6},{3},{2,4},{5}] => [1,1,1,2,1] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 0 + 6
[{1},{5},{3},{2,6},{4}] => [1,1,1,2,1] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 0 + 6
[{1},{6},{3},{2,5},{4}] => [1,1,1,2,1] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 0 + 6
[{1},{4},{5},{2,3},{6}] => [1,1,1,2,1] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 0 + 6
[{1},{4},{6},{2,3},{5}] => [1,1,1,2,1] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 0 + 6
[{1},{5},{4},{2,3},{6}] => [1,1,1,2,1] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 0 + 6
[{1},{6},{4},{2,3},{5}] => [1,1,1,2,1] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 0 + 6
[{1},{5},{6},{2,3},{4}] => [1,1,1,2,1] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 0 + 6
[{1},{6},{5},{2,3},{4}] => [1,1,1,2,1] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 0 + 6
[{1},{4},{5},{2,6},{3}] => [1,1,1,2,1] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 0 + 6
[{1},{4},{6},{2,5},{3}] => [1,1,1,2,1] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 0 + 6
[{1},{5},{4},{2,6},{3}] => [1,1,1,2,1] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 0 + 6
[{1},{6},{4},{2,5},{3}] => [1,1,1,2,1] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 0 + 6
[{1},{5},{6},{2,4},{3}] => [1,1,1,2,1] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 0 + 6
[{1},{6},{5},{2,4},{3}] => [1,1,1,2,1] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 0 + 6
[{1},{3},{4},{5,6},{2}] => [1,1,1,2,1] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 0 + 6
[{1},{3},{5},{4,6},{2}] => [1,1,1,2,1] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 0 + 6
Description
The pebbling number of a connected graph.
Matching statistic: St001771
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00286: Ordered set partitions —to permutation⟶ Permutations
Mp00069: Permutations —complement⟶ Permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
St001771: Signed permutations ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 25%
Mp00069: Permutations —complement⟶ Permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
St001771: Signed permutations ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 25%
Values
[{1,2},{3}] => [1,2,3] => [3,2,1] => [3,2,1] => 0
[{1,3},{2}] => [1,3,2] => [3,1,2] => [3,1,2] => 0
[{2,3},{1}] => [2,3,1] => [2,1,3] => [2,1,3] => 0
[{1},{2,3},{4}] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => 0
[{1},{2,4},{3}] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => 0
[{1},{3,4},{2}] => [1,3,4,2] => [4,2,1,3] => [4,2,1,3] => 0
[{2},{1,3},{4}] => [2,1,3,4] => [3,4,2,1] => [3,4,2,1] => 0
[{2},{1,4},{3}] => [2,1,4,3] => [3,4,1,2] => [3,4,1,2] => 0
[{3},{1,2},{4}] => [3,1,2,4] => [2,4,3,1] => [2,4,3,1] => 0
[{4},{1,2},{3}] => [4,1,2,3] => [1,4,3,2] => [1,4,3,2] => 0
[{3},{1,4},{2}] => [3,1,4,2] => [2,4,1,3] => [2,4,1,3] => 0
[{4},{1,3},{2}] => [4,1,3,2] => [1,4,2,3] => [1,4,2,3] => 0
[{2},{3,4},{1}] => [2,3,4,1] => [3,2,1,4] => [3,2,1,4] => 0
[{3},{2,4},{1}] => [3,2,4,1] => [2,3,1,4] => [2,3,1,4] => 0
[{4},{2,3},{1}] => [4,2,3,1] => [1,3,2,4] => [1,3,2,4] => 0
[{1,2},{3},{4}] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => 0
[{1,2},{4},{3}] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => 0
[{1,3},{2},{4}] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => 0
[{1,4},{2},{3}] => [1,4,2,3] => [4,1,3,2] => [4,1,3,2] => 0
[{1,3},{4},{2}] => [1,3,4,2] => [4,2,1,3] => [4,2,1,3] => 0
[{1,4},{3},{2}] => [1,4,3,2] => [4,1,2,3] => [4,1,2,3] => 0
[{2,3},{1},{4}] => [2,3,1,4] => [3,2,4,1] => [3,2,4,1] => 0
[{2,4},{1},{3}] => [2,4,1,3] => [3,1,4,2] => [3,1,4,2] => 0
[{3,4},{1},{2}] => [3,4,1,2] => [2,1,4,3] => [2,1,4,3] => 0
[{2,3},{4},{1}] => [2,3,4,1] => [3,2,1,4] => [3,2,1,4] => 0
[{2,4},{3},{1}] => [2,4,3,1] => [3,1,2,4] => [3,1,2,4] => 0
[{3,4},{2},{1}] => [3,4,2,1] => [2,1,3,4] => [2,1,3,4] => 0
[{1,2},{3,4}] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => 0
[{1,3},{2,4}] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => 0
[{1,4},{2,3}] => [1,4,2,3] => [4,1,3,2] => [4,1,3,2] => 0
[{2,3},{1,4}] => [2,3,1,4] => [3,2,4,1] => [3,2,4,1] => 0
[{2,4},{1,3}] => [2,4,1,3] => [3,1,4,2] => [3,1,4,2] => 0
[{3,4},{1,2}] => [3,4,1,2] => [2,1,4,3] => [2,1,4,3] => 0
[{1,2,3},{4}] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => 0
[{1,2,4},{3}] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => 0
[{1,3,4},{2}] => [1,3,4,2] => [4,2,1,3] => [4,2,1,3] => 0
[{2,3,4},{1}] => [2,3,4,1] => [3,2,1,4] => [3,2,1,4] => 0
[{1},{2},{3,4},{5}] => [1,2,3,4,5] => [5,4,3,2,1] => [5,4,3,2,1] => ? = 0
[{1},{2},{3,5},{4}] => [1,2,3,5,4] => [5,4,3,1,2] => [5,4,3,1,2] => ? = 0
[{1},{2},{4,5},{3}] => [1,2,4,5,3] => [5,4,2,1,3] => [5,4,2,1,3] => ? = 0
[{1},{3},{2,4},{5}] => [1,3,2,4,5] => [5,3,4,2,1] => [5,3,4,2,1] => ? = 0
[{1},{3},{2,5},{4}] => [1,3,2,5,4] => [5,3,4,1,2] => [5,3,4,1,2] => ? = 0
[{1},{4},{2,3},{5}] => [1,4,2,3,5] => [5,2,4,3,1] => [5,2,4,3,1] => ? = 0
[{1},{5},{2,3},{4}] => [1,5,2,3,4] => [5,1,4,3,2] => [5,1,4,3,2] => ? = 0
[{1},{4},{2,5},{3}] => [1,4,2,5,3] => [5,2,4,1,3] => [5,2,4,1,3] => ? = 0
[{1},{5},{2,4},{3}] => [1,5,2,4,3] => [5,1,4,2,3] => [5,1,4,2,3] => ? = 0
[{1},{3},{4,5},{2}] => [1,3,4,5,2] => [5,3,2,1,4] => [5,3,2,1,4] => ? = 0
[{1},{4},{3,5},{2}] => [1,4,3,5,2] => [5,2,3,1,4] => [5,2,3,1,4] => ? = 0
[{1},{5},{3,4},{2}] => [1,5,3,4,2] => [5,1,3,2,4] => [5,1,3,2,4] => ? = 0
[{2},{1},{3,4},{5}] => [2,1,3,4,5] => [4,5,3,2,1] => [4,5,3,2,1] => ? = 0
[{2},{1},{3,5},{4}] => [2,1,3,5,4] => [4,5,3,1,2] => [4,5,3,1,2] => ? = 0
[{2},{1},{4,5},{3}] => [2,1,4,5,3] => [4,5,2,1,3] => [4,5,2,1,3] => ? = 0
