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Your data matches 5 different statistics following compositions of up to 3 maps.
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Matching statistic: St001563
(load all 6 compositions to match this statistic)
(load all 6 compositions to match this statistic)
St001563: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1]
=> 1
[2]
=> 1
[1,1]
=> 4
[3]
=> 1
[2,1]
=> 4
[1,1,1]
=> 27
[4]
=> 1
[3,1]
=> 4
[2,2]
=> 4
[2,1,1]
=> 27
[1,1,1,1]
=> 256
[5]
=> 1
[4,1]
=> 4
[3,2]
=> 4
[3,1,1]
=> 27
[2,2,1]
=> 27
[2,1,1,1]
=> 256
[1,1,1,1,1]
=> 3125
[6]
=> 1
[5,1]
=> 4
[4,2]
=> 4
[4,1,1]
=> 27
[3,3]
=> 4
[3,2,1]
=> 27
[3,1,1,1]
=> 256
[2,2,2]
=> 27
[2,2,1,1]
=> 256
[2,1,1,1,1]
=> 3125
[1,1,1,1,1,1]
=> 46656
[7]
=> 1
[6,1]
=> 4
[5,2]
=> 4
[5,1,1]
=> 27
[4,3]
=> 4
[4,2,1]
=> 27
[4,1,1,1]
=> 256
[3,3,1]
=> 27
[3,2,2]
=> 27
[3,2,1,1]
=> 256
[3,1,1,1,1]
=> 3125
[2,2,2,1]
=> 256
[2,2,1,1,1]
=> 3125
[2,1,1,1,1,1]
=> 46656
[1,1,1,1,1,1,1]
=> 823543
Description
The value of the power-sum symmetric function evaluated at 1.
The statistic is $p_\lambda(x_1,\dotsc,x_k)$ evaluated at $x_1=x_2=\dotsb=x_k$,
where $\lambda$ has $k$ parts.
Matching statistic: St001632
Mp00042: Integer partitions —initial tableau⟶ Standard tableaux
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001632: Posets ⟶ ℤResult quality: 14% ●values known / values provided: 14%●distinct values known / distinct values provided: 14%
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001632: Posets ⟶ ℤResult quality: 14% ●values known / values provided: 14%●distinct values known / distinct values provided: 14%
Values
[1]
=> [[1]]
=> [1] => ([],1)
=> ? = 1
[2]
=> [[1,2]]
=> [1,2] => ([(0,1)],2)
=> 1
[1,1]
=> [[1],[2]]
=> [2,1] => ([],2)
=> ? = 4
[3]
=> [[1,2,3]]
=> [1,2,3] => ([(0,2),(2,1)],3)
=> 1
[2,1]
=> [[1,2],[3]]
=> [3,1,2] => ([(1,2)],3)
=> ? ∊ {4,27}
[1,1,1]
=> [[1],[2],[3]]
=> [3,2,1] => ([],3)
=> ? ∊ {4,27}
[4]
=> [[1,2,3,4]]
=> [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 1
[3,1]
=> [[1,2,3],[4]]
=> [4,1,2,3] => ([(1,2),(2,3)],4)
=> ? ∊ {4,4,27,256}
[2,2]
=> [[1,2],[3,4]]
=> [3,4,1,2] => ([(0,3),(1,2)],4)
=> ? ∊ {4,4,27,256}
[2,1,1]
=> [[1,2],[3],[4]]
=> [4,3,1,2] => ([(2,3)],4)
=> ? ∊ {4,4,27,256}
[1,1,1,1]
=> [[1],[2],[3],[4]]
=> [4,3,2,1] => ([],4)
=> ? ∊ {4,4,27,256}
[5]
=> [[1,2,3,4,5]]
=> [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[4,1]
=> [[1,2,3,4],[5]]
=> [5,1,2,3,4] => ([(1,4),(3,2),(4,3)],5)
=> ? ∊ {4,4,27,27,256,3125}
[3,2]
=> [[1,2,3],[4,5]]
=> [4,5,1,2,3] => ([(0,3),(1,4),(4,2)],5)
=> ? ∊ {4,4,27,27,256,3125}
[3,1,1]
=> [[1,2,3],[4],[5]]
=> [5,4,1,2,3] => ([(2,3),(3,4)],5)
=> ? ∊ {4,4,27,27,256,3125}
[2,2,1]
=> [[1,2],[3,4],[5]]
=> [5,3,4,1,2] => ([(1,4),(2,3)],5)
=> ? ∊ {4,4,27,27,256,3125}
[2,1,1,1]
=> [[1,2],[3],[4],[5]]
=> [5,4,3,1,2] => ([(3,4)],5)
=> ? ∊ {4,4,27,27,256,3125}
[1,1,1,1,1]
=> [[1],[2],[3],[4],[5]]
=> [5,4,3,2,1] => ([],5)
=> ? ∊ {4,4,27,27,256,3125}
[6]
=> [[1,2,3,4,5,6]]
=> [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1
[5,1]
=> [[1,2,3,4,5],[6]]
=> [6,1,2,3,4,5] => ([(1,5),(3,4),(4,2),(5,3)],6)
=> ? ∊ {4,4,4,27,27,27,256,256,3125,46656}
[4,2]
=> [[1,2,3,4],[5,6]]
=> [5,6,1,2,3,4] => ([(0,5),(1,3),(4,2),(5,4)],6)
