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Your data matches 98 different statistics following compositions of up to 3 maps.
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Matching statistic: St000929
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
St000929: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
St000929: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0,1,0,1,0,1,0]
=> [3,2,1]
=> [2,1]
=> [2,1]
=> 0
[1,0,1,0,1,1,0,0]
=> [2,2,1]
=> [2,1]
=> [2,1]
=> 0
[1,0,1,1,0,0,1,0]
=> [3,1,1]
=> [1,1]
=> [2]
=> 0
[1,0,1,1,0,1,0,0]
=> [2,1,1]
=> [1,1]
=> [2]
=> 0
[1,0,1,1,1,0,0,0]
=> [1,1,1]
=> [1,1]
=> [2]
=> 0
[1,1,0,0,1,0,1,0]
=> [3,2]
=> [2]
=> [1,1]
=> 1
[1,1,0,0,1,1,0,0]
=> [2,2]
=> [2]
=> [1,1]
=> 1
[1,0,1,0,1,0,1,0,1,0]
=> [4,3,2,1]
=> [3,2,1]
=> [3,2,1]
=> 0
[1,0,1,0,1,0,1,1,0,0]
=> [3,3,2,1]
=> [3,2,1]
=> [3,2,1]
=> 0
[1,0,1,0,1,1,0,0,1,0]
=> [4,2,2,1]
=> [2,2,1]
=> [3,2]
=> 0
[1,0,1,0,1,1,0,1,0,0]
=> [3,2,2,1]
=> [2,2,1]
=> [3,2]
=> 0
[1,0,1,0,1,1,1,0,0,0]
=> [2,2,2,1]
=> [2,2,1]
=> [3,2]
=> 0
[1,0,1,1,0,0,1,0,1,0]
=> [4,3,1,1]
=> [3,1,1]
=> [3,1,1]
=> 0
[1,0,1,1,0,0,1,1,0,0]
=> [3,3,1,1]
=> [3,1,1]
=> [3,1,1]
=> 0
[1,0,1,1,0,1,0,0,1,0]
=> [4,2,1,1]
=> [2,1,1]
=> [3,1]
=> 0
[1,0,1,1,0,1,0,1,0,0]
=> [3,2,1,1]
=> [2,1,1]
=> [3,1]
=> 0
[1,0,1,1,0,1,1,0,0,0]
=> [2,2,1,1]
=> [2,1,1]
=> [3,1]
=> 0
[1,0,1,1,1,0,0,0,1,0]
=> [4,1,1,1]
=> [1,1,1]
=> [3]
=> 0
[1,0,1,1,1,0,0,1,0,0]
=> [3,1,1,1]
=> [1,1,1]
=> [3]
=> 0
[1,0,1,1,1,0,1,0,0,0]
=> [2,1,1,1]
=> [1,1,1]
=> [3]
=> 0
[1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1]
=> [1,1,1]
=> [3]
=> 0
[1,1,0,0,1,0,1,0,1,0]
=> [4,3,2]
=> [3,2]
=> [2,2,1]
=> 0
[1,1,0,0,1,0,1,1,0,0]
=> [3,3,2]
=> [3,2]
=> [2,2,1]
=> 0
[1,1,0,0,1,1,0,0,1,0]
=> [4,2,2]
=> [2,2]
=> [2,2]
=> 0
[1,1,0,0,1,1,0,1,0,0]
=> [3,2,2]
=> [2,2]
=> [2,2]
=> 0
[1,1,0,0,1,1,1,0,0,0]
=> [2,2,2]
=> [2,2]
=> [2,2]
=> 0
[1,1,0,1,0,0,1,0,1,0]
=> [4,3,1]
=> [3,1]
=> [2,1,1]
=> 0
[1,1,0,1,0,0,1,1,0,0]
=> [3,3,1]
=> [3,1]
=> [2,1,1]
=> 0
[1,1,0,1,0,1,0,0,1,0]
=> [4,2,1]
=> [2,1]
=> [2,1]
=> 0
[1,1,0,1,0,1,0,1,0,0]
=> [3,2,1]
=> [2,1]
=> [2,1]
=> 0
[1,1,0,1,0,1,1,0,0,0]
=> [2,2,1]
=> [2,1]
=> [2,1]
=> 0
[1,1,0,1,1,0,0,0,1,0]
=> [4,1,1]
=> [1,1]
=> [2]
=> 0
[1,1,0,1,1,0,0,1,0,0]
=> [3,1,1]
=> [1,1]
=> [2]
=> 0
[1,1,0,1,1,0,1,0,0,0]
=> [2,1,1]
=> [1,1]
=> [2]
=> 0
[1,1,0,1,1,1,0,0,0,0]
=> [1,1,1]
=> [1,1]
=> [2]
=> 0
[1,1,1,0,0,0,1,0,1,0]
=> [4,3]
=> [3]
=> [1,1,1]
=> 1
[1,1,1,0,0,0,1,1,0,0]
=> [3,3]
=> [3]
=> [1,1,1]
=> 1
[1,1,1,0,0,1,0,0,1,0]
=> [4,2]
=> [2]
=> [1,1]
=> 1
[1,1,1,0,0,1,0,1,0,0]
=> [3,2]
=> [2]
=> [1,1]
=> 1
[1,1,1,0,0,1,1,0,0,0]
=> [2,2]
=> [2]
=> [1,1]
=> 1
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [5,4,3,2,1]
=> [4,3,2,1]
=> [4,3,2,1]
=> 0
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [4,4,3,2,1]
=> [4,3,2,1]
=> [4,3,2,1]
=> 0
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [5,3,3,2,1]
=> [3,3,2,1]
=> [4,3,2]
=> 0
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [4,3,3,2,1]
=> [3,3,2,1]
=> [4,3,2]
=> 0
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [3,3,3,2,1]
=> [3,3,2,1]
=> [4,3,2]
=> 0
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [5,4,2,2,1]
=> [4,2,2,1]
=> [4,3,1,1]
=> 0
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [4,4,2,2,1]
=> [4,2,2,1]
=> [4,3,1,1]
=> 0
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [5,3,2,2,1]
=> [3,2,2,1]
=> [4,3,1]
=> 0
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [4,3,2,2,1]
=> [3,2,2,1]
=> [4,3,1]
=> 0
[1,0,1,0,1,1,0,1,1,0,0,0]
=> [3,3,2,2,1]
=> [3,2,2,1]
=> [4,3,1]
=> 0
Description
The constant term of the character polynomial of an integer partition.
The definition of the character polynomial can be found in [1]. Indeed, this constant term is 0 for partitions λ≠1n and 1 for λ=1n.
Matching statistic: St000264
(load all 11 compositions to match this statistic)
(load all 11 compositions to match this statistic)
Mp00102: Dyck paths —rise composition⟶ Integer compositions
Mp00133: Integer compositions —delta morphism⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000264: Graphs ⟶ ℤResult quality: 50% ●values known / values provided: 66%●distinct values known / distinct values provided: 50%
Mp00133: Integer compositions —delta morphism⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000264: Graphs ⟶ ℤResult quality: 50% ●values known / values provided: 66%●distinct values known / distinct values provided: 50%
Values
[1,0,1,0,1,0,1,0]
=> [1,1,1,1] => [4] => ([],4)
=> ? = 0 + 3
[1,0,1,0,1,1,0,0]
=> [1,1,2] => [2,1] => ([(0,2),(1,2)],3)
=> ? = 0 + 3
[1,0,1,1,0,0,1,0]
=> [1,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3 = 0 + 3
[1,0,1,1,0,1,0,0]
=> [1,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3 = 0 + 3
[1,0,1,1,1,0,0,0]
=> [1,3] => [1,1] => ([(0,1)],2)
=> ? = 0 + 3
[1,1,0,0,1,0,1,0]
=> [2,1,1] => [1,2] => ([(1,2)],3)
=> ? = 1 + 3
[1,1,0,0,1,1,0,0]
=> [2,2] => [2] => ([],2)
=> ? = 1 + 3
[1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1] => [5] => ([],5)
=> ? = 0 + 3
[1,0,1,0,1,0,1,1,0,0]
=> [1,1,1,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> ? = 0 + 3
[1,0,1,0,1,1,0,0,1,0]
=> [1,1,2,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 3 = 0 + 3
[1,0,1,0,1,1,0,1,0,0]
=> [1,1,2,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 3 = 0 + 3
[1,0,1,0,1,1,1,0,0,0]
=> [1,1,3] => [2,1] => ([(0,2),(1,2)],3)
=> ? = 0 + 3
[1,0,1,1,0,0,1,0,1,0]
=> [1,2,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
=> 3 = 0 + 3
[1,0,1,1,0,0,1,1,0,0]
=> [1,2,2] => [1,2] => ([(1,2)],3)
=> ? = 0 + 3
[1,0,1,1,0,1,0,0,1,0]
=> [1,2,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
=> 3 = 0 + 3
[1,0,1,1,0,1,0,1,0,0]
=> [1,2,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
=> 3 = 0 + 3
[1,0,1,1,0,1,1,0,0,0]
=> [1,2,2] => [1,2] => ([(1,2)],3)
=> ? = 0 + 3
[1,0,1,1,1,0,0,0,1,0]
=> [1,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3 = 0 + 3
[1,0,1,1,1,0,0,1,0,0]
=> [1,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3 = 0 + 3
[1,0,1,1,1,0,1,0,0,0]
=> [1,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3 = 0 + 3
[1,0,1,1,1,1,0,0,0,0]
=> [1,4] => [1,1] => ([(0,1)],2)
=> ? = 0 + 3
[1,1,0,0,1,0,1,0,1,0]
=> [2,1,1,1] => [1,3] => ([(2,3)],4)
=> ? = 0 + 3
[1,1,0,0,1,0,1,1,0,0]
=> [2,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3 = 0 + 3
[1,1,0,0,1,1,0,0,1,0]
=> [2,2,1] => [2,1] => ([(0,2),(1,2)],3)
=> ? = 0 + 3
[1,1,0,0,1,1,0,1,0,0]
=> [2,2,1] => [2,1] => ([(0,2),(1,2)],3)
=> ? = 0 + 3
[1,1,0,0,1,1,1,0,0,0]
=> [2,3] => [1,1] => ([(0,1)],2)
=> ? = 0 + 3
[1,1,0,1,0,0,1,0,1,0]
=> [2,1,1,1] => [1,3] => ([(2,3)],4)
=> ? = 0 + 3
[1,1,0,1,0,0,1,1,0,0]
=> [2,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3 = 0 + 3
[1,1,0,1,0,1,0,0,1,0]