[{3},{1},{2,4},{5}] => [3,1,2,4,5] => [3,5,4,2,1] => [3,5,4,2,1] => ? = 0
[{3},{1},{2,5},{4}] => [3,1,2,5,4] => [3,5,4,1,2] => [3,5,4,1,2] => ? = 0
[{4},{1},{2,3},{5}] => [4,1,2,3,5] => [2,5,4,3,1] => [2,5,4,3,1] => ? = 0
[{5},{1},{2,3},{4}] => [5,1,2,3,4] => [1,5,4,3,2] => [1,5,4,3,2] => 0
[{4},{1},{2,5},{3}] => [4,1,2,5,3] => [2,5,4,1,3] => [2,5,4,1,3] => ? = 0
[{5},{1},{2,4},{3}] => [5,1,2,4,3] => [1,5,4,2,3] => [1,5,4,2,3] => 0
[{3},{1},{4,5},{2}] => [3,1,4,5,2] => [3,5,2,1,4] => [3,5,2,1,4] => ? = 0
[{4},{1},{3,5},{2}] => [4,1,3,5,2] => [2,5,3,1,4] => [2,5,3,1,4] => ? = 0
[{5},{1},{3,4},{2}] => [5,1,3,4,2] => [1,5,3,2,4] => [1,5,3,2,4] => 0
[{2},{3},{1,4},{5}] => [2,3,1,4,5] => [4,3,5,2,1] => [4,3,5,2,1] => ? = 0
[{2},{3},{1,5},{4}] => [2,3,1,5,4] => [4,3,5,1,2] => [4,3,5,1,2] => ? = 0
[{2},{4},{1,3},{5}] => [2,4,1,3,5] => [4,2,5,3,1] => [4,2,5,3,1] => ? = 0
[{2},{5},{1,3},{4}] => [2,5,1,3,4] => [4,1,5,3,2] => [4,1,5,3,2] => ? = 0
[{2},{4},{1,5},{3}] => [2,4,1,5,3] => [4,2,5,1,3] => [4,2,5,1,3] => ? = 0
[{2},{5},{1,4},{3}] => [2,5,1,4,3] => [4,1,5,2,3] => [4,1,5,2,3] => ? = 0
[{3},{2},{1,4},{5}] => [3,2,1,4,5] => [3,4,5,2,1] => [3,4,5,2,1] => ? = 0
[{3},{2},{1,5},{4}] => [3,2,1,5,4] => [3,4,5,1,2] => [3,4,5,1,2] => ? = 0
[{4},{2},{1,3},{5}] => [4,2,1,3,5] => [2,4,5,3,1] => [2,4,5,3,1] => ? = 0
[{5},{2},{1,3},{4}] => [5,2,1,3,4] => [1,4,5,3,2] => [1,4,5,3,2] => 0
[{4},{2},{1,5},{3}] => [4,2,1,5,3] => [2,4,5,1,3] => [2,4,5,1,3] => ? = 0
[{5},{2},{1,4},{3}] => [5,2,1,4,3] => [1,4,5,2,3] => [1,4,5,2,3] => 0
[{3},{4},{1,2},{5}] => [3,4,1,2,5] => [3,2,5,4,1] => [3,2,5,4,1] => ? = 0
[{3},{5},{1,2},{4}] => [3,5,1,2,4] => [3,1,5,4,2] => [3,1,5,4,2] => ? = 0
[{4},{3},{1,2},{5}] => [4,3,1,2,5] => [2,3,5,4,1] => [2,3,5,4,1] => ? = 0
[{5},{3},{1,2},{4}] => [5,3,1,2,4] => [1,3,5,4,2] => [1,3,5,4,2] => 0
[{4},{5},{1,2},{3}] => [4,5,1,2,3] => [2,1,5,4,3] => [2,1,5,4,3] => ? = 0
[{5},{4},{1,2},{3}] => [5,4,1,2,3] => [1,2,5,4,3] => [1,2,5,4,3] => 0
[{3},{4},{1,5},{2}] => [3,4,1,5,2] => [3,2,5,1,4] => [3,2,5,1,4] => ? = 0
[{3},{5},{1,4},{2}] => [3,5,1,4,2] => [3,1,5,2,4] => [3,1,5,2,4] => ? = 0
[{4},{3},{1,5},{2}] => [4,3,1,5,2] => [2,3,5,1,4] => [2,3,5,1,4] => ? = 0
[{5},{3},{1,4},{2}] => [5,3,1,4,2] => [1,3,5,2,4] => [1,3,5,2,4] => 0
[{4},{5},{1,3},{2}] => [4,5,1,3,2] => [2,1,5,3,4] => [2,1,5,3,4] => ? = 0
[{5},{4},{1,3},{2}] => [5,4,1,3,2] => [1,2,5,3,4] => [1,2,5,3,4] => 0
[{2},{3},{4,5},{1}] => [2,3,4,5,1] => [4,3,2,1,5] => [4,3,2,1,5] => ? = 0
[{2},{4},{3,5},{1}] => [2,4,3,5,1] => [4,2,3,1,5] => [4,2,3,1,5] => ? = 0
[{2},{5},{3,4},{1}] => [2,5,3,4,1] => [4,1,3,2,5] => [4,1,3,2,5] => ? = 0
[{3},{2},{4,5},{1}] => [3,2,4,5,1] => [3,4,2,1,5] => [3,4,2,1,5] => ? = 0
[{4},{2},{3,5},{1}] => [4,2,3,5,1] => [2,4,3,1,5] => [2,4,3,1,5] => ? = 0
[{5},{2},{3,4},{1}] => [5,2,3,4,1] => [1,4,3,2,5] => [1,4,3,2,5] => 0
[{3},{4},{2,5},{1}] => [3,4,2,5,1] => [3,2,4,1,5] => [3,2,4,1,5] => ? = 0
[{3},{5},{2,4},{1}] => [3,5,2,4,1] => [3,1,4,2,5] => [3,1,4,2,5] => ? = 0
[{4},{3},{2,5},{1}] => [4,3,2,5,1] => [2,3,4,1,5] => [2,3,4,1,5] => ? = 0
[{5},{3},{2,4},{1}] => [5,3,2,4,1] => [1,3,4,2,5] => [1,3,4,2,5] => 0
[{4},{5},{2,3},{1}] => [4,5,2,3,1] => [2,1,4,3,5] => [2,1,4,3,5] => ? = 0
[{5},{4},{2,3},{1}] => [5,4,2,3,1] => [1,2,4,3,5] => [1,2,4,3,5] => 0
[{1},{2,3},{4},{5}] => [1,2,3,4,5] => [5,4,3,2,1] => [5,4,3,2,1] => ? = 0
[{1},{2,3},{5},{4}] => [1,2,3,5,4] => [5,4,3,1,2] => [5,4,3,1,2] => ? = 0
[{5},{1,2},{3},{4}] => [5,1,2,3,4] => [1,5,4,3,2] => [1,5,4,3,2] => 0
Description
The number of occurrences of the signed pattern 1-2 in a signed permutation.
This is the number of pairs $1\leq i < j\leq n$ such that $0 < \pi(i) < -\pi(j)$.
Matching statistic: St001870
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00286: Ordered set partitions —to permutation⟶ Permutations
Mp00069: Permutations —complement⟶ Permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
St001870: Signed permutations ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 25%
Mp00069: Permutations —complement⟶ Permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
St001870: Signed permutations ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 25%
Values
[{1,2},{3}] => [1,2,3] => [3,2,1] => [3,2,1] => 0
[{1,3},{2}] => [1,3,2] => [3,1,2] => [3,1,2] => 0
[{2,3},{1}] => [2,3,1] => [2,1,3] => [2,1,3] => 0
[{1},{2,3},{4}] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => 0
[{1},{2,4},{3}] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => 0
[{1},{3,4},{2}] => [1,3,4,2] => [4,2,1,3] => [4,2,1,3] => 0
[{2},{1,3},{4}] => [2,1,3,4] => [3,4,2,1] => [3,4,2,1] => 0
[{2},{1,4},{3}] => [2,1,4,3] => [3,4,1,2] => [3,4,1,2] => 0
[{3},{1,2},{4}] => [3,1,2,4] => [2,4,3,1] => [2,4,3,1] => 0
[{4},{1,2},{3}] => [4,1,2,3] => [1,4,3,2] => [1,4,3,2] => 0
[{3},{1,4},{2}] => [3,1,4,2] => [2,4,1,3] => [2,4,1,3] => 0
[{4},{1,3},{2}] => [4,1,3,2] => [1,4,2,3] => [1,4,2,3] => 0
[{2},{3,4},{1}] => [2,3,4,1] => [3,2,1,4] => [3,2,1,4] => 0
[{3},{2,4},{1}] => [3,2,4,1] => [2,3,1,4] => [2,3,1,4] => 0
[{4},{2,3},{1}] => [4,2,3,1] => [1,3,2,4] => [1,3,2,4] => 0
[{1,2},{3},{4}] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => 0
[{1,2},{4},{3}] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => 0
[{1,3},{2},{4}] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => 0
[{1,4},{2},{3}] => [1,4,2,3] => [4,1,3,2] => [4,1,3,2] => 0
[{1,3},{4},{2}] => [1,3,4,2] => [4,2,1,3] => [4,2,1,3] => 0
[{1,4},{3},{2}] => [1,4,3,2] => [4,1,2,3] => [4,1,2,3] => 0
[{2,3},{1},{4}] => [2,3,1,4] => [3,2,4,1] => [3,2,4,1] => 0
[{2,4},{1},{3}] => [2,4,1,3] => [3,1,4,2] => [3,1,4,2] => 0