=> ? ∊ {4,4,4,27,27,27,256,256,3125,46656}
[4,1,1]
=> [[1,2,3,4],[5],[6]]
=> [6,5,1,2,3,4] => ([(2,3),(3,5),(5,4)],6)
=> ? ∊ {4,4,4,27,27,27,256,256,3125,46656}
[3,3]
=> [[1,2,3],[4,5,6]]
=> [4,5,6,1,2,3] => ([(0,5),(1,4),(4,2),(5,3)],6)
=> ? ∊ {4,4,4,27,27,27,256,256,3125,46656}
[3,2,1]
=> [[1,2,3],[4,5],[6]]
=> [6,4,5,1,2,3] => ([(1,3),(2,4),(4,5)],6)
=> ? ∊ {4,4,4,27,27,27,256,256,3125,46656}
[3,1,1,1]
=> [[1,2,3],[4],[5],[6]]
=> [6,5,4,1,2,3] => ([(3,4),(4,5)],6)
=> ? ∊ {4,4,4,27,27,27,256,256,3125,46656}
[2,2,2]
=> [[1,2],[3,4],[5,6]]
=> [5,6,3,4,1,2] => ([(0,5),(1,4),(2,3)],6)
=> ? ∊ {4,4,4,27,27,27,256,256,3125,46656}
[2,2,1,1]
=> [[1,2],[3,4],[5],[6]]
=> [6,5,3,4,1,2] => ([(2,5),(3,4)],6)
=> ? ∊ {4,4,4,27,27,27,256,256,3125,46656}
[2,1,1,1,1]
=> [[1,2],[3],[4],[5],[6]]
=> [6,5,4,3,1,2] => ([(4,5)],6)
=> ? ∊ {4,4,4,27,27,27,256,256,3125,46656}
[1,1,1,1,1,1]
=> [[1],[2],[3],[4],[5],[6]]
=> [6,5,4,3,2,1] => ([],6)
=> ? ∊ {4,4,4,27,27,27,256,256,3125,46656}
[7]
=> [[1,2,3,4,5,6,7]]
=> [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 1
[6,1]
=> [[1,2,3,4,5,6],[7]]
=> [7,1,2,3,4,5,6] => ([(1,6),(3,5),(4,3),(5,2),(6,4)],7)
=> ? ∊ {4,4,4,27,27,27,27,256,256,256,3125,3125,46656,823543}
[5,2]
=> [[1,2,3,4,5],[6,7]]
=> [6,7,1,2,3,4,5] => ([(0,6),(1,3),(4,5),(5,2),(6,4)],7)
=> ? ∊ {4,4,4,27,27,27,27,256,256,256,3125,3125,46656,823543}
[5,1,1]
=> [[1,2,3,4,5],[6],[7]]
=> [7,6,1,2,3,4,5] => ([(2,6),(4,5),(5,3),(6,4)],7)
=> ? ∊ {4,4,4,27,27,27,27,256,256,256,3125,3125,46656,823543}
[4,3]
=> [[1,2,3,4],[5,6,7]]
=> [5,6,7,1,2,3,4] => ([(0,5),(1,6),(4,3),(5,4),(6,2)],7)
=> ? ∊ {4,4,4,27,27,27,27,256,256,256,3125,3125,46656,823543}
[4,2,1]
=> [[1,2,3,4],[5,6],[7]]
=> [7,5,6,1,2,3,4] => ([(1,6),(2,4),(5,3),(6,5)],7)
=> ? ∊ {4,4,4,27,27,27,27,256,256,256,3125,3125,46656,823543}
[4,1,1,1]
=> [[1,2,3,4],[5],[6],[7]]
=> [7,6,5,1,2,3,4] => ([(3,4),(4,6),(6,5)],7)
=> ? ∊ {4,4,4,27,27,27,27,256,256,256,3125,3125,46656,823543}
[3,3,1]
=> [[1,2,3],[4,5,6],[7]]
=> [7,4,5,6,1,2,3] => ([(1,6),(2,5),(5,3),(6,4)],7)
=> ? ∊ {4,4,4,27,27,27,27,256,256,256,3125,3125,46656,823543}
[3,2,2]
=> [[1,2,3],[4,5],[6,7]]
=> [6,7,4,5,1,2,3] => ([(0,5),(1,4),(2,6),(6,3)],7)
=> ? ∊ {4,4,4,27,27,27,27,256,256,256,3125,3125,46656,823543}
[3,2,1,1]
=> [[1,2,3],[4,5],[6],[7]]
=> [7,6,4,5,1,2,3] => ([(2,4),(3,5),(5,6)],7)
=> ? ∊ {4,4,4,27,27,27,27,256,256,256,3125,3125,46656,823543}
[3,1,1,1,1]
=> [[1,2,3],[4],[5],[6],[7]]
=> [7,6,5,4,1,2,3] => ([(4,5),(5,6)],7)
=> ? ∊ {4,4,4,27,27,27,27,256,256,256,3125,3125,46656,823543}
[2,2,2,1]
=> [[1,2],[3,4],[5,6],[7]]
=> [7,5,6,3,4,1,2] => ([(1,6),(2,5),(3,4)],7)
=> ? ∊ {4,4,4,27,27,27,27,256,256,256,3125,3125,46656,823543}
[2,2,1,1,1]
=> [[1,2],[3,4],[5],[6],[7]]
=> [7,6,5,3,4,1,2] => ([(3,6),(4,5)],7)
=> ? ∊ {4,4,4,27,27,27,27,256,256,256,3125,3125,46656,823543}
[2,1,1,1,1,1]
=> [[1,2],[3],[4],[5],[6],[7]]
=> [7,6,5,4,3,1,2] => ([(5,6)],7)
=> ? ∊ {4,4,4,27,27,27,27,256,256,256,3125,3125,46656,823543}
[1,1,1,1,1,1,1]
=> [[1],[2],[3],[4],[5],[6],[7]]
=> [7,6,5,4,3,2,1] => ([],7)
=> ? ∊ {4,4,4,27,27,27,27,256,256,256,3125,3125,46656,823543}
Description
The number of indecomposable injective modules $I$ with $dim Ext^1(I,A)=1$ for the incidence algebra A of a poset.