=> [2,1,1,1] => [1,3] => ([(2,3)],4)
=> ? = 0 + 3
[1,1,0,1,0,1,0,1,0,0]
=> [2,1,1,1] => [1,3] => ([(2,3)],4)
=> ? = 0 + 3
[1,1,0,1,0,1,1,0,0,0]
=> [2,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3 = 0 + 3
[1,1,0,1,1,0,0,0,1,0]
=> [2,2,1] => [2,1] => ([(0,2),(1,2)],3)
=> ? = 0 + 3
[1,1,0,1,1,0,0,1,0,0]
=> [2,2,1] => [2,1] => ([(0,2),(1,2)],3)
=> ? = 0 + 3
[1,1,0,1,1,0,1,0,0,0]
=> [2,2,1] => [2,1] => ([(0,2),(1,2)],3)
=> ? = 0 + 3
[1,1,0,1,1,1,0,0,0,0]
=> [2,3] => [1,1] => ([(0,1)],2)
=> ? = 0 + 3
[1,1,1,0,0,0,1,0,1,0]
=> [3,1,1] => [1,2] => ([(1,2)],3)
=> ? = 1 + 3
[1,1,1,0,0,0,1,1,0,0]
=> [3,2] => [1,1] => ([(0,1)],2)
=> ? = 1 + 3
[1,1,1,0,0,1,0,0,1,0]
=> [3,1,1] => [1,2] => ([(1,2)],3)
=> ? = 1 + 3
[1,1,1,0,0,1,0,1,0,0]
=> [3,1,1] => [1,2] => ([(1,2)],3)
=> ? = 1 + 3
[1,1,1,0,0,1,1,0,0,0]
=> [3,2] => [1,1] => ([(0,1)],2)
=> ? = 1 + 3
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1] => [6] => ([],6)
=> ? = 0 + 3
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,1,1,1,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? = 0 + 3
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,2,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3 = 0 + 3
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,1,1,2,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3 = 0 + 3
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,3] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> ? = 0 + 3
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,2,1,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3 = 0 + 3
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [1,1,2,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 3
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,1,2,1,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3 = 0 + 3
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,2,1,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3 = 0 + 3
[1,0,1,0,1,1,0,1,1,0,0,0]
=> [1,1,2,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 3
[1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,1,3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 3 = 0 + 3
[1,0,1,0,1,1,1,0,0,1,0,0]
=> [1,1,3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 3 = 0 + 3
[1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,1,3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 3 = 0 + 3
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,4] => [2,1] => ([(0,2),(1,2)],3)
=> ? = 0 + 3
[1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,2,1,1,1] => [1,1,3] => ([(2,3),(2,4),(3,4)],5)
=> 3 = 0 + 3
[1,0,1,1,0,0,1,0,1,1,0,0]
=> [1,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 3 = 0 + 3
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 3 = 0 + 3
[1,0,1,1,0,0,1,1,0,1,0,0]
=> [1,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 3 = 0 + 3
[1,0,1,1,0,0,1,1,1,0,0,0]
=> [1,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3 = 0 + 3
[1,0,1,1,0,1,0,0,1,0,1,0]
=> [1,2,1,1,1] => [1,1,3] => ([(2,3),(2,4),(3,4)],5)
=> 3 = 0 + 3
[1,0,1,1,0,1,0,0,1,1,0,0]
=> [1,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 3 = 0 + 3
[1,0,1,1,0,1,0,1,0,0,1,0]
=> [1,2,1,1,1] => [1,1,3] => ([(2,3),(2,4),(3,4)],5)
=> 3 = 0 + 3
[1,0,1,1,0,1,0,1,0,1,0,0]
=> [1,2,1,1,1] => [1,1,3] => ([(2,3),(2,4),(3,4)],5)
=> 3 = 0 + 3
[1,0,1,1,0,1,0,1,1,0,0,0]
=> [1,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 3 = 0 + 3
[1,0,1,1,0,1,1,0,0,0,1,0]
=> [1,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 3 = 0 + 3
[1,0,1,1,0,1,1,0,0,1,0,0]
=> [1,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 3 = 0 + 3
[1,0,1,1,0,1,1,0,1,0,0,0]
=> [1,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 3 = 0 + 3
[1,0,1,1,0,1,1,1,0,0,0,0]
=> [1,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3 = 0 + 3
[1,0,1,1,1,0,0,0,1,0,1,0]
=> [1,3,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
=> 3 = 0 + 3
[1,0,1,1,1,0,0,0,1,1,0,0]
=> [1,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3 = 0 + 3
[1,0,1,1,1,0,0,1,0,0,1,0]
=> [1,3,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
=> 3 = 0 + 3
[1,0,1,1,1,0,0,1,0,1,0,0]
=> [1,3,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
=> 3 = 0 + 3
[1,0,1,1,1,0,0,1,1,0,0,0]
=> [1,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3 = 0 + 3
[1,0,1,1,1,0,1,0,0,0,1,0]
=> [1,3,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
=> 3 = 0 + 3
[1,0,1,1,1,0,1,0,0,1,0,0]
=> [1,3,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
=> 3 = 0 + 3
[1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,3,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
=> 3 = 0 + 3
[1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3 = 0 + 3
[1,0,1,1,1,1,0,0,0,0,1,0]
=> [1,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3 = 0 + 3
[1,0,1,1,1,1,0,0,0,1,0,0]
=> [1,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3 = 0 + 3
[1,0,1,1,1,1,0,0,1,0,0,0]
=> [1,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3 = 0 + 3
[1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3 = 0 + 3
[1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,5] => [1,1] => ([(0,1)],2)
=> ? = 0 + 3
[1,1,0,0,1,0,1,0,1,0,1,0]
=> [2,1,1,1,1] => [1,4] => ([(3,4)],5)
=> ? = 0 + 3
[1,1,0,0,1,0,1,0,1,1,0,0]
=> [2,1,1,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 3 = 0 + 3
[1,1,0,0,1,0,1,1,0,0,1,0]
=> [2,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 3 = 0 + 3
[1,1,0,0,1,1,0,0,1,0,1,0]
=> [2,2,1,1] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 3
[1,1,0,0,1,1,0,0,1,1,0,0]
=> [2,2,2] => [3] => ([],3)
=> ? = 0 + 3
[1,1,0,0,1,1,0,1,0,0,1,0]
=> [2,2,1,1] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 3
[1,1,0,0,1,1,0,1,0,1,0,0]
=> [2,2,1,1] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 3
[1,1,0,0,1,1,0,1,1,0,0,0]
=> [2,2,2] => [3] => ([],3)
=> ? = 0 + 3
[1,1,0,0,1,1,1,1,0,0,0,0]
=> [2,4] => [1,1] => ([(0,1)],2)
=> ? = 0 + 3
[1,1,0,1,0,0,1,0,1,0,1,0]
=> [2,1,1,1,1] => [1,4] => ([(3,4)],5)
=> ? = 0 + 3
[1,1,0,1,0,1,0,0,1,0,1,0]
=> [2,1,1,1,1] => [1,4] => ([(3,4)],5)
=> ? = 0 + 3
[1,1,0,1,0,1,0,1,0,0,1,0]
=> [2,1,1,1,1] => [1,4] => ([(3,4)],5)
=> ? = 0 + 3
[1,1,0,1,0,1,0,1,0,1,0,0]
=> [2,1,1,1,1] => [1,4] => ([(3,4)],5)
=> ? = 0 + 3
[1,1,0,1,1,0,0,0,1,0,1,0]
=> [2,2,1,1] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 3
[1,1,0,1,1,0,0,0,1,1,0,0]
=> [2,2,2] => [3] => ([],3)
=> ? = 0 + 3
[1,1,0,1,1,0,0,1,0,0,1,0]
=> [2,2,1,1] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 3
[1,1,0,1,1,0,0,1,0,1,0,0]
=> [2,2,1,1] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 3
[1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,2,2] => [3] => ([],3)
=> ? = 0 + 3
Description
The girth of a graph, which is not a tree.
This is the length of the shortest cycle in the graph.