[{3,4},{1},{2}] => [3,4,1,2] => [2,1,4,3] => [2,1,4,3] => 0
[{2,3},{4},{1}] => [2,3,4,1] => [3,2,1,4] => [3,2,1,4] => 0
[{2,4},{3},{1}] => [2,4,3,1] => [3,1,2,4] => [3,1,2,4] => 0
[{3,4},{2},{1}] => [3,4,2,1] => [2,1,3,4] => [2,1,3,4] => 0
[{1,2},{3,4}] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => 0
[{1,3},{2,4}] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => 0
[{1,4},{2,3}] => [1,4,2,3] => [4,1,3,2] => [4,1,3,2] => 0
[{2,3},{1,4}] => [2,3,1,4] => [3,2,4,1] => [3,2,4,1] => 0
[{2,4},{1,3}] => [2,4,1,3] => [3,1,4,2] => [3,1,4,2] => 0
[{3,4},{1,2}] => [3,4,1,2] => [2,1,4,3] => [2,1,4,3] => 0
[{1,2,3},{4}] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => 0
[{1,2,4},{3}] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => 0
[{1,3,4},{2}] => [1,3,4,2] => [4,2,1,3] => [4,2,1,3] => 0
[{2,3,4},{1}] => [2,3,4,1] => [3,2,1,4] => [3,2,1,4] => 0
[{1},{2},{3,4},{5}] => [1,2,3,4,5] => [5,4,3,2,1] => [5,4,3,2,1] => ? = 0
[{1},{2},{3,5},{4}] => [1,2,3,5,4] => [5,4,3,1,2] => [5,4,3,1,2] => ? = 0
[{1},{2},{4,5},{3}] => [1,2,4,5,3] => [5,4,2,1,3] => [5,4,2,1,3] => ? = 0
[{1},{3},{2,4},{5}] => [1,3,2,4,5] => [5,3,4,2,1] => [5,3,4,2,1] => ? = 0
[{1},{3},{2,5},{4}] => [1,3,2,5,4] => [5,3,4,1,2] => [5,3,4,1,2] => ? = 0
[{1},{4},{2,3},{5}] => [1,4,2,3,5] => [5,2,4,3,1] => [5,2,4,3,1] => ? = 0
[{1},{5},{2,3},{4}] => [1,5,2,3,4] => [5,1,4,3,2] => [5,1,4,3,2] => ? = 0
[{1},{4},{2,5},{3}] => [1,4,2,5,3] => [5,2,4,1,3] => [5,2,4,1,3] => ? = 0
[{1},{5},{2,4},{3}] => [1,5,2,4,3] => [5,1,4,2,3] => [5,1,4,2,3] => ? = 0
[{1},{3},{4,5},{2}] => [1,3,4,5,2] => [5,3,2,1,4] => [5,3,2,1,4] => ? = 0
[{1},{4},{3,5},{2}] => [1,4,3,5,2] => [5,2,3,1,4] => [5,2,3,1,4] => ? = 0
[{1},{5},{3,4},{2}] => [1,5,3,4,2] => [5,1,3,2,4] => [5,1,3,2,4] => ? = 0
[{2},{1},{3,4},{5}] => [2,1,3,4,5] => [4,5,3,2,1] => [4,5,3,2,1] => ? = 0
[{2},{1},{3,5},{4}] => [2,1,3,5,4] => [4,5,3,1,2] => [4,5,3,1,2] => ? = 0
[{2},{1},{4,5},{3}] => [2,1,4,5,3] => [4,5,2,1,3] => [4,5,2,1,3] => ? = 0
[{3},{1},{2,4},{5}] => [3,1,2,4,5] => [3,5,4,2,1] => [3,5,4,2,1] => ? = 0
[{3},{1},{2,5},{4}] => [3,1,2,5,4] => [3,5,4,1,2] => [3,5,4,1,2] => ? = 0
[{4},{1},{2,3},{5}] => [4,1,2,3,5] => [2,5,4,3,1] => [2,5,4,3,1] => ? = 0
[{5},{1},{2,3},{4}] => [5,1,2,3,4] => [1,5,4,3,2] => [1,5,4,3,2] => 0
[{4},{1},{2,5},{3}] => [4,1,2,5,3] => [2,5,4,1,3] => [2,5,4,1,3] => ? = 0
[{5},{1},{2,4},{3}] => [5,1,2,4,3] => [1,5,4,2,3] => [1,5,4,2,3] => 0
[{3},{1},{4,5},{2}] => [3,1,4,5,2] => [3,5,2,1,4] => [3,5,2,1,4] => ? = 0
[{4},{1},{3,5},{2}] => [4,1,3,5,2] => [2,5,3,1,4] => [2,5,3,1,4] => ? = 0
[{5},{1},{3,4},{2}] => [5,1,3,4,2] => [1,5,3,2,4] => [1,5,3,2,4] => 0
[{2},{3},{1,4},{5}] => [2,3,1,4,5] => [4,3,5,2,1] => [4,3,5,2,1] => ? = 0
[{2},{3},{1,5},{4}] => [2,3,1,5,4] => [4,3,5,1,2] => [4,3,5,1,2] => ? = 0
[{2},{4},{1,3},{5}] => [2,4,1,3,5] => [4,2,5,3,1] => [4,2,5,3,1] => ? = 0
[{2},{5},{1,3},{4}] => [2,5,1,3,4] => [4,1,5,3,2] => [4,1,5,3,2] => ? = 0
[{2},{4},{1,5},{3}] => [2,4,1,5,3] => [4,2,5,1,3] => [4,2,5,1,3] => ? = 0
[{2},{5},{1,4},{3}] => [2,5,1,4,3] => [4,1,5,2,3] => [4,1,5,2,3] => ? = 0
[{3},{2},{1,4},{5}] => [3,2,1,4,5] => [3,4,5,2,1] => [3,4,5,2,1] => ? = 0
[{3},{2},{1,5},{4}] => [3,2,1,5,4] => [3,4,5,1,2] => [3,4,5,1,2] => ? = 0
[{4},{2},{1,3},{5}] => [4,2,1,3,5] => [2,4,5,3,1] => [2,4,5,3,1] => ? = 0
[{5},{2},{1,3},{4}] => [5,2,1,3,4] => [1,4,5,3,2] => [1,4,5,3,2] => 0
[{4},{2},{1,5},{3}] => [4,2,1,5,3] => [2,4,5,1,3] => [2,4,5,1,3] => ? = 0
[{5},{2},{1,4},{3}] => [5,2,1,4,3] => [1,4,5,2,3] => [1,4,5,2,3] => 0
[{3},{4},{1,2},{5}] => [3,4,1,2,5] => [3,2,5,4,1] => [3,2,5,4,1] => ? = 0
[{3},{5},{1,2},{4}] => [3,5,1,2,4] => [3,1,5,4,2] => [3,1,5,4,2] => ? = 0
[{4},{3},{1,2},{5}] => [4,3,1,2,5] => [2,3,5,4,1] => [2,3,5,4,1] => ? = 0
[{5},{3},{1,2},{4}] => [5,3,1,2,4] => [1,3,5,4,2] => [1,3,5,4,2] => 0
[{4},{5},{1,2},{3}] => [4,5,1,2,3] => [2,1,5,4,3] => [2,1,5,4,3] => ? = 0
[{5},{4},{1,2},{3}] => [5,4,1,2,3] => [1,2,5,4,3] => [1,2,5,4,3] => 0
[{3},{4},{1,5},{2}] => [3,4,1,5,2] => [3,2,5,1,4] => [3,2,5,1,4] => ? = 0
[{3},{5},{1,4},{2}] => [3,5,1,4,2] => [3,1,5,2,4] => [3,1,5,2,4] => ? = 0
[{4},{3},{1,5},{2}] => [4,3,1,5,2] => [2,3,5,1,4] => [2,3,5,1,4] => ? = 0
[{5},{3},{1,4},{2}] => [5,3,1,4,2] => [1,3,5,2,4] => [1,3,5,2,4] => 0
[{4},{5},{1,3},{2}] => [4,5,1,3,2] => [2,1,5,3,4] => [2,1,5,3,4] => ? = 0
[{5},{4},{1,3},{2}] => [5,4,1,3,2] => [1,2,5,3,4] => [1,2,5,3,4] => 0
[{2},{3},{4,5},{1}] => [2,3,4,5,1] => [4,3,2,1,5] => [4,3,2,1,5] => ? = 0
[{2},{4},{3,5},{1}] => [2,4,3,5,1] => [4,2,3,1,5] => [4,2,3,1,5] => ? = 0
[{2},{5},{3,4},{1}] => [2,5,3,4,1] => [4,1,3,2,5] => [4,1,3,2,5] => ? = 0
[{3},{2},{4,5},{1}] => [3,2,4,5,1] => [3,4,2,1,5] => [3,4,2,1,5] => ? = 0
[{4},{2},{3,5},{1}] => [4,2,3,5,1] => [2,4,3,1,5] => [2,4,3,1,5] => ? = 0
[{5},{2},{3,4},{1}] => [5,2,3,4,1] => [1,4,3,2,5] => [1,4,3,2,5] => 0
[{3},{4},{2,5},{1}] => [3,4,2,5,1] => [3,2,4,1,5] => [3,2,4,1,5] => ? = 0
[{3},{5},{2,4},{1}] => [3,5,2,4,1] => [3,1,4,2,5] => [3,1,4,2,5] => ? = 0
[{4},{3},{2,5},{1}] => [4,3,2,5,1] => [2,3,4,1,5] => [2,3,4,1,5] => ? = 0
[{5},{3},{2,4},{1}] => [5,3,2,4,1] => [1,3,4,2,5] => [1,3,4,2,5] => 0
[{4},{5},{2,3},{1}] => [4,5,2,3,1] => [2,1,4,3,5] => [2,1,4,3,5] => ? = 0
[{5},{4},{2,3},{1}] => [5,4,2,3,1] => [1,2,4,3,5] => [1,2,4,3,5] => 0
[{1},{2,3},{4},{5}] => [1,2,3,4,5] => [5,4,3,2,1] => [5,4,3,2,1] => ? = 0
[{1},{2,3},{5},{4}] => [1,2,3,5,4] => [5,4,3,1,2] => [5,4,3,1,2] => ? = 0
[{5},{1,2},{3},{4}] => [5,1,2,3,4] => [1,5,4,3,2] => [1,5,4,3,2] => 0
Description
The number of positive entries followed by a negative entry in a signed permutation.