Matching statistic: St000089
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00033: Dyck paths —to two-row standard tableau⟶ Standard tableaux
Mp00295: Standard tableaux —valley composition⟶ Integer compositions
St000089: Integer compositions ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 29%
Mp00033: Dyck paths —to two-row standard tableau⟶ Standard tableaux
Mp00295: Standard tableaux —valley composition⟶ Integer compositions
St000089: Integer compositions ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 29%
Values
[1]
=> [1,0,1,0]
=> [[1,3],[2,4]]
=> [2,2] => 0 = 1 - 1
[2]
=> [1,1,0,0,1,0]
=> [[1,2,5],[3,4,6]]
=> [3,3] => 0 = 1 - 1
[1,1]
=> [1,0,1,1,0,0]
=> [[1,3,4],[2,5,6]]
=> [2,3,1] => 3 = 4 - 1
[3]
=> [1,1,1,0,0,0,1,0]
=> [[1,2,3,7],[4,5,6,8]]
=> [4,4] => ? ∊ {4,27} - 1
[2,1]
=> [1,0,1,0,1,0]
=> [[1,3,5],[2,4,6]]
=> [2,2,2] => 0 = 1 - 1
[1,1,1]
=> [1,0,1,1,1,0,0,0]
=> [[1,3,4,5],[2,6,7,8]]
=> [2,4,2] => ? ∊ {4,27} - 1
[4]
=> [1,1,1,1,0,0,0,0,1,0]
=> [[1,2,3,4,9],[5,6,7,8,10]]
=> [5,5] => ? ∊ {1,4,4,27,256} - 1
[3,1]
=> [1,1,0,1,0,0,1,0]
=> [[1,2,4,7],[3,5,6,8]]
=> [3,2,3] => ? ∊ {1,4,4,27,256} - 1
[2,2]
=> [1,1,0,0,1,1,0,0]
=> [[1,2,5,6],[3,4,7,8]]
=> [3,4,1] => ? ∊ {1,4,4,27,256} - 1
[2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> [2,3,2,1] => ? ∊ {1,4,4,27,256} - 1
[1,1,1,1]
=> [1,0,1,1,1,1,0,0,0,0]
=> [[1,3,4,5,6],[2,7,8,9,10]]
=> [2,5,3] => ? ∊ {1,4,4,27,256} - 1
[5]
=> [1,1,1,1,1,0,0,0,0,0,1,0]
=> [[1,2,3,4,5,11],[6,7,8,9,10,12]]
=> [6,6] => ? ∊ {1,4,4,27,27,256,3125} - 1
[4,1]
=> [1,1,1,0,1,0,0,0,1,0]
=> [[1,2,3,5,9],[4,6,7,8,10]]
=> [4,2,4] => ? ∊ {1,4,4,27,27,256,3125} - 1
[3,2]
=> [1,1,0,0,1,0,1,0]
=> [[1,2,5,7],[3,4,6,8]]
=> [3,3,2] => ? ∊ {1,4,4,27,27,256,3125} - 1
[3,1,1]
=> [1,0,1,1,0,0,1,0]
=> [[1,3,4,7],[2,5,6,8]]
=> [2,3,3] => ? ∊ {1,4,4,27,27,256,3125} - 1
[2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [[1,3,5,6],[2,4,7,8]]
=> [2,2,3,1] => ? ∊ {1,4,4,27,27,256,3125} - 1
[2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [[1,3,4,5,7],[2,6,8,9,10]]
=> [2,4,2,2] => ? ∊ {1,4,4,27,27,256,3125} - 1
[1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,0,0,0,0]
=> [[1,3,4,5,6,7],[2,8,9,10,11,12]]
=> [2,6,4] => ? ∊ {1,4,4,27,27,256,3125} - 1
[6]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
=> [[1,2,3,4,5,6,13],[7,8,9,10,11,12,14]]
=> [7,7] => ? ∊ {1,4,4,4,27,27,27,256,256,3125,46656} - 1
[5,1]
=> [1,1,1,1,0,1,0,0,0,0,1,0]
=> [[1,2,3,4,6,11],[5,7,8,9,10,12]]
=> [5,2,5] => ? ∊ {1,4,4,4,27,27,27,256,256,3125,46656} - 1
[4,2]
=> [1,1,1,0,0,1,0,0,1,0]
=> [[1,2,3,6,9],[4,5,7,8,10]]
=> [4,3,3] => ? ∊ {1,4,4,4,27,27,27,256,256,3125,46656} - 1
[4,1,1]
=> [1,1,0,1,1,0,0,0,1,0]
=> [[1,2,4,5,9],[3,6,7,8,10]]
=> [3,3,4] => ? ∊ {1,4,4,4,27,27,27,256,256,3125,46656} - 1
[3,3]
=> [1,1,1,0,0,0,1,1,0,0]
=> [[1,2,3,7,8],[4,5,6,9,10]]
=> [4,5,1] => ? ∊ {1,4,4,4,27,27,27,256,256,3125,46656} - 1
[3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [[1,3,5,7],[2,4,6,8]]
=> [2,2,2,2] => ? ∊ {1,4,4,4,27,27,27,256,256,3125,46656} - 1
[3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [[1,3,4,5,8],[2,6,7,9,10]]