Matching statistic: St000617
Mp00119: Dyck paths —to 321-avoiding permutation (Krattenthaler)⟶ Permutations
Mp00068: Permutations —Simion-Schmidt map⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
St000617: Dyck paths ⟶ ℤResult quality: 59% ●values known / values provided: 59%●distinct values known / distinct values provided: 100%
Mp00068: Permutations —Simion-Schmidt map⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
St000617: Dyck paths ⟶ ℤResult quality: 59% ●values known / values provided: 59%●distinct values known / distinct values provided: 100%
Values
[1,0,1,0,1,0,1,0]
=> [1,2,3,4] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
=> 1 = 0 + 1
[1,0,1,0,1,1,0,0]
=> [1,2,4,3] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
=> 1 = 0 + 1
[1,0,1,1,0,0,1,0]
=> [1,3,2,4] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
=> 1 = 0 + 1
[1,0,1,1,0,1,0,0]
=> [1,3,4,2] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
=> 1 = 0 + 1
[1,0,1,1,1,0,0,0]
=> [1,4,2,3] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
=> 1 = 0 + 1
[1,1,0,0,1,0,1,0]
=> [2,1,3,4] => [2,1,4,3] => [1,1,0,0,1,1,0,0]
=> 2 = 1 + 1
[1,1,0,0,1,1,0,0]
=> [2,1,4,3] => [2,1,4,3] => [1,1,0,0,1,1,0,0]
=> 2 = 1 + 1
[1,0,1,0,1,0,1,0,1,0]
=> [1,2,3,4,5] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0]
=> 1 = 0 + 1
[1,0,1,0,1,0,1,1,0,0]
=> [1,2,3,5,4] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0]
=> 1 = 0 + 1
[1,0,1,0,1,1,0,0,1,0]
=> [1,2,4,3,5] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0]
=> 1 = 0 + 1
[1,0,1,0,1,1,0,1,0,0]
=> [1,2,4,5,3] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0]
=> 1 = 0 + 1
[1,0,1,0,1,1,1,0,0,0]
=> [1,2,5,3,4] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0]
=> 1 = 0 + 1
[1,0,1,1,0,0,1,0,1,0]
=> [1,3,2,4,5] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0]
=> 1 = 0 + 1
[1,0,1,1,0,0,1,1,0,0]
=> [1,3,2,5,4] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0]
=> 1 = 0 + 1
[1,0,1,1,0,1,0,0,1,0]
=> [1,3,4,2,5] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0]
=> 1 = 0 + 1
[1,0,1,1,0,1,0,1,0,0]
=> [1,3,4,5,2] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0]
=> 1 = 0 + 1
[1,0,1,1,0,1,1,0,0,0]
=> [1,3,5,2,4] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0]
=> 1 = 0 + 1
[1,0,1,1,1,0,0,0,1,0]
=> [1,4,2,3,5] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0]
=> 1 = 0 + 1
[1,0,1,1,1,0,0,1,0,0]
=> [1,4,2,5,3] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0]
=> 1 = 0 + 1
[1,0,1,1,1,0,1,0,0,0]
=> [1,4,5,2,3] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0]
=> 1 = 0 + 1
[1,0,1,1,1,1,0,0,0,0]
=> [1,5,2,3,4] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0]
=> 1 = 0 + 1
[1,1,0,0,1,0,1,0,1,0]
=> [2,1,3,4,5] => [2,1,5,4,3] => [1,1,0,0,1,1,1,0,0,0]
=> 1 = 0 + 1
[1,1,0,0,1,0,1,1,0,0]
=> [2,1,3,5,4] => [2,1,5,4,3] => [1,1,0,0,1,1,1,0,0,0]
=> 1 = 0 + 1
[1,1,0,0,1,1,0,0,1,0]
=> [2,1,4,3,5] => [2,1,5,4,3] => [1,1,0,0,1,1,1,0,0,0]
=> 1 = 0 + 1
[1,1,0,0,1,1,0,1,0,0]
=> [2,1,4,5,3] => [2,1,5,4,3] => [1,1,0,0,1,1,1,0,0,0]
=> 1 = 0 + 1
[1,1,0,0,1,1,1,0,0,0]
=> [2,1,5,3,4] => [2,1,5,4,3] => [1,1,0,0,1,1,1,0,0,0]
=> 1 = 0 + 1
[1,1,0,1,0,0,1,0,1,0]
=> [2,3,1,4,5] => [2,5,1,4,3] => [1,1,0,1,1,1,0,0,0,0]
=> 1 = 0 + 1
[1,1,0,1,0,0,1,1,0,0]
=> [2,3,1,5,4] => [2,5,1,4,3] => [1,1,0,1,1,1,0,0,0,0]
=> 1 = 0 + 1
[1,1,0,1,0,1,0,0,1,0]
=> [2,3,4,1,5] => [2,5,4,1,3] => [1,1,0,1,1,1,0,0,0,0]
=> 1 = 0 + 1
[1,1,0,1,0,1,0,1,0,0]
=> [2,3,4,5,1] => [2,5,4,3,1] => [1,1,0,1,1,1,0,0,0,0]
=> 1 = 0 + 1
[1,1,0,1,0,1,1,0,0,0]
=> [2,3,5,1,4] => [2,5,4,1,3] => [1,1,0,1,1,1,0,0,0,0]
=> 1 = 0 + 1
[1,1,0,1,1,0,0,0,1,0]
=> [2,4,1,3,5] => [2,5,1,4,3] => [1,1,0,1,1,1,0,0,0,0]
=> 1 = 0 + 1
[1,1,0,1,1,0,0,1,0,0]
=> [2,4,1,5,3] => [2,5,1,4,3] => [1,1,0,1,1,1,0,0,0,0]
=> 1 = 0 + 1
[1,1,0,1,1,0,1,0,0,0]
=> [2,4,5,1,3] => [2,5,4,1,3] => [1,1,0,1,1,1,0,0,0,0]
=> 1 = 0 + 1
[1,1,0,1,1,1,0,0,0,0]
=> [2,5,1,3,4] => [2,5,1,4,3] => [1,1,0,1,1,1,0,0,0,0]
=> 1 = 0 + 1
[1,1,1,0,0,0,1,0,1,0]
=> [3,1,2,4,5] => [3,1,5,4,2] => [1,1,1,0,0,1,1,0,0,0]
=> 2 = 1 + 1
[1,1,1,0,0,0,1,1,0,0]
=> [3,1,2,5,4] => [3,1,5,4,2] => [1,1,1,0,0,1,1,0,0,0]
=> 2 = 1 + 1
[1,1,1,0,0,1,0,0,1,0]
=> [3,1,4,2,5] => [3,1,5,4,2] => [1,1,1,0,0,1,1,0,0,0]
=> 2 = 1 + 1
[1,1,1,0,0,1,0,1,0,0]
=> [3,1,4,5,2] => [3,1,5,4,2] => [1,1,1,0,0,1,1,0,0,0]
=> 2 = 1 + 1
[1,1,1,0,0,1,1,0,0,0]
=> [3,1,5,2,4] => [3,1,5,4,2] => [1,1,1,0,0,1,1,0,0,0]
=> 2 = 1 + 1
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,2,3,4,5,6] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0]
=> 1 = 0 + 1
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,2,3,4,6,5] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0]
=> 1 = 0 + 1
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,2,3,5,4,6] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0]
=> 1 = 0 + 1
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,2,3,5,6,4] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0]
=> 1 = 0 + 1
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,2,3,6,4,5] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0]
=> 1 = 0 + 1
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,2,4,3,5,6] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0]
=> 1 = 0 + 1
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [1,2,4,3,6,5] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0]
=> 1 = 0 + 1
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,2,4,5,3,6] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0]
=> 1 = 0 + 1
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,2,4,5,6,3] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0]
=> 1 = 0 + 1
[1,0,1,0,1,1,0,1,1,0,0,0]
=> [1,2,4,6,3,5] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0]
=> 1 = 0 + 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]
=> [3,1,2,4,5,6,7] => [3,1,7,6,5,4,2] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]
=> [3,1,2,4,5,7,6] => [3,1,7,6,5,4,2] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]
=> [3,1,2,4,6,5,7] => [3,1,7,6,5,4,2] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]
=> [3,1,2,4,6,7,5] => [3,1,7,6,5,4,2] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]
=> [3,1,2,4,7,5,6] => [3,1,7,6,5,4,2] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]
=> [3,1,2,5,4,6,7] => [3,1,7,6,5,4,2] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]
=> [3,1,2,5,4,7,6] => [3,1,7,6,5,4,2] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]
=> [3,1,2,5,6,4,7] => [3,1,7,6,5,4,2] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]
=> [3,1,2,5,6,7,4] => [3,1,7,6,5,4,2] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]
=> [3,1,2,5,7,4,6] => [3,1,7,6,5,4,2] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]
=> [3,1,2,6,4,5,7] => [3,1,7,6,5,4,2] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]
=> [3,1,2,6,4,7,5] => [3,1,7,6,5,4,2] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]
=> [3,1,2,6,7,4,5] => [3,1,7,6,5,4,2] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
=> [3,1,2,7,4,5,6] => [3,1,7,6,5,4,2] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]
=> [3,1,4,2,5,6,7] => [3,1,7,6,5,4,2] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]
=> [3,1,4,2,5,7,6] => [3,1,7,6,5,4,2] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]
=> [3,1,4,2,6,5,7] => [3,1,7,6,5,4,2] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]
=> [3,1,4,2,6,7,5] => [3,1,7,6,5,4,2] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]
=> [3,1,4,2,7,5,6] => [3,1,7,6,5,4,2] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]
=> [3,1,4,5,2,6,7] => [3,1,7,6,5,4,2] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]
=> [3,1,4,5,2,7,6] => [3,1,7,6,5,4,2] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]
=> [3,1,4,5,6,2,7] => [3,1,7,6,5,4,2] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]
=> [3,1,4,5,6,7,2] => [3,1,7,6,5,4,2] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]
=> [3,1,4,5,7,2,6] => [3,1,7,6,5,4,2] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]
=> [3,1,4,6,2,5,7] => [3,1,7,6,5,4,2] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]
=> [3,1,4,6,2,7,5] => [3,1,7,6,5,4,2] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]
=> [3,1,4,6,7,2,5] => [3,1,7,6,5,4,2] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [3,1,4,7,2,5,6] => [3,1,7,6,5,4,2] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]
=> [3,1,5,2,4,6,7] => [3,1,7,6,5,4,2] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]
=> [3,1,5,2,4,7,6] => [3,1,7,6,5,4,2] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]
=> [3,1,5,2,6,4,7] => [3,1,7,6,5,4,2] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]
=> [3,1,5,2,6,7,4] => [3,1,7,6,5,4,2] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]
=> [3,1,5,2,7,4,6] => [3,1,7,6,5,4,2] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]
=> [3,1,5,6,2,4,7] => [3,1,7,6,5,4,2] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]
=> [3,1,5,6,2,7,4] => [3,1,7,6,5,4,2] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]
=> [3,1,5,6,7,2,4] => [3,1,7,6,5,4,2] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [3,1,5,7,2,4,6] => [3,1,7,6,5,4,2] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]
=> [3,1,6,2,4,5,7] => [3,1,7,6,5,4,2] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]
=> [3,1,6,2,4,7,5] => [3,1,7,6,5,4,2] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]
=> [3,1,6,2,7,4,5] => [3,1,7,6,5,4,2] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]
=> [3,1,6,7,2,4,5] => [3,1,7,6,5,4,2] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
=> [3,1,7,2,4,5,6] => [3,1,7,6,5,4,2] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]
=> [4,1,2,3,5,6,7] => [4,1,7,6,5,3,2] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]
=> [4,1,2,3,5,7,6] => [4,1,7,6,5,3,2] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]
=> [4,1,2,3,6,5,7] => [4,1,7,6,5,3,2] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]
=> [4,1,2,3,6,7,5] => [4,1,7,6,5,3,2] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]
=> [4,1,2,3,7,5,6] => [4,1,7,6,5,3,2] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]
=> [4,1,2,5,3,6,7] => [4,1,7,6,5,3,2] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]
=> [4,1,2,5,3,7,6] => [4,1,7,6,5,3,2] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]
=> [4,1,2,5,6,3,7] => [4,1,7,6,5,3,2] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
Description
The number of global maxima of a Dyck path.