For a signed permutation $\pi\in\mathfrak H_n$, this is the number of positive entries followed by a negative entry in $\pi(-n),\dots,\pi(-1),\pi(1),\dots,\pi(n)$.
Matching statistic: St001895
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00286: Ordered set partitions —to permutation⟶ Permutations
Mp00069: Permutations —complement⟶ Permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
St001895: Signed permutations ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 25%
Mp00069: Permutations —complement⟶ Permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
St001895: Signed permutations ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 25%
Values
[{1,2},{3}] => [1,2,3] => [3,2,1] => [3,2,1] => 0
[{1,3},{2}] => [1,3,2] => [3,1,2] => [3,1,2] => 0
[{2,3},{1}] => [2,3,1] => [2,1,3] => [2,1,3] => 0
[{1},{2,3},{4}] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => 0
[{1},{2,4},{3}] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => 0
[{1},{3,4},{2}] => [1,3,4,2] => [4,2,1,3] => [4,2,1,3] => 0
[{2},{1,3},{4}] => [2,1,3,4] => [3,4,2,1] => [3,4,2,1] => 0
[{2},{1,4},{3}] => [2,1,4,3] => [3,4,1,2] => [3,4,1,2] => 0
[{3},{1,2},{4}] => [3,1,2,4] => [2,4,3,1] => [2,4,3,1] => 0
[{4},{1,2},{3}] => [4,1,2,3] => [1,4,3,2] => [1,4,3,2] => 0
[{3},{1,4},{2}] => [3,1,4,2] => [2,4,1,3] => [2,4,1,3] => 0
[{4},{1,3},{2}] => [4,1,3,2] => [1,4,2,3] => [1,4,2,3] => 0
[{2},{3,4},{1}] => [2,3,4,1] => [3,2,1,4] => [3,2,1,4] => 0
[{3},{2,4},{1}] => [3,2,4,1] => [2,3,1,4] => [2,3,1,4] => 0
[{4},{2,3},{1}] => [4,2,3,1] => [1,3,2,4] => [1,3,2,4] => 0
[{1,2},{3},{4}] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => 0
[{1,2},{4},{3}] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => 0
[{1,3},{2},{4}] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => 0
[{1,4},{2},{3}] => [1,4,2,3] => [4,1,3,2] => [4,1,3,2] => 0
[{1,3},{4},{2}] => [1,3,4,2] => [4,2,1,3] => [4,2,1,3] => 0
[{1,4},{3},{2}] => [1,4,3,2] => [4,1,2,3] => [4,1,2,3] => 0
[{2,3},{1},{4}] => [2,3,1,4] => [3,2,4,1] => [3,2,4,1] => 0
[{2,4},{1},{3}] => [2,4,1,3] => [3,1,4,2] => [3,1,4,2] => 0
[{3,4},{1},{2}] => [3,4,1,2] => [2,1,4,3] => [2,1,4,3] => 0
[{2,3},{4},{1}] => [2,3,4,1] => [3,2,1,4] => [3,2,1,4] => 0
[{2,4},{3},{1}] => [2,4,3,1] => [3,1,2,4] => [3,1,2,4] => 0
[{3,4},{2},{1}] => [3,4,2,1] => [2,1,3,4] => [2,1,3,4] => 0
[{1,2},{3,4}] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => 0
[{1,3},{2,4}] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => 0
[{1,4},{2,3}] => [1,4,2,3] => [4,1,3,2] => [4,1,3,2] => 0
[{2,3},{1,4}] => [2,3,1,4] => [3,2,4,1] => [3,2,4,1] => 0
[{2,4},{1,3}] => [2,4,1,3] => [3,1,4,2] => [3,1,4,2] => 0
[{3,4},{1,2}] => [3,4,1,2] => [2,1,4,3] => [2,1,4,3] => 0
[{1,2,3},{4}] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => 0
[{1,2,4},{3}] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => 0
[{1,3,4},{2}] => [1,3,4,2] => [4,2,1,3] => [4,2,1,3] => 0
[{2,3,4},{1}] => [2,3,4,1] => [3,2,1,4] => [3,2,1,4] => 0
[{1},{2},{3,4},{5}] => [1,2,3,4,5] => [5,4,3,2,1] => [5,4,3,2,1] => ? = 0
[{1},{2},{3,5},{4}] => [1,2,3,5,4] => [5,4,3,1,2] => [5,4,3,1,2] => ? = 0
[{1},{2},{4,5},{3}] => [1,2,4,5,3] => [5,4,2,1,3] => [5,4,2,1,3] => ? = 0
[{1},{3},{2,4},{5}] => [1,3,2,4,5] => [5,3,4,2,1] => [5,3,4,2,1] => ? = 0
[{1},{3},{2,5},{4}] => [1,3,2,5,4] => [5,3,4,1,2] => [5,3,4,1,2] => ? = 0
[{1},{4},{2,3},{5}] => [1,4,2,3,5] => [5,2,4,3,1] => [5,2,4,3,1] => ? = 0
[{1},{5},{2,3},{4}] => [1,5,2,3,4] => [5,1,4,3,2] => [5,1,4,3,2] => ? = 0
[{1},{4},{2,5},{3}] => [1,4,2,5,3] => [5,2,4,1,3] => [5,2,4,1,3] => ? = 0
[{1},{5},{2,4},{3}] => [1,5,2,4,3] => [5,1,4,2,3] => [5,1,4,2,3] => ? = 0
[{1},{3},{4,5},{2}] => [1,3,4,5,2] => [5,3,2,1,4] => [5,3,2,1,4] => ? = 0
[{1},{4},{3,5},{2}] => [1,4,3,5,2] => [5,2,3,1,4] => [5,2,3,1,4] => ? = 0
[{1},{5},{3,4},{2}] => [1,5,3,4,2] => [5,1,3,2,4] => [5,1,3,2,4] => ? = 0
[{2},{1},{3,4},{5}] => [2,1,3,4,5] => [4,5,3,2,1] => [4,5,3,2,1] => ? = 0
[{2},{1},{3,5},{4}] => [2,1,3,5,4] => [4,5,3,1,2] => [4,5,3,1,2] => ? = 0
[{2},{1},{4,5},{3}] => [2,1,4,5,3] => [4,5,2,1,3] => [4,5,2,1,3] => ? = 0
[{3},{1},{2,4},{5}] => [3,1,2,4,5] => [3,5,4,2,1] => [3,5,4,2,1] => ? = 0
[{3},{1},{2,5},{4}] => [3,1,2,5,4] => [3,5,4,1,2] => [3,5,4,1,2] => ? = 0
[{4},{1},{2,3},{5}] => [4,1,2,3,5] => [2,5,4,3,1] => [2,5,4,3,1] => ? = 0
[{5},{1},{2,3},{4}] => [5,1,2,3,4] => [1,5,4,3,2] => [1,5,4,3,2] => 0
[{4},{1},{2,5},{3}] => [4,1,2,5,3] => [2,5,4,1,3] => [2,5,4,1,3] => ? = 0
[{5},{1},{2,4},{3}] => [5,1,2,4,3] => [1,5,4,2,3] => [1,5,4,2,3] => 0
[{3},{1},{4,5},{2}] => [3,1,4,5,2] => [3,5,2,1,4] => [3,5,2,1,4] => ? = 0