=> [2,4,3,1] => ? ∊ {1,4,4,4,27,27,27,256,256,3125,46656} - 1
[2,2,2]
=> [1,1,0,0,1,1,1,0,0,0]
=> [[1,2,5,6,7],[3,4,8,9,10]]
=> [3,5,2] => ? ∊ {1,4,4,4,27,27,27,256,256,3125,46656} - 1
[2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [[1,3,4,6,7],[2,5,8,9,10]]
=> [2,3,3,2] => ? ∊ {1,4,4,4,27,27,27,256,256,3125,46656} - 1
[2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [[1,3,4,5,6,8],[2,7,9,10,11,12]]
=> [2,5,2,3] => ? ∊ {1,4,4,4,27,27,27,256,256,3125,46656} - 1
[1,1,1,1,1,1]
=> [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> [[1,3,4,5,6,7,8],[2,9,10,11,12,13,14]]
=> [2,7,5] => ? ∊ {1,4,4,4,27,27,27,256,256,3125,46656} - 1
[7]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
=> [[1,2,3,4,5,6,7,15],[8,9,10,11,12,13,14,16]]
=> [8,8] => ? ∊ {1,4,4,4,27,27,27,27,256,256,256,3125,3125,46656,823543} - 1
[6,1]
=> [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
=> [[1,2,3,4,5,7,13],[6,8,9,10,11,12,14]]
=> [6,2,6] => ? ∊ {1,4,4,4,27,27,27,27,256,256,256,3125,3125,46656,823543} - 1
[5,2]
=> [1,1,1,1,0,0,1,0,0,0,1,0]
=> [[1,2,3,4,7,11],[5,6,8,9,10,12]]
=> [5,3,4] => ? ∊ {1,4,4,4,27,27,27,27,256,256,256,3125,3125,46656,823543} - 1
[5,1,1]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> [[1,2,3,5,6,11],[4,7,8,9,10,12]]
=> [4,3,5] => ? ∊ {1,4,4,4,27,27,27,27,256,256,256,3125,3125,46656,823543} - 1
[4,3]
=> [1,1,1,0,0,0,1,0,1,0]
=> [[1,2,3,7,9],[4,5,6,8,10]]
=> [4,4,2] => ? ∊ {1,4,4,4,27,27,27,27,256,256,256,3125,3125,46656,823543} - 1
[4,2,1]
=> [1,1,0,1,0,1,0,0,1,0]
=> [[1,2,4,6,9],[3,5,7,8,10]]
=> [3,2,2,3] => ? ∊ {1,4,4,4,27,27,27,27,256,256,256,3125,3125,46656,823543} - 1
[4,1,1,1]
=> [1,0,1,1,1,0,0,0,1,0]
=> [[1,3,4,5,9],[2,6,7,8,10]]
=> [2,4,4] => ? ∊ {1,4,4,4,27,27,27,27,256,256,256,3125,3125,46656,823543} - 1
[3,3,1]
=> [1,1,0,1,0,0,1,1,0,0]
=> [[1,2,4,7,8],[3,5,6,9,10]]
=> [3,2,4,1] => ? ∊ {1,4,4,4,27,27,27,27,256,256,256,3125,3125,46656,823543} - 1
[3,2,2]
=> [1,1,0,0,1,1,0,1,0,0]
=> [[1,2,5,6,8],[3,4,7,9,10]]
=> [3,4,2,1] => ? ∊ {1,4,4,4,27,27,27,27,256,256,256,3125,3125,46656,823543} - 1
[3,2,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> [[1,3,4,6,8],[2,5,7,9,10]]
=> [2,3,2,2,1] => ? ∊ {1,4,4,4,27,27,27,27,256,256,256,3125,3125,46656,823543} - 1
[3,1,1,1,1]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> [[1,3,4,5,6,9],[2,7,8,10,11,12]]
=> [2,5,3,2] => ? ∊ {1,4,4,4,27,27,27,27,256,256,256,3125,3125,46656,823543} - 1
[2,2,2,1]
=> [1,0,1,0,1,1,1,0,0,0]
=> [[1,3,5,6,7],[2,4,8,9,10]]
=> [2,2,4,2] => ? ∊ {1,4,4,4,27,27,27,27,256,256,256,3125,3125,46656,823543} - 1
[2,2,1,1,1]
=> [1,0,1,1,1,0,1,1,0,0,0,0]
=> [[1,3,4,5,7,8],[2,6,9,10,11,12]]
=> [2,4,3,3] => ? ∊ {1,4,4,4,27,27,27,27,256,256,256,3125,3125,46656,823543} - 1
[2,1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [[1,3,4,5,6,7,9],[2,8,10,11,12,13,14]]
=> [2,6,2,4] => ? ∊ {1,4,4,4,27,27,27,27,256,256,256,3125,3125,46656,823543} - 1
[1,1,1,1,1,1,1]
=> [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> [[1,3,4,5,6,7,8,9],[2,10,11,12,13,14,15,16]]
=> [2,8,6] => ? ∊ {1,4,4,4,27,27,27,27,256,256,256,3125,3125,46656,823543} - 1
Description
The absolute variation of a composition.