Matching statistic: St001603
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00129: Dyck paths —to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶ Permutations
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001603: Integer partitions ⟶ ℤResult quality: 36% ●values known / values provided: 36%●distinct values known / distinct values provided: 50%
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001603: Integer partitions ⟶ ℤResult quality: 36% ●values known / values provided: 36%●distinct values known / distinct values provided: 50%
Values
[1,0,1,0,1,0,1,0]
=> [2,3,4,1] => [3,1]
=> [1]
=> ? = 0 + 1
[1,0,1,0,1,1,0,0]
=> [2,3,1,4] => [3,1]
=> [1]
=> ? = 0 + 1
[1,0,1,1,0,0,1,0]
=> [2,1,4,3] => [2,2]
=> [2]
=> ? = 0 + 1
[1,0,1,1,0,1,0,0]
=> [2,4,1,3] => [2,2]
=> [2]
=> ? = 0 + 1
[1,0,1,1,1,0,0,0]
=> [2,1,3,4] => [3,1]
=> [1]
=> ? = 0 + 1
[1,1,0,0,1,0,1,0]
=> [1,3,4,2] => [3,1]
=> [1]
=> ? = 1 + 1
[1,1,0,0,1,1,0,0]
=> [1,3,2,4] => [3,1]
=> [1]
=> ? = 1 + 1
[1,0,1,0,1,0,1,0,1,0]
=> [2,3,4,5,1] => [4,1]
=> [1]
=> ? = 0 + 1
[1,0,1,0,1,0,1,1,0,0]
=> [2,3,4,1,5] => [4,1]
=> [1]
=> ? = 0 + 1
[1,0,1,0,1,1,0,0,1,0]
=> [2,3,1,5,4] => [3,2]
=> [2]
=> ? = 0 + 1
[1,0,1,0,1,1,0,1,0,0]
=> [2,3,5,1,4] => [3,2]
=> [2]
=> ? = 0 + 1
[1,0,1,0,1,1,1,0,0,0]
=> [2,3,1,4,5] => [4,1]
=> [1]
=> ? = 0 + 1
[1,0,1,1,0,0,1,0,1,0]
=> [2,1,4,5,3] => [3,2]
=> [2]
=> ? = 0 + 1
[1,0,1,1,0,0,1,1,0,0]
=> [2,1,4,3,5] => [3,2]
=> [2]
=> ? = 0 + 1
[1,0,1,1,0,1,0,0,1,0]
=> [2,4,1,5,3] => [3,2]
=> [2]
=> ? = 0 + 1
[1,0,1,1,0,1,0,1,0,0]
=> [2,4,5,1,3] => [3,2]
=> [2]
=> ? = 0 + 1
[1,0,1,1,0,1,1,0,0,0]
=> [2,4,1,3,5] => [3,2]
=> [2]
=> ? = 0 + 1
[1,0,1,1,1,0,0,0,1,0]
=> [2,1,3,5,4] => [3,2]
=> [2]
=> ? = 0 + 1
[1,0,1,1,1,0,0,1,0,0]
=> [2,1,5,3,4] => [3,2]
=> [2]
=> ? = 0 + 1
[1,0,1,1,1,0,1,0,0,0]
=> [2,5,1,3,4] => [3,2]
=> [2]
=> ? = 0 + 1
[1,0,1,1,1,1,0,0,0,0]
=> [2,1,3,4,5] => [4,1]
=> [1]
=> ? = 0 + 1
[1,1,0,0,1,0,1,0,1,0]
=> [1,3,4,5,2] => [4,1]
=> [1]
=> ? = 0 + 1
[1,1,0,0,1,0,1,1,0,0]
=> [1,3,4,2,5] => [4,1]
=> [1]
=> ? = 0 + 1
[1,1,0,0,1,1,0,0,1,0]
=> [1,3,2,5,4] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,0,0,1,1,0,1,0,0]
=> [1,3,5,2,4] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,0,0,1,1,1,0,0,0]
=> [1,3,2,4,5] => [4,1]
=> [1]
=> ? = 0 + 1
[1,1,0,1,0,0,1,0,1,0]
=> [3,1,4,5,2] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,0,1,0,0,1,1,0,0]
=> [3,1,4,2,5] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,0,1,0,1,0,0,1,0]
=> [3,4,1,5,2] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,0,1,0,1,0,1,0,0]
=> [3,4,5,1,2] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,0,1,0,1,1,0,0,0]
=> [3,4,1,2,5] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,0,1,1,0,0,0,1,0]
=> [3,1,2,5,4] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,0,1,1,0,0,1,0,0]
=> [3,1,5,2,4] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,0,1,1,0,1,0,0,0]
=> [3,5,1,2,4] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,0,1,1,1,0,0,0,0]
=> [3,1,2,4,5] => [4,1]
=> [1]
=> ? = 0 + 1
[1,1,1,0,0,0,1,0,1,0]
=> [1,2,4,5,3] => [4,1]
=> [1]
=> ? = 1 + 1
[1,1,1,0,0,0,1,1,0,0]
=> [1,2,4,3,5] => [4,1]
=> [1]
=> ? = 1 + 1
[1,1,1,0,0,1,0,0,1,0]
=> [1,4,2,5,3] => [3,2]
=> [2]
=> ? = 1 + 1
[1,1,1,0,0,1,0,1,0,0]
=> [1,4,5,2,3] => [3,2]
=> [2]
=> ? = 1 + 1
[1,1,1,0,0,1,1,0,0,0]
=> [1,4,2,3,5] => [4,1]
=> [1]
=> ? = 1 + 1
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [2,3,4,5,6,1] => [5,1]
=> [1]
=> ? = 0 + 1
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [2,3,4,5,1,6] => [5,1]
=> [1]
=> ? = 0 + 1
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [2,3,4,1,6,5] => [4,2]
=> [2]
=> ? = 0 + 1
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [2,3,4,6,1,5] => [4,2]
=> [2]
=> ? = 0 + 1
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [2,3,4,1,5,6] => [5,1]
=> [1]
=> ? = 0 + 1
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [2,3,1,5,6,4] => [4,2]
=> [2]
=> ? = 0 + 1
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [2,3,1,5,4,6] => [4,2]
=> [2]
=> ? = 0 + 1
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [2,3,5,1,6,4] => [4,2]
=> [2]
=> ? = 0 + 1
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [2,3,5,6,1,4] => [4,2]
=> [2]
=> ? = 0 + 1
[1,0,1,0,1,1,0,1,1,0,0,0]
=> [2,3,5,1,4,6] => [4,2]
=> [2]
=> ? = 0 + 1
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [2,1,4,3,6,5] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,0,1,1,0,1,0,0]
=> [2,1,4,6,3,5] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,1,1,0,0,0,1,0]
=> [2,4,1,3,6,5] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,1,1,0,0,1,0,0]
=> [2,4,1,6,3,5] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,1,1,0,1,0,0,0]
=> [2,4,6,1,3,5] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,1,0,0,1,0,0,1,0]
=> [2,1,5,3,6,4] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,1,0,0,1,0,1,0,0]
=> [2,1,5,6,3,4] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,1,0,1,0,0,0,1,0]
=> [2,5,1,3,6,4] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,1,0,1,0,0,1,0,0]
=> [2,5,1,6,3,4] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,1,0,1,0,1,0,0,0]
=> [2,5,6,1,3,4] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,0,0,1,1,0,0,1,0]
=> [3,1,4,2,6,5] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,0,0,1,1,0,1,0,0]
=> [3,1,4,6,2,5] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,0,1,1,0,0,0,1,0]
=> [3,4,1,2,6,5] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,0,1,1,0,0,1,0,0]
=> [3,4,1,6,2,5] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,0,1,1,0,1,0,0,0]
=> [3,4,6,1,2,5] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,1,0,0,1,0,0,1,0]
=> [3,1,5,2,6,4] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,1,0,0,1,0,1,0,0]
=> [3,1,5,6,2,4] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,1,0,1,0,0,0,1,0]
=> [3,5,1,2,6,4] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,1,0,1,0,0,1,0,0]
=> [3,5,1,6,2,4] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,1,0,1,0,1,0,0,0]
=> [3,5,6,1,2,4] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,0,0,1,0,0,1,0]
=> [4,1,5,2,6,3] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,0,0,1,0,1,0,0]
=> [4,1,5,6,2,3] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,0,1,0,0,0,1,0]
=> [4,5,1,2,6,3] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,0,1,0,0,1,0,0]
=> [4,5,1,6,2,3] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,0,1,0,1,0,0,0]
=> [4,5,6,1,2,3] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]
=> [2,3,5,1,4,7,6] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]
=> [2,3,5,1,7,4,6] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]
=> [2,3,5,7,1,4,6] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]
=> [2,3,1,6,4,7,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]
=> [2,3,1,6,7,4,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]
=> [2,3,6,1,4,7,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]
=> [2,3,6,1,7,4,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]
=> [2,3,6,7,1,4,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]
=> [2,1,4,6,3,7,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]
=> [2,1,4,6,7,3,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]
=> [2,1,4,6,3,5,7] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> [2,1,4,3,5,7,6] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]
=> [2,1,4,3,7,5,6] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]
=> [2,1,4,7,3,5,6] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]
=> [2,4,1,5,3,7,6] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]
=> [2,4,1,5,7,3,6] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]
=> [2,4,5,1,3,7,6] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]
=> [2,4,5,1,7,3,6] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]
=> [2,4,5,7,1,3,6] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]
=> [2,4,1,3,6,7,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]
=> [2,4,1,3,6,5,7] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]
=> [2,4,1,6,3,7,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]
=> [2,4,1,6,7,3,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,4,1,6,3,5,7] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]
=> [2,4,6,1,3,7,5] => [4,3]
=> [3]
=> 1 = 0 + 1
Description
The number of colourings of a polygon such that the multiplicities of a colour are given by a partition.
Two colourings are considered equal, if they are obtained by an action of the dihedral group.
This statistic is only defined for partitions of size at least 3, to avoid ambiguity.