[{4},{1},{3,5},{2}] => [4,1,3,5,2] => [2,5,3,1,4] => [2,5,3,1,4] => ? = 0
[{5},{1},{3,4},{2}] => [5,1,3,4,2] => [1,5,3,2,4] => [1,5,3,2,4] => 0
[{2},{3},{1,4},{5}] => [2,3,1,4,5] => [4,3,5,2,1] => [4,3,5,2,1] => ? = 0
[{2},{3},{1,5},{4}] => [2,3,1,5,4] => [4,3,5,1,2] => [4,3,5,1,2] => ? = 0
[{2},{4},{1,3},{5}] => [2,4,1,3,5] => [4,2,5,3,1] => [4,2,5,3,1] => ? = 0
[{2},{5},{1,3},{4}] => [2,5,1,3,4] => [4,1,5,3,2] => [4,1,5,3,2] => ? = 0
[{2},{4},{1,5},{3}] => [2,4,1,5,3] => [4,2,5,1,3] => [4,2,5,1,3] => ? = 0
[{2},{5},{1,4},{3}] => [2,5,1,4,3] => [4,1,5,2,3] => [4,1,5,2,3] => ? = 0
[{3},{2},{1,4},{5}] => [3,2,1,4,5] => [3,4,5,2,1] => [3,4,5,2,1] => ? = 0
[{3},{2},{1,5},{4}] => [3,2,1,5,4] => [3,4,5,1,2] => [3,4,5,1,2] => ? = 0
[{4},{2},{1,3},{5}] => [4,2,1,3,5] => [2,4,5,3,1] => [2,4,5,3,1] => ? = 0
[{5},{2},{1,3},{4}] => [5,2,1,3,4] => [1,4,5,3,2] => [1,4,5,3,2] => 0
[{4},{2},{1,5},{3}] => [4,2,1,5,3] => [2,4,5,1,3] => [2,4,5,1,3] => ? = 0
[{5},{2},{1,4},{3}] => [5,2,1,4,3] => [1,4,5,2,3] => [1,4,5,2,3] => 0
[{3},{4},{1,2},{5}] => [3,4,1,2,5] => [3,2,5,4,1] => [3,2,5,4,1] => ? = 0
[{3},{5},{1,2},{4}] => [3,5,1,2,4] => [3,1,5,4,2] => [3,1,5,4,2] => ? = 0
[{4},{3},{1,2},{5}] => [4,3,1,2,5] => [2,3,5,4,1] => [2,3,5,4,1] => ? = 0
[{5},{3},{1,2},{4}] => [5,3,1,2,4] => [1,3,5,4,2] => [1,3,5,4,2] => 0
[{4},{5},{1,2},{3}] => [4,5,1,2,3] => [2,1,5,4,3] => [2,1,5,4,3] => ? = 0
[{5},{4},{1,2},{3}] => [5,4,1,2,3] => [1,2,5,4,3] => [1,2,5,4,3] => 0
[{3},{4},{1,5},{2}] => [3,4,1,5,2] => [3,2,5,1,4] => [3,2,5,1,4] => ? = 0
[{3},{5},{1,4},{2}] => [3,5,1,4,2] => [3,1,5,2,4] => [3,1,5,2,4] => ? = 0
[{4},{3},{1,5},{2}] => [4,3,1,5,2] => [2,3,5,1,4] => [2,3,5,1,4] => ? = 0
[{5},{3},{1,4},{2}] => [5,3,1,4,2] => [1,3,5,2,4] => [1,3,5,2,4] => 0
[{4},{5},{1,3},{2}] => [4,5,1,3,2] => [2,1,5,3,4] => [2,1,5,3,4] => ? = 0
[{5},{4},{1,3},{2}] => [5,4,1,3,2] => [1,2,5,3,4] => [1,2,5,3,4] => 0
[{2},{3},{4,5},{1}] => [2,3,4,5,1] => [4,3,2,1,5] => [4,3,2,1,5] => ? = 0
[{2},{4},{3,5},{1}] => [2,4,3,5,1] => [4,2,3,1,5] => [4,2,3,1,5] => ? = 0
[{2},{5},{3,4},{1}] => [2,5,3,4,1] => [4,1,3,2,5] => [4,1,3,2,5] => ? = 0
[{3},{2},{4,5},{1}] => [3,2,4,5,1] => [3,4,2,1,5] => [3,4,2,1,5] => ? = 0
[{4},{2},{3,5},{1}] => [4,2,3,5,1] => [2,4,3,1,5] => [2,4,3,1,5] => ? = 0
[{5},{2},{3,4},{1}] => [5,2,3,4,1] => [1,4,3,2,5] => [1,4,3,2,5] => 0
[{3},{4},{2,5},{1}] => [3,4,2,5,1] => [3,2,4,1,5] => [3,2,4,1,5] => ? = 0
[{3},{5},{2,4},{1}] => [3,5,2,4,1] => [3,1,4,2,5] => [3,1,4,2,5] => ? = 0
[{4},{3},{2,5},{1}] => [4,3,2,5,1] => [2,3,4,1,5] => [2,3,4,1,5] => ? = 0
[{5},{3},{2,4},{1}] => [5,3,2,4,1] => [1,3,4,2,5] => [1,3,4,2,5] => 0
[{4},{5},{2,3},{1}] => [4,5,2,3,1] => [2,1,4,3,5] => [2,1,4,3,5] => ? = 0
[{5},{4},{2,3},{1}] => [5,4,2,3,1] => [1,2,4,3,5] => [1,2,4,3,5] => 0
[{1},{2,3},{4},{5}] => [1,2,3,4,5] => [5,4,3,2,1] => [5,4,3,2,1] => ? = 0
[{1},{2,3},{5},{4}] => [1,2,3,5,4] => [5,4,3,1,2] => [5,4,3,1,2] => ? = 0
[{5},{1,2},{3},{4}] => [5,1,2,3,4] => [1,5,4,3,2] => [1,5,4,3,2] => 0
Description
The oddness of a signed permutation.
The direct sum of two signed permutations $\sigma\in\mathfrak H_k$ and $\tau\in\mathfrak H_m$ is the signed permutation in $\mathfrak H_{k+m}$ obtained by concatenating $\sigma$ with the result of increasing the absolute value of every entry in $\tau$ by $k$.
This statistic records the number of blocks with an odd number of signs in the direct sum decomposition of a signed permutation.
Matching statistic: St000188
(load all 5 compositions to match this statistic)
(load all 5 compositions to match this statistic)
Mp00286: Ordered set partitions —to permutation⟶ Permutations
Mp00305: Permutations —parking function⟶ Parking functions
St000188: Parking functions ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 25%
Mp00305: Permutations —parking function⟶ Parking functions
St000188: Parking functions ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 25%
Values
[{1,2},{3}] => [1,2,3] => [1,2,3] => 0
[{1,3},{2}] => [1,3,2] => [1,3,2] => 0
[{2,3},{1}] => [2,3,1] => [2,3,1] => 0
[{1},{2,3},{4}] => [1,2,3,4] => [1,2,3,4] => 0
[{1},{2,4},{3}] => [1,2,4,3] => [1,2,4,3] => 0
[{1},{3,4},{2}] => [1,3,4,2] => [1,3,4,2] => 0
[{2},{1,3},{4}] => [2,1,3,4] => [2,1,3,4] => 0
[{2},{1,4},{3}] => [2,1,4,3] => [2,1,4,3] => 0
[{3},{1,2},{4}] => [3,1,2,4] => [3,1,2,4] => 0
[{4},{1,2},{3}] => [4,1,2,3] => [4,1,2,3] => 0
[{3},{1,4},{2}] => [3,1,4,2] => [3,1,4,2] => 0
[{4},{1,3},{2}] => [4,1,3,2] => [4,1,3,2] => 0
[{2},{3,4},{1}] => [2,3,4,1] => [2,3,4,1] => 0
[{3},{2,4},{1}] => [3,2,4,1] => [3,2,4,1] => 0
[{4},{2,3},{1}] => [4,2,3,1] => [4,2,3,1] => 0