Matching statistic: St000709
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00146: Dyck paths —to tunnel matching⟶ Perfect matchings
Mp00058: Perfect matchings —to permutation⟶ Permutations
St000709: Permutations ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 29%
Mp00146: Dyck paths —to tunnel matching⟶ Perfect matchings
Mp00058: Perfect matchings —to permutation⟶ Permutations
St000709: Permutations ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 29%
Values
[1]
=> [1,0,1,0]
=> [(1,2),(3,4)]
=> [2,1,4,3] => 0 = 1 - 1
[2]
=> [1,1,0,0,1,0]
=> [(1,4),(2,3),(5,6)]
=> [4,3,2,1,6,5] => 0 = 1 - 1
[1,1]
=> [1,0,1,1,0,0]
=> [(1,2),(3,6),(4,5)]
=> [2,1,6,5,4,3] => 3 = 4 - 1
[3]
=> [1,1,1,0,0,0,1,0]
=> [(1,6),(2,5),(3,4),(7,8)]
=> [6,5,4,3,2,1,8,7] => ? ∊ {4,27} - 1
[2,1]
=> [1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6)]
=> [2,1,4,3,6,5] => 0 = 1 - 1
[1,1,1]
=> [1,0,1,1,1,0,0,0]
=> [(1,2),(3,8),(4,7),(5,6)]
=> [2,1,8,7,6,5,4,3] => ? ∊ {4,27} - 1
[4]
=> [1,1,1,1,0,0,0,0,1,0]
=> [(1,8),(2,7),(3,6),(4,5),(9,10)]
=> [8,7,6,5,4,3,2,1,10,9] => ? ∊ {1,4,4,27,256} - 1
[3,1]
=> [1,1,0,1,0,0,1,0]
=> [(1,6),(2,3),(4,5),(7,8)]
=> [6,3,2,5,4,1,8,7] => ? ∊ {1,4,4,27,256} - 1
[2,2]
=> [1,1,0,0,1,1,0,0]
=> [(1,4),(2,3),(5,8),(6,7)]
=> [4,3,2,1,8,7,6,5] => ? ∊ {1,4,4,27,256} - 1
[2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [(1,2),(3,8),(4,5),(6,7)]
=> [2,1,8,5,4,7,6,3] => ? ∊ {1,4,4,27,256} - 1
[1,1,1,1]
=> [1,0,1,1,1,1,0,0,0,0]
=> [(1,2),(3,10),(4,9),(5,8),(6,7)]
=> [2,1,10,9,8,7,6,5,4,3] => ? ∊ {1,4,4,27,256} - 1
[5]
=> [1,1,1,1,1,0,0,0,0,0,1,0]
=> [(1,10),(2,9),(3,8),(4,7),(5,6),(11,12)]
=> [10,9,8,7,6,5,4,3,2,1,12,11] => ? ∊ {1,4,4,27,27,256,3125} - 1
[4,1]
=> [1,1,1,0,1,0,0,0,1,0]
=> [(1,8),(2,7),(3,4),(5,6),(9,10)]
=> [8,7,4,3,6,5,2,1,10,9] => ? ∊ {1,4,4,27,27,256,3125} - 1
[3,2]
=> [1,1,0,0,1,0,1,0]
=> [(1,4),(2,3),(5,6),(7,8)]
=> [4,3,2,1,6,5,8,7] => ? ∊ {1,4,4,27,27,256,3125} - 1
[3,1,1]
=> [1,0,1,1,0,0,1,0]
=> [(1,2),(3,6),(4,5),(7,8)]
=> [2,1,6,5,4,3,8,7] => ? ∊ {1,4,4,27,27,256,3125} - 1
[2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [(1,2),(3,4),(5,8),(6,7)]
=> [2,1,4,3,8,7,6,5] => ? ∊ {1,4,4,27,27,256,3125} - 1
[2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [(1,2),(3,10),(4,9),(5,6),(7,8)]
=> [2,1,10,9,6,5,8,7,4,3] => ? ∊ {1,4,4,27,27,256,3125} - 1
[1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,0,0,0,0]
=> [(1,2),(3,12),(4,11),(5,10),(6,9),(7,8)]
=> [2,1,12,11,10,9,8,7,6,5,4,3] => ? ∊ {1,4,4,27,27,256,3125} - 1
[6]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
=> [(1,12),(2,11),(3,10),(4,9),(5,8),(6,7),(13,14)]
=> [12,11,10,9,8,7,6,5,4,3,2,1,14,13] => ? ∊ {1,4,4,4,27,27,27,256,256,3125,46656} - 1
[5,1]
=> [1,1,1,1,0,1,0,0,0,0,1,0]
=> [(1,10),(2,9),(3,8),(4,5),(6,7),(11,12)]
=> [10,9,8,5,4,7,6,3,2,1,12,11] => ? ∊ {1,4,4,4,27,27,27,256,256,3125,46656} - 1
[4,2]
=> [1,1,1,0,0,1,0,0,1,0]
=> [(1,8),(2,5),(3,4),(6,7),(9,10)]
=> [8,5,4,3,2,7,6,1,10,9] => ? ∊ {1,4,4,4,27,27,27,256,256,3125,46656} - 1
[4,1,1]
=> [1,1,0,1,1,0,0,0,1,0]
=> [(1,8),(2,3),(4,7),(5,6),(9,10)]
=> [8,3,2,7,6,5,4,1,10,9] => ? ∊ {1,4,4,4,27,27,27,256,256,3125,46656} - 1
[3,3]
=> [1,1,1,0,0,0,1,1,0,0]
=> [(1,6),(2,5),(3,4),(7,10),(8,9)]
=> [6,5,4,3,2,1,10,9,8,7] => ? ∊ {1,4,4,4,27,27,27,256,256,3125,46656} - 1
[3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6),(7,8)]
=> [2,1,4,3,6,5,8,7] => ? ∊ {1,4,4,4,27,27,27,256,256,3125,46656} - 1
[3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [(1,2),(3,10),(4,7),(5,6),(8,9)]
=> [2,1,10,7,6,5,4,9,8,3] => ? ∊ {1,4,4,4,27,27,27,256,256,3125,46656} - 1
[2,2,2]
=> [1,1,0,0,1,1,1,0,0,0]
=> [(1,4),(2,3),(5,10),(6,9),(7,8)]