Matching statistic: St001604
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00129: Dyck paths —to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶ Permutations
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001604: Integer partitions ⟶ ℤResult quality: 36% ●values known / values provided: 36%●distinct values known / distinct values provided: 50%
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001604: Integer partitions ⟶ ℤResult quality: 36% ●values known / values provided: 36%●distinct values known / distinct values provided: 50%
Values
[1,0,1,0,1,0,1,0]
=> [2,3,4,1] => [3,1]
=> [1]
=> ? = 0 + 1
[1,0,1,0,1,1,0,0]
=> [2,3,1,4] => [3,1]
=> [1]
=> ? = 0 + 1
[1,0,1,1,0,0,1,0]
=> [2,1,4,3] => [2,2]
=> [2]
=> ? = 0 + 1
[1,0,1,1,0,1,0,0]
=> [2,4,1,3] => [2,2]
=> [2]
=> ? = 0 + 1
[1,0,1,1,1,0,0,0]
=> [2,1,3,4] => [3,1]
=> [1]
=> ? = 0 + 1
[1,1,0,0,1,0,1,0]
=> [1,3,4,2] => [3,1]
=> [1]
=> ? = 1 + 1
[1,1,0,0,1,1,0,0]
=> [1,3,2,4] => [3,1]
=> [1]
=> ? = 1 + 1
[1,0,1,0,1,0,1,0,1,0]
=> [2,3,4,5,1] => [4,1]
=> [1]
=> ? = 0 + 1
[1,0,1,0,1,0,1,1,0,0]
=> [2,3,4,1,5] => [4,1]
=> [1]
=> ? = 0 + 1
[1,0,1,0,1,1,0,0,1,0]
=> [2,3,1,5,4] => [3,2]
=> [2]
=> ? = 0 + 1
[1,0,1,0,1,1,0,1,0,0]
=> [2,3,5,1,4] => [3,2]
=> [2]
=> ? = 0 + 1
[1,0,1,0,1,1,1,0,0,0]
=> [2,3,1,4,5] => [4,1]
=> [1]
=> ? = 0 + 1
[1,0,1,1,0,0,1,0,1,0]
=> [2,1,4,5,3] => [3,2]
=> [2]
=> ? = 0 + 1
[1,0,1,1,0,0,1,1,0,0]
=> [2,1,4,3,5] => [3,2]
=> [2]
=> ? = 0 + 1
[1,0,1,1,0,1,0,0,1,0]
=> [2,4,1,5,3] => [3,2]
=> [2]
=> ? = 0 + 1
[1,0,1,1,0,1,0,1,0,0]
=> [2,4,5,1,3] => [3,2]
=> [2]
=> ? = 0 + 1
[1,0,1,1,0,1,1,0,0,0]
=> [2,4,1,3,5] => [3,2]
=> [2]
=> ? = 0 + 1
[1,0,1,1,1,0,0,0,1,0]
=> [2,1,3,5,4] => [3,2]
=> [2]
=> ? = 0 + 1
[1,0,1,1,1,0,0,1,0,0]
=> [2,1,5,3,4] => [3,2]
=> [2]
=> ? = 0 + 1
[1,0,1,1,1,0,1,0,0,0]
=> [2,5,1,3,4] => [3,2]
=> [2]
=> ? = 0 + 1
[1,0,1,1,1,1,0,0,0,0]
=> [2,1,3,4,5] => [4,1]
=> [1]
=> ? = 0 + 1
[1,1,0,0,1,0,1,0,1,0]
=> [1,3,4,5,2] => [4,1]
=> [1]
=> ? = 0 + 1
[1,1,0,0,1,0,1,1,0,0]
=> [1,3,4,2,5] => [4,1]
=> [1]
=> ? = 0 + 1
[1,1,0,0,1,1,0,0,1,0]
=> [1,3,2,5,4] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,0,0,1,1,0,1,0,0]
=> [1,3,5,2,4] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,0,0,1,1,1,0,0,0]
=> [1,3,2,4,5] => [4,1]
=> [1]
=> ? = 0 + 1
[1,1,0,1,0,0,1,0,1,0]
=> [3,1,4,5,2] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,0,1,0,0,1,1,0,0]
=> [3,1,4,2,5] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,0,1,0,1,0,0,1,0]
=> [3,4,1,5,2] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,0,1,0,1,0,1,0,0]
=> [3,4,5,1,2] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,0,1,0,1,1,0,0,0]
=> [3,4,1,2,5] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,0,1,1,0,0,0,1,0]
=> [3,1,2,5,4] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,0,1,1,0,0,1,0,0]
=> [3,1,5,2,4] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,0,1,1,0,1,0,0,0]
=> [3,5,1,2,4] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,0,1,1,1,0,0,0,0]
=> [3,1,2,4,5] => [4,1]
=> [1]
=> ? = 0 + 1
[1,1,1,0,0,0,1,0,1,0]
=> [1,2,4,5,3] => [4,1]
=> [1]
=> ? = 1 + 1
[1,1,1,0,0,0,1,1,0,0]
=> [1,2,4,3,5] => [4,1]
=> [1]
=> ? = 1 + 1
[1,1,1,0,0,1,0,0,1,0]
=> [1,4,2,5,3] => [3,2]
=> [2]
=> ? = 1 + 1
[1,1,1,0,0,1,0,1,0,0]
=> [1,4,5,2,3] => [3,2]
=> [2]
=> ? = 1 + 1
[1,1,1,0,0,1,1,0,0,0]
=> [1,4,2,3,5] => [4,1]
=> [1]
=> ? = 1 + 1
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [2,3,4,5,6,1] => [5,1]
=> [1]
=> ? = 0 + 1
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [2,3,4,5,1,6] => [5,1]
=> [1]
=> ? = 0 + 1
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [2,3,4,1,6,5] => [4,2]
=> [2]
=> ? = 0 + 1
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [2,3,4,6,1,5] => [4,2]
=> [2]
=> ? = 0 + 1
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [2,3,4,1,5,6] => [5,1]
=> [1]
=> ? = 0 + 1
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [2,3,1,5,6,4] => [4,2]
=> [2]
=> ? = 0 + 1
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [2,3,1,5,4,6] => [4,2]
=> [2]
=> ? = 0 + 1
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [2,3,5,1,6,4] => [4,2]
=> [2]
=> ? = 0 + 1
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [2,3,5,6,1,4] => [4,2]
=> [2]
=> ? = 0 + 1
[1,0,1,0,1,1,0,1,1,0,0,0]
=> [2,3,5,1,4,6] => [4,2]
=> [2]
=> ? = 0 + 1
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [2,1,4,3,6,5] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,0,1,1,0,1,0,0]
=> [2,1,4,6,3,5] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,1,1,0,0,0,1,0]
=> [2,4,1,3,6,5] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,1,1,0,0,1,0,0]
=> [2,4,1,6,3,5] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,1,1,0,1,0,0,0]
=> [2,4,6,1,3,5] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,1,0,0,1,0,0,1,0]
=> [2,1,5,3,6,4] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,1,0,0,1,0,1,0,0]
=> [2,1,5,6,3,4] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,1,0,1,0,0,0,1,0]
=> [2,5,1,3,6,4] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,1,0,1,0,0,1,0,0]
=> [2,5,1,6,3,4] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,1,0,1,0,1,0,0,0]
=> [2,5,6,1,3,4] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,0,0,1,1,0,0,1,0]
=> [3,1,4,2,6,5] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,0,0,1,1,0,1,0,0]
=> [3,1,4,6,2,5] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,0,1,1,0,0,0,1,0]
=> [3,4,1,2,6,5] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,0,1,1,0,0,1,0,0]
=> [3,4,1,6,2,5] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,0,1,1,0,1,0,0,0]
=> [3,4,6,1,2,5] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,1,0,0,1,0,0,1,0]
=> [3,1,5,2,6,4] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,1,0,0,1,0,1,0,0]
=> [3,1,5,6,2,4] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,1,0,1,0,0,0,1,0]
=> [3,5,1,2,6,4] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,1,0,1,0,0,1,0,0]
=> [3,5,1,6,2,4] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,1,0,1,0,1,0,0,0]
=> [3,5,6,1,2,4] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,0,0,1,0,0,1,0]
=> [4,1,5,2,6,3] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,0,0,1,0,1,0,0]
=> [4,1,5,6,2,3] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,0,1,0,0,0,1,0]
=> [4,5,1,2,6,3] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,0,1,0,0,1,0,0]
=> [4,5,1,6,2,3] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,0,1,0,1,0,0,0]
=> [4,5,6,1,2,3] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]
=> [2,3,5,1,4,7,6] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]
=> [2,3,5,1,7,4,6] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]
=> [2,3,5,7,1,4,6] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]
=> [2,3,1,6,4,7,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]
=> [2,3,1,6,7,4,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]
=> [2,3,6,1,4,7,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]
=> [2,3,6,1,7,4,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]
=> [2,3,6,7,1,4,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]
=> [2,1,4,6,3,7,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]
=> [2,1,4,6,7,3,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]
=> [2,1,4,6,3,5,7] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> [2,1,4,3,5,7,6] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]
=> [2,1,4,3,7,5,6] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]
=> [2,1,4,7,3,5,6] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]
=> [2,4,1,5,3,7,6] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]
=> [2,4,1,5,7,3,6] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]
=> [2,4,5,1,3,7,6] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]
=> [2,4,5,1,7,3,6] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]
=> [2,4,5,7,1,3,6] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]
=> [2,4,1,3,6,7,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]
=> [2,4,1,3,6,5,7] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]
=> [2,4,1,6,3,7,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]
=> [2,4,1,6,7,3,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,4,1,6,3,5,7] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]
=> [2,4,6,1,3,7,5] => [4,3]
=> [3]
=> 1 = 0 + 1
Description
The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on polygons.
Equivalently, this is the multiplicity of the irreducible representation corresponding to a partition in the cycle index of the dihedral group.
This statistic is only defined for partitions of size at least 3, to avoid ambiguity.