[{1,2},{3},{4}] => [1,2,3,4] => [1,2,3,4] => 0
[{1,2},{4},{3}] => [1,2,4,3] => [1,2,4,3] => 0
[{1,3},{2},{4}] => [1,3,2,4] => [1,3,2,4] => 0
[{1,4},{2},{3}] => [1,4,2,3] => [1,4,2,3] => 0
[{1,3},{4},{2}] => [1,3,4,2] => [1,3,4,2] => 0
[{1,4},{3},{2}] => [1,4,3,2] => [1,4,3,2] => 0
[{2,3},{1},{4}] => [2,3,1,4] => [2,3,1,4] => 0
[{2,4},{1},{3}] => [2,4,1,3] => [2,4,1,3] => 0
[{3,4},{1},{2}] => [3,4,1,2] => [3,4,1,2] => 0
[{2,3},{4},{1}] => [2,3,4,1] => [2,3,4,1] => 0
[{2,4},{3},{1}] => [2,4,3,1] => [2,4,3,1] => 0
[{3,4},{2},{1}] => [3,4,2,1] => [3,4,2,1] => 0
[{1,2},{3,4}] => [1,2,3,4] => [1,2,3,4] => 0
[{1,3},{2,4}] => [1,3,2,4] => [1,3,2,4] => 0
[{1,4},{2,3}] => [1,4,2,3] => [1,4,2,3] => 0
[{2,3},{1,4}] => [2,3,1,4] => [2,3,1,4] => 0
[{2,4},{1,3}] => [2,4,1,3] => [2,4,1,3] => 0
[{3,4},{1,2}] => [3,4,1,2] => [3,4,1,2] => 0
[{1,2,3},{4}] => [1,2,3,4] => [1,2,3,4] => 0
[{1,2,4},{3}] => [1,2,4,3] => [1,2,4,3] => 0
[{1,3,4},{2}] => [1,3,4,2] => [1,3,4,2] => 0
[{2,3,4},{1}] => [2,3,4,1] => [2,3,4,1] => 0
[{1},{2},{3,4},{5}] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 0
[{1},{2},{3,5},{4}] => [1,2,3,5,4] => [1,2,3,5,4] => ? = 0
[{1},{2},{4,5},{3}] => [1,2,4,5,3] => [1,2,4,5,3] => ? = 0
[{1},{3},{2,4},{5}] => [1,3,2,4,5] => [1,3,2,4,5] => ? = 0
[{1},{3},{2,5},{4}] => [1,3,2,5,4] => [1,3,2,5,4] => ? = 0
[{1},{4},{2,3},{5}] => [1,4,2,3,5] => [1,4,2,3,5] => ? = 0
[{1},{5},{2,3},{4}] => [1,5,2,3,4] => [1,5,2,3,4] => ? = 0
[{1},{4},{2,5},{3}] => [1,4,2,5,3] => [1,4,2,5,3] => ? = 0
[{1},{5},{2,4},{3}] => [1,5,2,4,3] => [1,5,2,4,3] => ? = 0
[{1},{3},{4,5},{2}] => [1,3,4,5,2] => [1,3,4,5,2] => ? = 0
[{1},{4},{3,5},{2}] => [1,4,3,5,2] => [1,4,3,5,2] => ? = 0
[{1},{5},{3,4},{2}] => [1,5,3,4,2] => [1,5,3,4,2] => ? = 0
[{2},{1},{3,4},{5}] => [2,1,3,4,5] => [2,1,3,4,5] => ? = 0
[{2},{1},{3,5},{4}] => [2,1,3,5,4] => [2,1,3,5,4] => ? = 0
[{2},{1},{4,5},{3}] => [2,1,4,5,3] => [2,1,4,5,3] => ? = 0
[{3},{1},{2,4},{5}] => [3,1,2,4,5] => [3,1,2,4,5] => ? = 0
[{3},{1},{2,5},{4}] => [3,1,2,5,4] => [3,1,2,5,4] => ? = 0
[{4},{1},{2,3},{5}] => [4,1,2,3,5] => [4,1,2,3,5] => ? = 0
[{5},{1},{2,3},{4}] => [5,1,2,3,4] => [5,1,2,3,4] => ? = 0
[{4},{1},{2,5},{3}] => [4,1,2,5,3] => [4,1,2,5,3] => ? = 0
[{5},{1},{2,4},{3}] => [5,1,2,4,3] => [5,1,2,4,3] => ? = 0
[{3},{1},{4,5},{2}] => [3,1,4,5,2] => [3,1,4,5,2] => ? = 0
[{4},{1},{3,5},{2}] => [4,1,3,5,2] => [4,1,3,5,2] => ? = 0
[{5},{1},{3,4},{2}] => [5,1,3,4,2] => [5,1,3,4,2] => ? = 0
[{2},{3},{1,4},{5}] => [2,3,1,4,5] => [2,3,1,4,5] => ? = 0
[{2},{3},{1,5},{4}] => [2,3,1,5,4] => [2,3,1,5,4] => ? = 0
[{2},{4},{1,3},{5}] => [2,4,1,3,5] => [2,4,1,3,5] => ? = 0
[{2},{5},{1,3},{4}] => [2,5,1,3,4] => [2,5,1,3,4] => ? = 0
[{2},{4},{1,5},{3}] => [2,4,1,5,3] => [2,4,1,5,3] => ? = 0
[{2},{5},{1,4},{3}] => [2,5,1,4,3] => [2,5,1,4,3] => ? = 0
[{3},{2},{1,4},{5}] => [3,2,1,4,5] => [3,2,1,4,5] => ? = 0
[{3},{2},{1,5},{4}] => [3,2,1,5,4] => [3,2,1,5,4] => ? = 0
[{4},{2},{1,3},{5}] => [4,2,1,3,5] => [4,2,1,3,5] => ? = 0
[{5},{2},{1,3},{4}] => [5,2,1,3,4] => [5,2,1,3,4] => ? = 0
[{4},{2},{1,5},{3}] => [4,2,1,5,3] => [4,2,1,5,3] => ? = 0
[{5},{2},{1,4},{3}] => [5,2,1,4,3] => [5,2,1,4,3] => ? = 0
[{3},{4},{1,2},{5}] => [3,4,1,2,5] => [3,4,1,2,5] => ? = 0
[{3},{5},{1,2},{4}] => [3,5,1,2,4] => [3,5,1,2,4] => ? = 0
[{4},{3},{1,2},{5}] => [4,3,1,2,5] => [4,3,1,2,5] => ? = 0
[{5},{3},{1,2},{4}] => [5,3,1,2,4] => [5,3,1,2,4] => ? = 0
[{4},{5},{1,2},{3}] => [4,5,1,2,3] => [4,5,1,2,3] => ? = 0
[{5},{4},{1,2},{3}] => [5,4,1,2,3] => [5,4,1,2,3] => ? = 0
[{3},{4},{1,5},{2}] => [3,4,1,5,2] => [3,4,1,5,2] => ? = 0
[{3},{5},{1,4},{2}] => [3,5,1,4,2] => [3,5,1,4,2] => ? = 0
[{4},{3},{1,5},{2}] => [4,3,1,5,2] => [4,3,1,5,2] => ? = 0
[{5},{3},{1,4},{2}] => [5,3,1,4,2] => [5,3,1,4,2] => ? = 0
[{4},{5},{1,3},{2}] => [4,5,1,3,2] => [4,5,1,3,2] => ? = 0
[{5},{4},{1,3},{2}] => [5,4,1,3,2] => [5,4,1,3,2] => ? = 0
[{2},{3},{4,5},{1}] => [2,3,4,5,1] => [2,3,4,5,1] => ? = 0
[{2},{4},{3,5},{1}] => [2,4,3,5,1] => [2,4,3,5,1] => ? = 0
Description
The area of the Dyck path corresponding to a parking function and the total displacement of a parking function.
The area Dyck path corresponding to a parking function for a parking function $p_1,\ldots,p_n$ of length $n$, is given by $\binom{n+1}{2} - \sum_i p_i$.
The total displacement of a parking function $ p \in PF_n $ is defined by
$$
\operatorname{disp}(p) := \sum_{i=1}^{n} d_i,
$$
where the displacement vector $ d := (d_1, d_2, \ldots, d_n) $ and $ d_i := \pi^{-1}(i) - p_i $ for all $ i \in [n] $,
such that each $ d_i $ is the positive difference between the actual spot a car parks and its preferred spot.