=> [4,3,2,1,10,9,8,7,6,5] => ? ∊ {1,4,4,4,27,27,27,256,256,3125,46656} - 1
[2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [(1,2),(3,10),(4,5),(6,9),(7,8)]
=> [2,1,10,5,4,9,8,7,6,3] => ? ∊ {1,4,4,4,27,27,27,256,256,3125,46656} - 1
[2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [(1,2),(3,12),(4,11),(5,10),(6,7),(8,9)]
=> [2,1,12,11,10,7,6,9,8,5,4,3] => ? ∊ {1,4,4,4,27,27,27,256,256,3125,46656} - 1
[1,1,1,1,1,1]
=> [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> [(1,2),(3,14),(4,13),(5,12),(6,11),(7,10),(8,9)]
=> [2,1,14,13,12,11,10,9,8,7,6,5,4,3] => ? ∊ {1,4,4,4,27,27,27,256,256,3125,46656} - 1
[7]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
=> [(1,14),(2,13),(3,12),(4,11),(5,10),(6,9),(7,8),(15,16)]
=> [14,13,12,11,10,9,8,7,6,5,4,3,2,1,16,15] => ? ∊ {1,4,4,4,27,27,27,27,256,256,256,3125,3125,46656,823543} - 1
[6,1]
=> [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
=> [(1,12),(2,11),(3,10),(4,9),(5,6),(7,8),(13,14)]
=> [12,11,10,9,6,5,8,7,4,3,2,1,14,13] => ? ∊ {1,4,4,4,27,27,27,27,256,256,256,3125,3125,46656,823543} - 1
[5,2]
=> [1,1,1,1,0,0,1,0,0,0,1,0]
=> [(1,10),(2,9),(3,6),(4,5),(7,8),(11,12)]
=> [10,9,6,5,4,3,8,7,2,1,12,11] => ? ∊ {1,4,4,4,27,27,27,27,256,256,256,3125,3125,46656,823543} - 1
[5,1,1]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> [(1,10),(2,9),(3,4),(5,8),(6,7),(11,12)]
=> [10,9,4,3,8,7,6,5,2,1,12,11] => ? ∊ {1,4,4,4,27,27,27,27,256,256,256,3125,3125,46656,823543} - 1
[4,3]
=> [1,1,1,0,0,0,1,0,1,0]
=> [(1,6),(2,5),(3,4),(7,8),(9,10)]
=> [6,5,4,3,2,1,8,7,10,9] => ? ∊ {1,4,4,4,27,27,27,27,256,256,256,3125,3125,46656,823543} - 1
[4,2,1]
=> [1,1,0,1,0,1,0,0,1,0]
=> [(1,8),(2,3),(4,5),(6,7),(9,10)]
=> [8,3,2,5,4,7,6,1,10,9] => ? ∊ {1,4,4,4,27,27,27,27,256,256,256,3125,3125,46656,823543} - 1
[4,1,1,1]
=> [1,0,1,1,1,0,0,0,1,0]
=> [(1,2),(3,8),(4,7),(5,6),(9,10)]
=> [2,1,8,7,6,5,4,3,10,9] => ? ∊ {1,4,4,4,27,27,27,27,256,256,256,3125,3125,46656,823543} - 1
[3,3,1]
=> [1,1,0,1,0,0,1,1,0,0]
=> [(1,6),(2,3),(4,5),(7,10),(8,9)]
=> [6,3,2,5,4,1,10,9,8,7] => ? ∊ {1,4,4,4,27,27,27,27,256,256,256,3125,3125,46656,823543} - 1
[3,2,2]
=> [1,1,0,0,1,1,0,1,0,0]
=> [(1,4),(2,3),(5,10),(6,7),(8,9)]
=> [4,3,2,1,10,7,6,9,8,5] => ? ∊ {1,4,4,4,27,27,27,27,256,256,256,3125,3125,46656,823543} - 1
[3,2,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> [(1,2),(3,10),(4,5),(6,7),(8,9)]
=> [2,1,10,5,4,7,6,9,8,3] => ? ∊ {1,4,4,4,27,27,27,27,256,256,256,3125,3125,46656,823543} - 1
[3,1,1,1,1]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> [(1,2),(3,12),(4,11),(5,8),(6,7),(9,10)]
=> [2,1,12,11,8,7,6,5,10,9,4,3] => ? ∊ {1,4,4,4,27,27,27,27,256,256,256,3125,3125,46656,823543} - 1
[2,2,2,1]
=> [1,0,1,0,1,1,1,0,0,0]
=> [(1,2),(3,4),(5,10),(6,9),(7,8)]
=> [2,1,4,3,10,9,8,7,6,5] => ? ∊ {1,4,4,4,27,27,27,27,256,256,256,3125,3125,46656,823543} - 1
[2,2,1,1,1]
=> [1,0,1,1,1,0,1,1,0,0,0,0]
=> [(1,2),(3,12),(4,11),(5,6),(7,10),(8,9)]
=> [2,1,12,11,6,5,10,9,8,7,4,3] => ? ∊ {1,4,4,4,27,27,27,27,256,256,256,3125,3125,46656,823543} - 1
[2,1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [(1,2),(3,14),(4,13),(5,12),(6,11),(7,8),(9,10)]
=> [2,1,14,13,12,11,8,7,10,9,6,5,4,3] => ? ∊ {1,4,4,4,27,27,27,27,256,256,256,3125,3125,46656,823543} - 1
[1,1,1,1,1,1,1]
=> [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> [(1,2),(3,16),(4,15),(5,14),(6,13),(7,12),(8,11),(9,10)]
=> [2,1,16,15,14,13,12,11,10,9,8,7,6,5,4,3] => ? ∊ {1,4,4,4,27,27,27,27,256,256,256,3125,3125,46656,823543} - 1
Description
The number of occurrences of 14-2-3 or 14-3-2.
The number of permutations avoiding both of these patterns is the case $k=2$ of the third item in Corollary 34 of [1].