Matching statistic: St001605
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00129: Dyck paths —to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶ Permutations
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001605: Integer partitions ⟶ ℤResult quality: 36% ●values known / values provided: 36%●distinct values known / distinct values provided: 50%
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001605: Integer partitions ⟶ ℤResult quality: 36% ●values known / values provided: 36%●distinct values known / distinct values provided: 50%
Values
[1,0,1,0,1,0,1,0]
=> [2,3,4,1] => [3,1]
=> [1]
=> ? = 0 + 1
[1,0,1,0,1,1,0,0]
=> [2,3,1,4] => [3,1]
=> [1]
=> ? = 0 + 1
[1,0,1,1,0,0,1,0]
=> [2,1,4,3] => [2,2]
=> [2]
=> ? = 0 + 1
[1,0,1,1,0,1,0,0]
=> [2,4,1,3] => [2,2]
=> [2]
=> ? = 0 + 1
[1,0,1,1,1,0,0,0]
=> [2,1,3,4] => [3,1]
=> [1]
=> ? = 0 + 1
[1,1,0,0,1,0,1,0]
=> [1,3,4,2] => [3,1]
=> [1]
=> ? = 1 + 1
[1,1,0,0,1,1,0,0]
=> [1,3,2,4] => [3,1]
=> [1]
=> ? = 1 + 1
[1,0,1,0,1,0,1,0,1,0]
=> [2,3,4,5,1] => [4,1]
=> [1]
=> ? = 0 + 1
[1,0,1,0,1,0,1,1,0,0]
=> [2,3,4,1,5] => [4,1]
=> [1]
=> ? = 0 + 1
[1,0,1,0,1,1,0,0,1,0]
=> [2,3,1,5,4] => [3,2]
=> [2]
=> ? = 0 + 1
[1,0,1,0,1,1,0,1,0,0]
=> [2,3,5,1,4] => [3,2]
=> [2]
=> ? = 0 + 1
[1,0,1,0,1,1,1,0,0,0]
=> [2,3,1,4,5] => [4,1]
=> [1]
=> ? = 0 + 1
[1,0,1,1,0,0,1,0,1,0]
=> [2,1,4,5,3] => [3,2]
=> [2]
=> ? = 0 + 1
[1,0,1,1,0,0,1,1,0,0]
=> [2,1,4,3,5] => [3,2]
=> [2]
=> ? = 0 + 1
[1,0,1,1,0,1,0,0,1,0]
=> [2,4,1,5,3] => [3,2]
=> [2]
=> ? = 0 + 1
[1,0,1,1,0,1,0,1,0,0]
=> [2,4,5,1,3] => [3,2]
=> [2]
=> ? = 0 + 1
[1,0,1,1,0,1,1,0,0,0]
=> [2,4,1,3,5] => [3,2]
=> [2]
=> ? = 0 + 1
[1,0,1,1,1,0,0,0,1,0]
=> [2,1,3,5,4] => [3,2]
=> [2]
=> ? = 0 + 1
[1,0,1,1,1,0,0,1,0,0]
=> [2,1,5,3,4] => [3,2]
=> [2]
=> ? = 0 + 1
[1,0,1,1,1,0,1,0,0,0]
=> [2,5,1,3,4] => [3,2]
=> [2]
=> ? = 0 + 1
[1,0,1,1,1,1,0,0,0,0]
=> [2,1,3,4,5] => [4,1]
=> [1]
=> ? = 0 + 1
[1,1,0,0,1,0,1,0,1,0]
=> [1,3,4,5,2] => [4,1]
=> [1]
=> ? = 0 + 1
[1,1,0,0,1,0,1,1,0,0]
=> [1,3,4,2,5] => [4,1]
=> [1]
=> ? = 0 + 1
[1,1,0,0,1,1,0,0,1,0]
=> [1,3,2,5,4] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,0,0,1,1,0,1,0,0]
=> [1,3,5,2,4] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,0,0,1,1,1,0,0,0]
=> [1,3,2,4,5] => [4,1]
=> [1]
=> ? = 0 + 1
[1,1,0,1,0,0,1,0,1,0]
=> [3,1,4,5,2] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,0,1,0,0,1,1,0,0]
=> [3,1,4,2,5] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,0,1,0,1,0,0,1,0]
=> [3,4,1,5,2] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,0,1,0,1,0,1,0,0]
=> [3,4,5,1,2] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,0,1,0,1,1,0,0,0]
=> [3,4,1,2,5] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,0,1,1,0,0,0,1,0]
=> [3,1,2,5,4] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,0,1,1,0,0,1,0,0]
=> [3,1,5,2,4] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,0,1,1,0,1,0,0,0]
=> [3,5,1,2,4] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,0,1,1,1,0,0,0,0]
=> [3,1,2,4,5] => [4,1]
=> [1]
=> ? = 0 + 1
[1,1,1,0,0,0,1,0,1,0]
=> [1,2,4,5,3] => [4,1]
=> [1]
=> ? = 1 + 1
[1,1,1,0,0,0,1,1,0,0]
=> [1,2,4,3,5] => [4,1]
=> [1]
=> ? = 1 + 1
[1,1,1,0,0,1,0,0,1,0]
=> [1,4,2,5,3] => [3,2]
=> [2]
=> ? = 1 + 1
[1,1,1,0,0,1,0,1,0,0]
=> [1,4,5,2,3] => [3,2]
=> [2]
=> ? = 1 + 1
[1,1,1,0,0,1,1,0,0,0]
=> [1,4,2,3,5] => [4,1]
=> [1]
=> ? = 1 + 1
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [2,3,4,5,6,1] => [5,1]
=> [1]
=> ? = 0 + 1
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [2,3,4,5,1,6] => [5,1]
=> [1]
=> ? = 0 + 1
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [2,3,4,1,6,5] => [4,2]
=> [2]
=> ? = 0 + 1
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [2,3,4,6,1,5] => [4,2]
=> [2]
=> ? = 0 + 1
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [2,3,4,1,5,6] => [5,1]
=> [1]
=> ? = 0 + 1
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [2,3,1,5,6,4] => [4,2]
=> [2]
=> ? = 0 + 1
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [2,3,1,5,4,6] => [4,2]
=> [2]
=> ? = 0 + 1
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [2,3,5,1,6,4] => [4,2]
=> [2]
=> ? = 0 + 1
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [2,3,5,6,1,4] => [4,2]
=> [2]
=> ? = 0 + 1
[1,0,1,0,1,1,0,1,1,0,0,0]
=> [2,3,5,1,4,6] => [4,2]
=> [2]
=> ? = 0 + 1
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [2,1,4,3,6,5] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,0,1,1,0,1,0,0]
=> [2,1,4,6,3,5] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,1,1,0,0,0,1,0]
=> [2,4,1,3,6,5] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,1,1,0,0,1,0,0]
=> [2,4,1,6,3,5] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,1,1,0,1,0,0,0]
=> [2,4,6,1,3,5] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,1,0,0,1,0,0,1,0]
=> [2,1,5,3,6,4] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,1,0,0,1,0,1,0,0]
=> [2,1,5,6,3,4] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,1,0,1,0,0,0,1,0]
=> [2,5,1,3,6,4] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,1,0,1,0,0,1,0,0]
=> [2,5,1,6,3,4] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,1,0,1,0,1,0,0,0]
=> [2,5,6,1,3,4] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,0,0,1,1,0,0,1,0]
=> [3,1,4,2,6,5] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,0,0,1,1,0,1,0,0]
=> [3,1,4,6,2,5] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,0,1,1,0,0,0,1,0]
=> [3,4,1,2,6,5] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,0,1,1,0,0,1,0,0]
=> [3,4,1,6,2,5] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,0,1,1,0,1,0,0,0]
=> [3,4,6,1,2,5] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,1,0,0,1,0,0,1,0]
=> [3,1,5,2,6,4] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,1,0,0,1,0,1,0,0]
=> [3,1,5,6,2,4] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,1,0,1,0,0,0,1,0]
=> [3,5,1,2,6,4] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,1,0,1,0,0,1,0,0]
=> [3,5,1,6,2,4] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,1,0,1,0,1,0,0,0]
=> [3,5,6,1,2,4] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,0,0,1,0,0,1,0]
=> [4,1,5,2,6,3] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,0,0,1,0,1,0,0]
=> [4,1,5,6,2,3] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,0,1,0,0,0,1,0]
=> [4,5,1,2,6,3] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,0,1,0,0,1,0,0]
=> [4,5,1,6,2,3] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,0,1,0,1,0,0,0]
=> [4,5,6,1,2,3] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]
=> [2,3,5,1,4,7,6] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]
=> [2,3,5,1,7,4,6] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]
=> [2,3,5,7,1,4,6] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]
=> [2,3,1,6,4,7,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]
=> [2,3,1,6,7,4,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]
=> [2,3,6,1,4,7,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]
=> [2,3,6,1,7,4,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]
=> [2,3,6,7,1,4,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]
=> [2,1,4,6,3,7,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]
=> [2,1,4,6,7,3,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]
=> [2,1,4,6,3,5,7] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> [2,1,4,3,5,7,6] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]
=> [2,1,4,3,7,5,6] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]
=> [2,1,4,7,3,5,6] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]
=> [2,4,1,5,3,7,6] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]
=> [2,4,1,5,7,3,6] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]
=> [2,4,5,1,3,7,6] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]
=> [2,4,5,1,7,3,6] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]
=> [2,4,5,7,1,3,6] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]
=> [2,4,1,3,6,7,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]
=> [2,4,1,3,6,5,7] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]
=> [2,4,1,6,3,7,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]
=> [2,4,1,6,7,3,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,4,1,6,3,5,7] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]
=> [2,4,6,1,3,7,5] => [4,3]
=> [3]
=> 1 = 0 + 1
Description
The number of colourings of a cycle such that the multiplicities of colours are given by a partition.
Two colourings are considered equal, if they are obtained by an action of the cyclic group.
This statistic is only defined for partitions of size at least 3, to avoid ambiguity.