Matching statistic: St000195
(load all 5 compositions to match this statistic)
(load all 5 compositions to match this statistic)
Mp00286: Ordered set partitions —to permutation⟶ Permutations
Mp00305: Permutations —parking function⟶ Parking functions
St000195: Parking functions ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 25%
Mp00305: Permutations —parking function⟶ Parking functions
St000195: Parking functions ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 25%
Values
[{1,2},{3}] => [1,2,3] => [1,2,3] => 0
[{1,3},{2}] => [1,3,2] => [1,3,2] => 0
[{2,3},{1}] => [2,3,1] => [2,3,1] => 0
[{1},{2,3},{4}] => [1,2,3,4] => [1,2,3,4] => 0
[{1},{2,4},{3}] => [1,2,4,3] => [1,2,4,3] => 0
[{1},{3,4},{2}] => [1,3,4,2] => [1,3,4,2] => 0
[{2},{1,3},{4}] => [2,1,3,4] => [2,1,3,4] => 0
[{2},{1,4},{3}] => [2,1,4,3] => [2,1,4,3] => 0
[{3},{1,2},{4}] => [3,1,2,4] => [3,1,2,4] => 0
[{4},{1,2},{3}] => [4,1,2,3] => [4,1,2,3] => 0
[{3},{1,4},{2}] => [3,1,4,2] => [3,1,4,2] => 0
[{4},{1,3},{2}] => [4,1,3,2] => [4,1,3,2] => 0
[{2},{3,4},{1}] => [2,3,4,1] => [2,3,4,1] => 0
[{3},{2,4},{1}] => [3,2,4,1] => [3,2,4,1] => 0
[{4},{2,3},{1}] => [4,2,3,1] => [4,2,3,1] => 0
[{1,2},{3},{4}] => [1,2,3,4] => [1,2,3,4] => 0
[{1,2},{4},{3}] => [1,2,4,3] => [1,2,4,3] => 0
[{1,3},{2},{4}] => [1,3,2,4] => [1,3,2,4] => 0
[{1,4},{2},{3}] => [1,4,2,3] => [1,4,2,3] => 0
[{1,3},{4},{2}] => [1,3,4,2] => [1,3,4,2] => 0
[{1,4},{3},{2}] => [1,4,3,2] => [1,4,3,2] => 0
[{2,3},{1},{4}] => [2,3,1,4] => [2,3,1,4] => 0
[{2,4},{1},{3}] => [2,4,1,3] => [2,4,1,3] => 0
[{3,4},{1},{2}] => [3,4,1,2] => [3,4,1,2] => 0
[{2,3},{4},{1}] => [2,3,4,1] => [2,3,4,1] => 0
[{2,4},{3},{1}] => [2,4,3,1] => [2,4,3,1] => 0
[{3,4},{2},{1}] => [3,4,2,1] => [3,4,2,1] => 0
[{1,2},{3,4}] => [1,2,3,4] => [1,2,3,4] => 0
[{1,3},{2,4}] => [1,3,2,4] => [1,3,2,4] => 0
[{1,4},{2,3}] => [1,4,2,3] => [1,4,2,3] => 0
[{2,3},{1,4}] => [2,3,1,4] => [2,3,1,4] => 0
[{2,4},{1,3}] => [2,4,1,3] => [2,4,1,3] => 0
[{3,4},{1,2}] => [3,4,1,2] => [3,4,1,2] => 0
[{1,2,3},{4}] => [1,2,3,4] => [1,2,3,4] => 0
[{1,2,4},{3}] => [1,2,4,3] => [1,2,4,3] => 0
[{1,3,4},{2}] => [1,3,4,2] => [1,3,4,2] => 0
[{2,3,4},{1}] => [2,3,4,1] => [2,3,4,1] => 0
[{1},{2},{3,4},{5}] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 0
[{1},{2},{3,5},{4}] => [1,2,3,5,4] => [1,2,3,5,4] => ? = 0
[{1},{2},{4,5},{3}] => [1,2,4,5,3] => [1,2,4,5,3] => ? = 0
[{1},{3},{2,4},{5}] => [1,3,2,4,5] => [1,3,2,4,5] => ? = 0
[{1},{3},{2,5},{4}] => [1,3,2,5,4] => [1,3,2,5,4] => ? = 0
[{1},{4},{2,3},{5}] => [1,4,2,3,5] => [1,4,2,3,5] => ? = 0
[{1},{5},{2,3},{4}] => [1,5,2,3,4] => [1,5,2,3,4] => ? = 0
[{1},{4},{2,5},{3}] => [1,4,2,5,3] => [1,4,2,5,3] => ? = 0
[{1},{5},{2,4},{3}] => [1,5,2,4,3] => [1,5,2,4,3] => ? = 0
[{1},{3},{4,5},{2}] => [1,3,4,5,2] => [1,3,4,5,2] => ? = 0
[{1},{4},{3,5},{2}] => [1,4,3,5,2] => [1,4,3,5,2] => ? = 0
[{1},{5},{3,4},{2}] => [1,5,3,4,2] => [1,5,3,4,2] => ? = 0
[{2},{1},{3,4},{5}] => [2,1,3,4,5] => [2,1,3,4,5] => ? = 0
[{2},{1},{3,5},{4}] => [2,1,3,5,4] => [2,1,3,5,4] => ? = 0
[{2},{1},{4,5},{3}] => [2,1,4,5,3] => [2,1,4,5,3] => ? = 0
[{3},{1},{2,4},{5}] => [3,1,2,4,5] => [3,1,2,4,5] => ? = 0
[{3},{1},{2,5},{4}] => [3,1,2,5,4] => [3,1,2,5,4] => ? = 0
[{4},{1},{2,3},{5}] => [4,1,2,3,5] => [4,1,2,3,5] => ? = 0
[{5},{1},{2,3},{4}] => [5,1,2,3,4] => [5,1,2,3,4] => ? = 0
[{4},{1},{2,5},{3}] => [4,1,2,5,3] => [4,1,2,5,3] => ? = 0
[{5},{1},{2,4},{3}] => [5,1,2,4,3] => [5,1,2,4,3] => ? = 0
[{3},{1},{4,5},{2}] => [3,1,4,5,2] => [3,1,4,5,2] => ? = 0
[{4},{1},{3,5},{2}] => [4,1,3,5,2] => [4,1,3,5,2] => ? = 0
[{5},{1},{3,4},{2}] => [5,1,3,4,2] => [5,1,3,4,2] => ? = 0
[{2},{3},{1,4},{5}] => [2,3,1,4,5] => [2,3,1,4,5] => ? = 0
[{2},{3},{1,5},{4}] => [2,3,1,5,4] => [2,3,1,5,4] => ? = 0
[{2},{4},{1,3},{5}] => [2,4,1,3,5] => [2,4,1,3,5] => ? = 0
[{2},{5},{1,3},{4}] => [2,5,1,3,4] => [2,5,1,3,4] => ? = 0
[{2},{4},{1,5},{3}] => [2,4,1,5,3] => [2,4,1,5,3] => ? = 0
[{2},{5},{1,4},{3}] => [2,5,1,4,3] => [2,5,1,4,3] => ? = 0
[{3},{2},{1,4},{5}] => [3,2,1,4,5] => [3,2,1,4,5] => ? = 0
[{3},{2},{1,5},{4}] => [3,2,1,5,4] => [3,2,1,5,4] => ? = 0
[{4},{2},{1,3},{5}] => [4,2,1,3,5] => [4,2,1,3,5] => ? = 0
[{5},{2},{1,3},{4}] => [5,2,1,3,4] => [5,2,1,3,4] => ? = 0
[{4},{2},{1,5},{3}] => [4,2,1,5,3] => [4,2,1,5,3] => ? = 0
[{5},{2},{1,4},{3}] => [5,2,1,4,3] => [5,2,1,4,3] => ? = 0
[{3},{4},{1,2},{5}] => [3,4,1,2,5] => [3,4,1,2,5] => ? = 0
[{3},{5},{1,2},{4}] => [3,5,1,2,4] => [3,5,1,2,4] => ? = 0
[{4},{3},{1,2},{5}] => [4,3,1,2,5] => [4,3,1,2,5] => ? = 0
[{5},{3},{1,2},{4}] => [5,3,1,2,4] => [5,3,1,2,4] => ? = 0
[{4},{5},{1,2},{3}] => [4,5,1,2,3] => [4,5,1,2,3] => ? = 0
[{5},{4},{1,2},{3}] => [5,4,1,2,3] => [5,4,1,2,3] => ? = 0
[{3},{4},{1,5},{2}] => [3,4,1,5,2] => [3,4,1,5,2] => ? = 0
[{3},{5},{1,4},{2}] => [3,5,1,4,2] => [3,5,1,4,2] => ? = 0
[{4},{3},{1,5},{2}] => [4,3,1,5,2] => [4,3,1,5,2] => ? = 0
[{5},{3},{1,4},{2}] => [5,3,1,4,2] => [5,3,1,4,2] => ? = 0
[{4},{5},{1,3},{2}] => [4,5,1,3,2] => [4,5,1,3,2] => ? = 0
[{5},{4},{1,3},{2}] => [5,4,1,3,2] => [5,4,1,3,2] => ? = 0
[{2},{3},{4,5},{1}] => [2,3,4,5,1] => [2,3,4,5,1] => ? = 0
[{2},{4},{3,5},{1}] => [2,4,3,5,1] => [2,4,3,5,1] => ? = 0
Description
The number of secondary dinversion pairs of the dyck path corresponding to a parking function.