Matching statistic: St000802
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00146: Dyck paths —to tunnel matching⟶ Perfect matchings
Mp00058: Perfect matchings —to permutation⟶ Permutations
St000802: Permutations ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 29%
Mp00146: Dyck paths —to tunnel matching⟶ Perfect matchings
Mp00058: Perfect matchings —to permutation⟶ Permutations
St000802: Permutations ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 29%
Values
[1]
=> [1,0,1,0]
=> [(1,2),(3,4)]
=> [2,1,4,3] => 0 = 1 - 1
[2]
=> [1,1,0,0,1,0]
=> [(1,4),(2,3),(5,6)]
=> [4,3,2,1,6,5] => 3 = 4 - 1
[1,1]
=> [1,0,1,1,0,0]
=> [(1,2),(3,6),(4,5)]
=> [2,1,6,5,4,3] => 0 = 1 - 1
[3]
=> [1,1,1,0,0,0,1,0]
=> [(1,6),(2,5),(3,4),(7,8)]
=> [6,5,4,3,2,1,8,7] => ? ∊ {4,27} - 1
[2,1]
=> [1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6)]
=> [2,1,4,3,6,5] => 0 = 1 - 1
[1,1,1]
=> [1,0,1,1,1,0,0,0]
=> [(1,2),(3,8),(4,7),(5,6)]
=> [2,1,8,7,6,5,4,3] => ? ∊ {4,27} - 1
[4]
=> [1,1,1,1,0,0,0,0,1,0]
=> [(1,8),(2,7),(3,6),(4,5),(9,10)]
=> [8,7,6,5,4,3,2,1,10,9] => ? ∊ {1,4,4,27,256} - 1
[3,1]
=> [1,1,0,1,0,0,1,0]
=> [(1,6),(2,3),(4,5),(7,8)]
=> [6,3,2,5,4,1,8,7] => ? ∊ {1,4,4,27,256} - 1
[2,2]
=> [1,1,0,0,1,1,0,0]
=> [(1,4),(2,3),(5,8),(6,7)]
=> [4,3,2,1,8,7,6,5] => ? ∊ {1,4,4,27,256} - 1
[2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [(1,2),(3,8),(4,5),(6,7)]
=> [2,1,8,5,4,7,6,3] => ? ∊ {1,4,4,27,256} - 1
[1,1,1,1]
=> [1,0,1,1,1,1,0,0,0,0]
=> [(1,2),(3,10),(4,9),(5,8),(6,7)]
=> [2,1,10,9,8,7,6,5,4,3] => ? ∊ {1,4,4,27,256} - 1
[5]
=> [1,1,1,1,1,0,0,0,0,0,1,0]
=> [(1,10),(2,9),(3,8),(4,7),(5,6),(11,12)]
=> [10,9,8,7,6,5,4,3,2,1,12,11] => ? ∊ {1,4,4,27,27,256,3125} - 1
[4,1]
=> [1,1,1,0,1,0,0,0,1,0]
=> [(1,8),(2,7),(3,4),(5,6),(9,10)]
=> [8,7,4,3,6,5,2,1,10,9] => ? ∊ {1,4,4,27,27,256,3125} - 1
[3,2]
=> [1,1,0,0,1,0,1,0]
=> [(1,4),(2,3),(5,6),(7,8)]
=> [4,3,2,1,6,5,8,7] => ? ∊ {1,4,4,27,27,256,3125} - 1
[3,1,1]
=> [1,0,1,1,0,0,1,0]
=> [(1,2),(3,6),(4,5),(7,8)]
=> [2,1,6,5,4,3,8,7] => ? ∊ {1,4,4,27,27,256,3125} - 1
[2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [(1,2),(3,4),(5,8),(6,7)]
=> [2,1,4,3,8,7,6,5] => ? ∊ {1,4,4,27,27,256,3125} - 1
[2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [(1,2),(3,10),(4,9),(5,6),(7,8)]
=> [2,1,10,9,6,5,8,7,4,3] => ? ∊ {1,4,4,27,27,256,3125} - 1
[1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,0,0,0,0]
=> [(1,2),(3,12),(4,11),(5,10),(6,9),(7,8)]
=> [2,1,12,11,10,9,8,7,6,5,4,3] => ? ∊ {1,4,4,27,27,256,3125} - 1
[6]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
=> [(1,12),(2,11),(3,10),(4,9),(5,8),(6,7),(13,14)]
=> [12,11,10,9,8,7,6,5,4,3,2,1,14,13] => ? ∊ {1,4,4,4,27,27,27,256,256,3125,46656} - 1
[5,1]
=> [1,1,1,1,0,1,0,0,0,0,1,0]
=> [(1,10),(2,9),(3,8),(4,5),(6,7),(11,12)]
=> [10,9,8,5,4,7,6,3,2,1,12,11] => ? ∊ {1,4,4,4,27,27,27,256,256,3125,46656} - 1
[4,2]
=> [1,1,1,0,0,1,0,0,1,0]
=> [(1,8),(2,5),(3,4),(6,7),(9,10)]
=> [8,5,4,3,2,7,6,1,10,9] => ? ∊ {1,4,4,4,27,27,27,256,256,3125,46656} - 1
[4,1,1]
=> [1,1,0,1,1,0,0,0,1,0]
=> [(1,8),(2,3),(4,7),(5,6),(9,10)]
=> [8,3,2,7,6,5,4,1,10,9] => ? ∊ {1,4,4,4,27,27,27,256,256,3125,46656} - 1
[3,3]
=> [1,1,1,0,0,0,1,1,0,0]
=> [(1,6),(2,5),(3,4),(7,10),(8,9)]
=> [6,5,4,3,2,1,10,9,8,7] => ? ∊ {1,4,4,4,27,27,27,256,256,3125,46656} - 1
[3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6),(7,8)]
=> [2,1,4,3,6,5,8,7] => ? ∊ {1,4,4,4,27,27,27,256,256,3125,46656} - 1
[3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [(1,2),(3,10),(4,7),(5,6),(8,9)]
=> [2,1,10,7,6,5,4,9,8,3] => ? ∊ {1,4,4,4,27,27,27,256,256,3125,46656} - 1
[2,2,2]
=> [1,1,0,0,1,1,1,0,0,0]
=> [(1,4),(2,3),(5,10),(6,9),(7,8)]
=> [4,3,2,1,10,9,8,7,6,5] => ? ∊ {1,4,4,4,27,27,27,256,256,3125,46656} - 1