Matching statistic: St000661
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
Mp00066: Permutations —inverse⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
St000661: Dyck paths ⟶ ℤResult quality: 32% ●values known / values provided: 32%●distinct values known / distinct values provided: 100%
Mp00066: Permutations —inverse⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
St000661: Dyck paths ⟶ ℤResult quality: 32% ●values known / values provided: 32%●distinct values known / distinct values provided: 100%
Values
[1,0,1,0,1,0,1,0]
=> [4,3,2,1] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
=> 0
[1,0,1,0,1,1,0,0]
=> [3,4,2,1] => [4,3,1,2] => [1,1,1,1,0,0,0,0]
=> 0
[1,0,1,1,0,0,1,0]
=> [4,2,3,1] => [4,2,3,1] => [1,1,1,1,0,0,0,0]
=> 0
[1,0,1,1,0,1,0,0]
=> [3,2,4,1] => [4,2,1,3] => [1,1,1,1,0,0,0,0]
=> 0
[1,0,1,1,1,0,0,0]
=> [2,3,4,1] => [4,1,2,3] => [1,1,1,1,0,0,0,0]
=> 0
[1,1,0,0,1,0,1,0]
=> [4,3,1,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
=> 1
[1,1,0,0,1,1,0,0]
=> [3,4,1,2] => [3,4,1,2] => [1,1,1,0,1,0,0,0]
=> 1
[1,0,1,0,1,0,1,0,1,0]
=> [5,4,3,2,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> 0
[1,0,1,0,1,0,1,1,0,0]
=> [4,5,3,2,1] => [5,4,3,1,2] => [1,1,1,1,1,0,0,0,0,0]
=> 0
[1,0,1,0,1,1,0,0,1,0]
=> [5,3,4,2,1] => [5,4,2,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> 0
[1,0,1,0,1,1,0,1,0,0]
=> [4,3,5,2,1] => [5,4,2,1,3] => [1,1,1,1,1,0,0,0,0,0]
=> 0
[1,0,1,0,1,1,1,0,0,0]
=> [3,4,5,2,1] => [5,4,1,2,3] => [1,1,1,1,1,0,0,0,0,0]
=> 0
[1,0,1,1,0,0,1,0,1,0]
=> [5,4,2,3,1] => [5,3,4,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> 0
[1,0,1,1,0,0,1,1,0,0]
=> [4,5,2,3,1] => [5,3,4,1,2] => [1,1,1,1,1,0,0,0,0,0]
=> 0
[1,0,1,1,0,1,0,0,1,0]
=> [5,3,2,4,1] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> 0
[1,0,1,1,0,1,0,1,0,0]
=> [4,3,2,5,1] => [5,3,2,1,4] => [1,1,1,1,1,0,0,0,0,0]
=> 0
[1,0,1,1,0,1,1,0,0,0]
=> [3,4,2,5,1] => [5,3,1,2,4] => [1,1,1,1,1,0,0,0,0,0]
=> 0
[1,0,1,1,1,0,0,0,1,0]
=> [5,2,3,4,1] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> 0
[1,0,1,1,1,0,0,1,0,0]
=> [4,2,3,5,1] => [5,2,3,1,4] => [1,1,1,1,1,0,0,0,0,0]
=> 0
[1,0,1,1,1,0,1,0,0,0]
=> [3,2,4,5,1] => [5,2,1,3,4] => [1,1,1,1,1,0,0,0,0,0]
=> 0
[1,0,1,1,1,1,0,0,0,0]
=> [2,3,4,5,1] => [5,1,2,3,4] => [1,1,1,1,1,0,0,0,0,0]
=> 0
[1,1,0,0,1,0,1,0,1,0]
=> [5,4,3,1,2] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
=> 0
[1,1,0,0,1,0,1,1,0,0]
=> [4,5,3,1,2] => [4,5,3,1,2] => [1,1,1,1,0,1,0,0,0,0]
=> 0
[1,1,0,0,1,1,0,0,1,0]
=> [5,3,4,1,2] => [4,5,2,3,1] => [1,1,1,1,0,1,0,0,0,0]
=> 0
[1,1,0,0,1,1,0,1,0,0]
=> [4,3,5,1,2] => [4,5,2,1,3] => [1,1,1,1,0,1,0,0,0,0]
=> 0
[1,1,0,0,1,1,1,0,0,0]
=> [3,4,5,1,2] => [4,5,1,2,3] => [1,1,1,1,0,1,0,0,0,0]
=> 0
[1,1,0,1,0,0,1,0,1,0]
=> [5,4,2,1,3] => [4,3,5,2,1] => [1,1,1,1,0,0,1,0,0,0]
=> 0
[1,1,0,1,0,0,1,1,0,0]
=> [4,5,2,1,3] => [4,3,5,1,2] => [1,1,1,1,0,0,1,0,0,0]
=> 0
[1,1,0,1,0,1,0,0,1,0]
=> [5,3,2,1,4] => [4,3,2,5,1] => [1,1,1,1,0,0,0,1,0,0]
=> 0
[1,1,0,1,0,1,0,1,0,0]
=> [4,3,2,1,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
=> 0
[1,1,0,1,0,1,1,0,0,0]
=> [3,4,2,1,5] => [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0]
=> 0
[1,1,0,1,1,0,0,0,1,0]
=> [5,2,3,1,4] => [4,2,3,5,1] => [1,1,1,1,0,0,0,1,0,0]
=> 0
[1,1,0,1,1,0,0,1,0,0]
=> [4,2,3,1,5] => [4,2,3,1,5] => [1,1,1,1,0,0,0,0,1,0]
=> 0
[1,1,0,1,1,0,1,0,0,0]
=> [3,2,4,1,5] => [4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0]
=> 0
[1,1,0,1,1,1,0,0,0,0]
=> [2,3,4,1,5] => [4,1,2,3,5] => [1,1,1,1,0,0,0,0,1,0]
=> 0
[1,1,1,0,0,0,1,0,1,0]
=> [5,4,1,2,3] => [3,4,5,2,1] => [1,1,1,0,1,0,1,0,0,0]
=> 1
[1,1,1,0,0,0,1,1,0,0]
=> [4,5,1,2,3] => [3,4,5,1,2] => [1,1,1,0,1,0,1,0,0,0]
=> 1
[1,1,1,0,0,1,0,0,1,0]
=> [5,3,1,2,4] => [3,4,2,5,1] => [1,1,1,0,1,0,0,1,0,0]
=> 1
[1,1,1,0,0,1,0,1,0,0]
=> [4,3,1,2,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0]
=> 1
[1,1,1,0,0,1,1,0,0,0]
=> [3,4,1,2,5] => [3,4,1,2,5] => [1,1,1,0,1,0,0,0,1,0]
=> 1
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [6,5,4,3,2,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> 0
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [5,6,4,3,2,1] => [6,5,4,3,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> 0
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [6,4,5,3,2,1] => [6,5,4,2,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> 0
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [5,4,6,3,2,1] => [6,5,4,2,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> 0
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [4,5,6,3,2,1] => [6,5,4,1,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> 0
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [6,5,3,4,2,1] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> 0
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [5,6,3,4,2,1] => [6,5,3,4,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> 0
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [6,4,3,5,2,1] => [6,5,3,2,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> 0
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [5,4,3,6,2,1] => [6,5,3,2,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> 0
[1,0,1,0,1,1,0,1,1,0,0,0]
=> [4,5,3,6,2,1] => [6,5,3,1,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> 0
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]
=> [6,4,3,5,7,8,2,1] => [8,7,3,2,4,1,5,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 0
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]
=> [5,4,3,6,7,8,2,1] => [8,7,3,2,1,4,5,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 0
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]
=> [4,5,3,6,7,8,2,1] => [8,7,3,1,2,4,5,6] => ?
=> ? = 0
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
=> [8,3,4,5,6,7,2,1] => [8,7,2,3,4,5,6,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 0
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]
=> [7,3,4,5,6,8,2,1] => [8,7,2,3,4,5,1,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 0
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]
=> [6,3,4,5,7,8,2,1] => [8,7,2,3,4,1,5,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 0
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]
=> [5,3,4,6,7,8,2,1] => [8,7,2,3,1,4,5,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 0
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [4,3,5,6,7,8,2,1] => [8,7,2,1,3,4,5,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 0
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> [3,4,5,6,7,8,2,1] => [8,7,1,2,3,4,5,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 0
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]
=> [6,4,5,3,7,2,8,1] => [8,6,4,2,3,1,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 0
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]
=> [5,4,6,3,7,2,8,1] => [8,6,4,2,1,3,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 0
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]
=> [4,5,6,3,7,2,8,1] => [8,6,4,1,2,3,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 0
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]
=> [6,5,3,4,7,2,8,1] => [8,6,3,4,2,1,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 0
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]
=> [5,6,3,4,7,2,8,1] => [8,6,3,4,1,2,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 0
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]
=> [7,4,3,5,6,2,8,1] => [8,6,3,2,4,5,1,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 0
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]
=> [6,4,3,5,7,2,8,1] => [8,6,3,2,4,1,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 0
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]
=> [5,4,3,6,7,2,8,1] => [8,6,3,2,1,4,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 0
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]
=> [4,5,3,6,7,2,8,1] => [8,6,3,1,2,4,5,7] => ?
=> ? = 0
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]
=> [8,3,4,5,6,2,7,1] => [8,6,2,3,4,5,7,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 0
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]
=> [7,3,4,5,6,2,8,1] => [8,6,2,3,4,5,1,7] => ?
=> ? = 0
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]
=> [6,3,4,5,7,2,8,1] => [8,6,2,3,4,1,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 0
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]
=> [5,3,4,6,7,2,8,1] => [8,6,2,3,1,4,5,7] => ?
=> ? = 0
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]
=> [4,3,5,6,7,2,8,1] => [8,6,2,1,3,4,5,7] => ?
=> ? = 0
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
=> [3,4,5,6,7,2,8,1] => [8,6,1,2,3,4,5,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 0
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]
=> [6,4,5,7,2,3,8,1] => [8,5,6,2,3,1,4,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 0
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]
=> [5,4,6,7,2,3,8,1] => [8,5,6,2,1,3,4,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 0
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
=> [4,5,6,7,2,3,8,1] => [8,5,6,1,2,3,4,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 0
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]
=> [8,5,4,3,2,6,7,1] => [8,5,4,3,2,6,7,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 0
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]
=> [7,5,4,3,2,6,8,1] => [8,5,4,3,2,6,1,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 0
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [6,5,4,3,2,7,8,1] => [8,5,4,3,2,1,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 0
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]
=> [5,6,4,3,2,7,8,1] => [8,5,4,3,1,2,6,7] => ?
=> ? = 0
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]
=> [7,4,5,3,2,6,8,1] => [8,5,4,2,3,6,1,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 0
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]
=> [6,4,5,3,2,7,8,1] => [8,5,4,2,3,1,6,7] => ?
=> ? = 0
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]
=> [5,4,6,3,2,7,8,1] => [8,5,4,2,1,3,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 0
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]
=> [4,5,6,3,2,7,8,1] => [8,5,4,1,2,3,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 0
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]
=> [6,7,3,4,2,5,8,1] => [8,5,3,4,6,1,2,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 0
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]
=> [7,5,3,4,2,6,8,1] => [8,5,3,4,2,6,1,7] => ?