Matching statistic: St000943
(load all 5 compositions to match this statistic)
(load all 5 compositions to match this statistic)
Mp00286: Ordered set partitions —to permutation⟶ Permutations
Mp00305: Permutations —parking function⟶ Parking functions
St000943: Parking functions ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 25%
Mp00305: Permutations —parking function⟶ Parking functions
St000943: Parking functions ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 25%
Values
[{1,2},{3}] => [1,2,3] => [1,2,3] => 0
[{1,3},{2}] => [1,3,2] => [1,3,2] => 0
[{2,3},{1}] => [2,3,1] => [2,3,1] => 0
[{1},{2,3},{4}] => [1,2,3,4] => [1,2,3,4] => 0
[{1},{2,4},{3}] => [1,2,4,3] => [1,2,4,3] => 0
[{1},{3,4},{2}] => [1,3,4,2] => [1,3,4,2] => 0
[{2},{1,3},{4}] => [2,1,3,4] => [2,1,3,4] => 0
[{2},{1,4},{3}] => [2,1,4,3] => [2,1,4,3] => 0
[{3},{1,2},{4}] => [3,1,2,4] => [3,1,2,4] => 0
[{4},{1,2},{3}] => [4,1,2,3] => [4,1,2,3] => 0
[{3},{1,4},{2}] => [3,1,4,2] => [3,1,4,2] => 0
[{4},{1,3},{2}] => [4,1,3,2] => [4,1,3,2] => 0
[{2},{3,4},{1}] => [2,3,4,1] => [2,3,4,1] => 0
[{3},{2,4},{1}] => [3,2,4,1] => [3,2,4,1] => 0
[{4},{2,3},{1}] => [4,2,3,1] => [4,2,3,1] => 0
[{1,2},{3},{4}] => [1,2,3,4] => [1,2,3,4] => 0
[{1,2},{4},{3}] => [1,2,4,3] => [1,2,4,3] => 0
[{1,3},{2},{4}] => [1,3,2,4] => [1,3,2,4] => 0
[{1,4},{2},{3}] => [1,4,2,3] => [1,4,2,3] => 0
[{1,3},{4},{2}] => [1,3,4,2] => [1,3,4,2] => 0
[{1,4},{3},{2}] => [1,4,3,2] => [1,4,3,2] => 0
[{2,3},{1},{4}] => [2,3,1,4] => [2,3,1,4] => 0
[{2,4},{1},{3}] => [2,4,1,3] => [2,4,1,3] => 0
[{3,4},{1},{2}] => [3,4,1,2] => [3,4,1,2] => 0
[{2,3},{4},{1}] => [2,3,4,1] => [2,3,4,1] => 0
[{2,4},{3},{1}] => [2,4,3,1] => [2,4,3,1] => 0
[{3,4},{2},{1}] => [3,4,2,1] => [3,4,2,1] => 0
[{1,2},{3,4}] => [1,2,3,4] => [1,2,3,4] => 0
[{1,3},{2,4}] => [1,3,2,4] => [1,3,2,4] => 0
[{1,4},{2,3}] => [1,4,2,3] => [1,4,2,3] => 0
[{2,3},{1,4}] => [2,3,1,4] => [2,3,1,4] => 0
[{2,4},{1,3}] => [2,4,1,3] => [2,4,1,3] => 0
[{3,4},{1,2}] => [3,4,1,2] => [3,4,1,2] => 0
[{1,2,3},{4}] => [1,2,3,4] => [1,2,3,4] => 0
[{1,2,4},{3}] => [1,2,4,3] => [1,2,4,3] => 0
[{1,3,4},{2}] => [1,3,4,2] => [1,3,4,2] => 0
[{2,3,4},{1}] => [2,3,4,1] => [2,3,4,1] => 0
[{1},{2},{3,4},{5}] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 0
[{1},{2},{3,5},{4}] => [1,2,3,5,4] => [1,2,3,5,4] => ? = 0
[{1},{2},{4,5},{3}] => [1,2,4,5,3] => [1,2,4,5,3] => ? = 0
[{1},{3},{2,4},{5}] => [1,3,2,4,5] => [1,3,2,4,5] => ? = 0
[{1},{3},{2,5},{4}] => [1,3,2,5,4] => [1,3,2,5,4] => ? = 0
[{1},{4},{2,3},{5}] => [1,4,2,3,5] => [1,4,2,3,5] => ? = 0
[{1},{5},{2,3},{4}] => [1,5,2,3,4] => [1,5,2,3,4] => ? = 0
[{1},{4},{2,5},{3}] => [1,4,2,5,3] => [1,4,2,5,3] => ? = 0
[{1},{5},{2,4},{3}] => [1,5,2,4,3] => [1,5,2,4,3] => ? = 0
[{1},{3},{4,5},{2}] => [1,3,4,5,2] => [1,3,4,5,2] => ? = 0
[{1},{4},{3,5},{2}] => [1,4,3,5,2] => [1,4,3,5,2] => ? = 0
[{1},{5},{3,4},{2}] => [1,5,3,4,2] => [1,5,3,4,2] => ? = 0
[{2},{1},{3,4},{5}] => [2,1,3,4,5] => [2,1,3,4,5] => ? = 0
[{2},{1},{3,5},{4}] => [2,1,3,5,4] => [2,1,3,5,4] => ? = 0
[{2},{1},{4,5},{3}] => [2,1,4,5,3] => [2,1,4,5,3] => ? = 0
[{3},{1},{2,4},{5}] => [3,1,2,4,5] => [3,1,2,4,5] => ? = 0
[{3},{1},{2,5},{4}] => [3,1,2,5,4] => [3,1,2,5,4] => ? = 0
[{4},{1},{2,3},{5}] => [4,1,2,3,5] => [4,1,2,3,5] => ? = 0
[{5},{1},{2,3},{4}] => [5,1,2,3,4] => [5,1,2,3,4] => ? = 0
[{4},{1},{2,5},{3}] => [4,1,2,5,3] => [4,1,2,5,3] => ? = 0
[{5},{1},{2,4},{3}] => [5,1,2,4,3] => [5,1,2,4,3] => ? = 0
[{3},{1},{4,5},{2}] => [3,1,4,5,2] => [3,1,4,5,2] => ? = 0
[{4},{1},{3,5},{2}] => [4,1,3,5,2] => [4,1,3,5,2] => ? = 0
[{5},{1},{3,4},{2}] => [5,1,3,4,2] => [5,1,3,4,2] => ? = 0
[{2},{3},{1,4},{5}] => [2,3,1,4,5] => [2,3,1,4,5] => ? = 0
[{2},{3},{1,5},{4}] => [2,3,1,5,4] => [2,3,1,5,4] => ? = 0
[{2},{4},{1,3},{5}] => [2,4,1,3,5] => [2,4,1,3,5] => ? = 0
[{2},{5},{1,3},{4}] => [2,5,1,3,4] => [2,5,1,3,4] => ? = 0
[{2},{4},{1,5},{3}] => [2,4,1,5,3] => [2,4,1,5,3] => ? = 0
[{2},{5},{1,4},{3}] => [2,5,1,4,3] => [2,5,1,4,3] => ? = 0
[{3},{2},{1,4},{5}] => [3,2,1,4,5] => [3,2,1,4,5] => ? = 0
[{3},{2},{1,5},{4}] => [3,2,1,5,4] => [3,2,1,5,4] => ? = 0
[{4},{2},{1,3},{5}] => [4,2,1,3,5] => [4,2,1,3,5] => ? = 0
[{5},{2},{1,3},{4}] => [5,2,1,3,4] => [5,2,1,3,4] => ? = 0
[{4},{2},{1,5},{3}] => [4,2,1,5,3] => [4,2,1,5,3] => ? = 0
[{5},{2},{1,4},{3}] => [5,2,1,4,3] => [5,2,1,4,3] => ? = 0
[{3},{4},{1,2},{5}] => [3,4,1,2,5] => [3,4,1,2,5] => ? = 0
[{3},{5},{1,2},{4}] => [3,5,1,2,4] => [3,5,1,2,4] => ? = 0
[{4},{3},{1,2},{5}] => [4,3,1,2,5] => [4,3,1,2,5] => ? = 0
[{5},{3},{1,2},{4}] => [5,3,1,2,4] => [5,3,1,2,4] => ? = 0
[{4},{5},{1,2},{3}] => [4,5,1,2,3] => [4,5,1,2,3] => ? = 0
[{5},{4},{1,2},{3}] => [5,4,1,2,3] => [5,4,1,2,3] => ? = 0
[{3},{4},{1,5},{2}] => [3,4,1,5,2] => [3,4,1,5,2] => ? = 0
[{3},{5},{1,4},{2}] => [3,5,1,4,2] => [3,5,1,4,2] => ? = 0
[{4},{3},{1,5},{2}] => [4,3,1,5,2] => [4,3,1,5,2] => ? = 0
[{5},{3},{1,4},{2}] => [5,3,1,4,2] => [5,3,1,4,2] => ? = 0
[{4},{5},{1,3},{2}] => [4,5,1,3,2] => [4,5,1,3,2] => ? = 0
[{5},{4},{1,3},{2}] => [5,4,1,3,2] => [5,4,1,3,2] => ? = 0
[{2},{3},{4,5},{1}] => [2,3,4,5,1] => [2,3,4,5,1] => ? = 0
[{2},{4},{3,5},{1}] => [2,4,3,5,1] => [2,4,3,5,1] => ? = 0
Description
The number of spots the most unlucky car had to go further in a parking function.
The following 4 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St001371The length of the longest Yamanouchi prefix of a binary word. St001730The number of times the path corresponding to a binary word crosses the base line. St001195The global dimension of the algebra $A/AfA$ of the corresponding Nakayama algebra $A$ with minimal left faithful projective-injective module $Af$. St001208The number of connected components of the quiver of $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra $A$ of $K[x]/(x^n)$.
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