[2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [(1,2),(3,10),(4,5),(6,9),(7,8)]
=> [2,1,10,5,4,9,8,7,6,3] => ? ∊ {1,4,4,4,27,27,27,256,256,3125,46656} - 1
[2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [(1,2),(3,12),(4,11),(5,10),(6,7),(8,9)]
=> [2,1,12,11,10,7,6,9,8,5,4,3] => ? ∊ {1,4,4,4,27,27,27,256,256,3125,46656} - 1
[1,1,1,1,1,1]
=> [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> [(1,2),(3,14),(4,13),(5,12),(6,11),(7,10),(8,9)]
=> [2,1,14,13,12,11,10,9,8,7,6,5,4,3] => ? ∊ {1,4,4,4,27,27,27,256,256,3125,46656} - 1
[7]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
=> [(1,14),(2,13),(3,12),(4,11),(5,10),(6,9),(7,8),(15,16)]
=> [14,13,12,11,10,9,8,7,6,5,4,3,2,1,16,15] => ? ∊ {1,4,4,4,27,27,27,27,256,256,256,3125,3125,46656,823543} - 1
[6,1]
=> [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
=> [(1,12),(2,11),(3,10),(4,9),(5,6),(7,8),(13,14)]
=> [12,11,10,9,6,5,8,7,4,3,2,1,14,13] => ? ∊ {1,4,4,4,27,27,27,27,256,256,256,3125,3125,46656,823543} - 1
[5,2]
=> [1,1,1,1,0,0,1,0,0,0,1,0]
=> [(1,10),(2,9),(3,6),(4,5),(7,8),(11,12)]
=> [10,9,6,5,4,3,8,7,2,1,12,11] => ? ∊ {1,4,4,4,27,27,27,27,256,256,256,3125,3125,46656,823543} - 1
[5,1,1]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> [(1,10),(2,9),(3,4),(5,8),(6,7),(11,12)]
=> [10,9,4,3,8,7,6,5,2,1,12,11] => ? ∊ {1,4,4,4,27,27,27,27,256,256,256,3125,3125,46656,823543} - 1
[4,3]
=> [1,1,1,0,0,0,1,0,1,0]
=> [(1,6),(2,5),(3,4),(7,8),(9,10)]
=> [6,5,4,3,2,1,8,7,10,9] => ? ∊ {1,4,4,4,27,27,27,27,256,256,256,3125,3125,46656,823543} - 1
[4,2,1]
=> [1,1,0,1,0,1,0,0,1,0]
=> [(1,8),(2,3),(4,5),(6,7),(9,10)]
=> [8,3,2,5,4,7,6,1,10,9] => ? ∊ {1,4,4,4,27,27,27,27,256,256,256,3125,3125,46656,823543} - 1
[4,1,1,1]
=> [1,0,1,1,1,0,0,0,1,0]
=> [(1,2),(3,8),(4,7),(5,6),(9,10)]
=> [2,1,8,7,6,5,4,3,10,9] => ? ∊ {1,4,4,4,27,27,27,27,256,256,256,3125,3125,46656,823543} - 1
[3,3,1]
=> [1,1,0,1,0,0,1,1,0,0]
=> [(1,6),(2,3),(4,5),(7,10),(8,9)]
=> [6,3,2,5,4,1,10,9,8,7] => ? ∊ {1,4,4,4,27,27,27,27,256,256,256,3125,3125,46656,823543} - 1
[3,2,2]
=> [1,1,0,0,1,1,0,1,0,0]
=> [(1,4),(2,3),(5,10),(6,7),(8,9)]
=> [4,3,2,1,10,7,6,9,8,5] => ? ∊ {1,4,4,4,27,27,27,27,256,256,256,3125,3125,46656,823543} - 1
[3,2,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> [(1,2),(3,10),(4,5),(6,7),(8,9)]
=> [2,1,10,5,4,7,6,9,8,3] => ? ∊ {1,4,4,4,27,27,27,27,256,256,256,3125,3125,46656,823543} - 1
[3,1,1,1,1]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> [(1,2),(3,12),(4,11),(5,8),(6,7),(9,10)]
=> [2,1,12,11,8,7,6,5,10,9,4,3] => ? ∊ {1,4,4,4,27,27,27,27,256,256,256,3125,3125,46656,823543} - 1
[2,2,2,1]
=> [1,0,1,0,1,1,1,0,0,0]
=> [(1,2),(3,4),(5,10),(6,9),(7,8)]
=> [2,1,4,3,10,9,8,7,6,5] => ? ∊ {1,4,4,4,27,27,27,27,256,256,256,3125,3125,46656,823543} - 1
[2,2,1,1,1]
=> [1,0,1,1,1,0,1,1,0,0,0,0]
=> [(1,2),(3,12),(4,11),(5,6),(7,10),(8,9)]
=> [2,1,12,11,6,5,10,9,8,7,4,3] => ? ∊ {1,4,4,4,27,27,27,27,256,256,256,3125,3125,46656,823543} - 1
[2,1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [(1,2),(3,14),(4,13),(5,12),(6,11),(7,8),(9,10)]
=> [2,1,14,13,12,11,8,7,10,9,6,5,4,3] => ? ∊ {1,4,4,4,27,27,27,27,256,256,256,3125,3125,46656,823543} - 1
[1,1,1,1,1,1,1]
=> [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> [(1,2),(3,16),(4,15),(5,14),(6,13),(7,12),(8,11),(9,10)]
=> [2,1,16,15,14,13,12,11,10,9,8,7,6,5,4,3] => ? ∊ {1,4,4,4,27,27,27,27,256,256,256,3125,3125,46656,823543} - 1
Description
The number of occurrences of the vincular pattern |321 in a permutation.
This is the number of occurrences of the pattern $(3,2,1)$, such that the letter matched by $3$ is the first entry of the permutation.
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