=> ? = 0
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]
=> [6,5,3,4,2,7,8,1] => [8,5,3,4,2,1,6,7] => ?
=> ? = 0
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]
=> [5,6,3,4,2,7,8,1] => [8,5,3,4,1,2,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 0
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]
=> [8,4,3,5,2,6,7,1] => [8,5,3,2,4,6,7,1] => ?
=> ? = 0
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]
=> [7,4,3,5,2,6,8,1] => [8,5,3,2,4,6,1,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 0
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]
=> [6,4,3,5,2,7,8,1] => [8,5,3,2,4,1,6,7] => ?
=> ? = 0
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]
=> [5,4,3,6,2,7,8,1] => [8,5,3,2,1,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 0
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]
=> [4,5,3,6,2,7,8,1] => [8,5,3,1,2,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 0
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]
=> [8,3,4,5,2,6,7,1] => [8,5,2,3,4,6,7,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 0
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]
=> [7,3,4,5,2,6,8,1] => [8,5,2,3,4,6,1,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 0
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]
=> [6,3,4,5,2,7,8,1] => [8,5,2,3,4,1,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 0
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]
=> [5,3,4,6,2,7,8,1] => [8,5,2,3,1,4,6,7] => ?
=> ? = 0
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]
=> [4,3,5,6,2,7,8,1] => [8,5,2,1,3,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 0
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
=> [3,4,5,6,2,7,8,1] => [8,5,1,2,3,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 0
Description
The number of rises of length 3 of a Dyck path.
Matching statistic: St001087
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00119: Dyck paths —to 321-avoiding permutation (Krattenthaler)⟶ Permutations
Mp00068: Permutations —Simion-Schmidt map⟶ Permutations
Mp00062: Permutations —Lehmer-code to major-code bijection⟶ Permutations
St001087: Permutations ⟶ ℤResult quality: 31% ●values known / values provided: 31%●distinct values known / distinct values provided: 100%
Mp00068: Permutations —Simion-Schmidt map⟶ Permutations
Mp00062: Permutations —Lehmer-code to major-code bijection⟶ Permutations
St001087: Permutations ⟶ ℤResult quality: 31% ●values known / values provided: 31%●distinct values known / distinct values provided: 100%
Values
[1,0,1,0,1,0,1,0]
=> [1,2,3,4] => [1,4,3,2] => [4,3,1,2] => 0
[1,0,1,0,1,1,0,0]
=> [1,2,4,3] => [1,4,3,2] => [4,3,1,2] => 0
[1,0,1,1,0,0,1,0]
=> [1,3,2,4] => [1,4,3,2] => [4,3,1,2] => 0
[1,0,1,1,0,1,0,0]
=> [1,3,4,2] => [1,4,3,2] => [4,3,1,2] => 0
[1,0,1,1,1,0,0,0]
=> [1,4,2,3] => [1,4,3,2] => [4,3,1,2] => 0
[1,1,0,0,1,0,1,0]
=> [2,1,3,4] => [2,1,4,3] => [1,4,2,3] => 1
[1,1,0,0,1,1,0,0]
=> [2,1,4,3] => [2,1,4,3] => [1,4,2,3] => 1
[1,0,1,0,1,0,1,0,1,0]
=> [1,2,3,4,5] => [1,5,4,3,2] => [5,4,3,1,2] => 0
[1,0,1,0,1,0,1,1,0,0]
=> [1,2,3,5,4] => [1,5,4,3,2] => [5,4,3,1,2] => 0
[1,0,1,0,1,1,0,0,1,0]
=> [1,2,4,3,5] => [1,5,4,3,2] => [5,4,3,1,2] => 0
[1,0,1,0,1,1,0,1,0,0]
=> [1,2,4,5,3] => [1,5,4,3,2] => [5,4,3,1,2] => 0
[1,0,1,0,1,1,1,0,0,0]
=> [1,2,5,3,4] => [1,5,4,3,2] => [5,4,3,1,2] => 0
[1,0,1,1,0,0,1,0,1,0]
=> [1,3,2,4,5] => [1,5,4,3,2] => [5,4,3,1,2] => 0
[1,0,1,1,0,0,1,1,0,0]
=> [1,3,2,5,4] => [1,5,4,3,2] => [5,4,3,1,2] => 0
[1,0,1,1,0,1,0,0,1,0]
=> [1,3,4,2,5] => [1,5,4,3,2] => [5,4,3,1,2] => 0
[1,0,1,1,0,1,0,1,0,0]
=> [1,3,4,5,2] => [1,5,4,3,2] => [5,4,3,1,2] => 0
[1,0,1,1,0,1,1,0,0,0]
=> [1,3,5,2,4] => [1,5,4,3,2] => [5,4,3,1,2] => 0
[1,0,1,1,1,0,0,0,1,0]
=> [1,4,2,3,5] => [1,5,4,3,2] => [5,4,3,1,2] => 0
[1,0,1,1,1,0,0,1,0,0]
=> [1,4,2,5,3] => [1,5,4,3,2] => [5,4,3,1,2] => 0
[1,0,1,1,1,0,1,0,0,0]
=> [1,4,5,2,3] => [1,5,4,3,2] => [5,4,3,1,2] => 0
[1,0,1,1,1,1,0,0,0,0]
=> [1,5,2,3,4] => [1,5,4,3,2] => [5,4,3,1,2] => 0
[1,1,0,0,1,0,1,0,1,0]
=> [2,1,3,4,5] => [2,1,5,4,3] => [5,1,4,2,3] => 0
[1,1,0,0,1,0,1,1,0,0]
=> [2,1,3,5,4] => [2,1,5,4,3] => [5,1,4,2,3] => 0
[1,1,0,0,1,1,0,0,1,0]
=> [2,1,4,3,5] => [2,1,5,4,3] => [5,1,4,2,3] => 0
[1,1,0,0,1,1,0,1,0,0]
=> [2,1,4,5,3] => [2,1,5,4,3] => [5,1,4,2,3] => 0
[1,1,0,0,1,1,1,0,0,0]
=> [2,1,5,3,4] => [2,1,5,4,3] => [5,1,4,2,3] => 0
[1,1,0,1,0,0,1,0,1,0]
=> [2,3,1,4,5] => [2,5,1,4,3] => [5,1,3,4,2] => 0
[1,1,0,1,0,0,1,1,0,0]
=> [2,3,1,5,4] => [2,5,1,4,3] => [5,1,3,4,2] => 0
[1,1,0,1,0,1,0,0,1,0]
=> [2,3,4,1,5] => [2,5,4,1,3] => [4,5,1,3,2] => 0
[1,1,0,1,0,1,0,1,0,0]
=> [2,3,4,5,1] => [2,5,4,3,1] => [5,4,1,3,2] => 0
[1,1,0,1,0,1,1,0,0,0]
=> [2,3,5,1,4] => [2,5,4,1,3] => [4,5,1,3,2] => 0
[1,1,0,1,1,0,0,0,1,0]
=> [2,4,1,3,5] => [2,5,1,4,3] => [5,1,3,4,2] => 0
[1,1,0,1,1,0,0,1,0,0]
=> [2,4,1,5,3] => [2,5,1,4,3] => [5,1,3,4,2] => 0
[1,1,0,1,1,0,1,0,0,0]
=> [2,4,5,1,3] => [2,5,4,1,3] => [4,5,1,3,2] => 0
[1,1,0,1,1,1,0,0,0,0]
=> [2,5,1,3,4] => [2,5,1,4,3] => [5,1,3,4,2] => 0
[1,1,1,0,0,0,1,0,1,0]
=> [3,1,2,4,5] => [3,1,5,4,2] => [1,5,4,2,3] => 1
[1,1,1,0,0,0,1,1,0,0]
=> [3,1,2,5,4] => [3,1,5,4,2] => [1,5,4,2,3] => 1
[1,1,1,0,0,1,0,0,1,0]
=> [3,1,4,2,5] => [3,1,5,4,2] => [1,5,4,2,3] => 1
[1,1,1,0,0,1,0,1,0,0]
=> [3,1,4,5,2] => [3,1,5,4,2] => [1,5,4,2,3] => 1
[1,1,1,0,0,1,1,0,0,0]
=> [3,1,5,2,4] => [3,1,5,4,2] => [1,5,4,2,3] => 1
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,2,3,4,5,6] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => 0
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,2,3,4,6,5] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => 0
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,2,3,5,4,6] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => 0
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,2,3,5,6,4] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => 0
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,2,3,6,4,5] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => 0
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,2,4,3,5,6] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => 0
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [1,2,4,3,6,5] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => 0
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,2,4,5,3,6] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => 0
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,2,4,5,6,3] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => 0
[1,0,1,0,1,1,0,1,1,0,0,0]
=> [1,2,4,6,3,5] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => 0
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]
=> [2,1,3,5,6,4,7] => [2,1,7,6,5,4,3] => [7,6,5,1,4,2,3] => ? = 0
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]
=> [2,1,3,5,6,7,4] => [2,1,7,6,5,4,3] => [7,6,5,1,4,2,3] => ? = 0
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]
=> [2,1,3,5,7,4,6] => [2,1,7,6,5,4,3] => [7,6,5,1,4,2,3] => ? = 0
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]
=> [2,1,3,6,4,5,7] => [2,1,7,6,5,4,3] => [7,6,5,1,4,2,3] => ? = 0
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]
=> [2,1,3,6,4,7,5] => [2,1,7,6,5,4,3] => [7,6,5,1,4,2,3] => ? = 0
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]
=> [2,1,3,6,7,4,5] => [2,1,7,6,5,4,3] => [7,6,5,1,4,2,3] => ? = 0
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
=> [2,1,3,7,4,5,6] => [2,1,7,6,5,4,3] => [7,6,5,1,4,2,3] => ? = 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]
=> [2,1,4,3,6,5,7] => [2,1,7,6,5,4,3] => [7,6,5,1,4,2,3] => ? = 0
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]
=> [2,1,4,3,6,7,5] => [2,1,7,6,5,4,3] => [7,6,5,1,4,2,3] => ? = 0
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]
=> [2,1,4,3,7,5,6] => [2,1,7,6,5,4,3] => [7,6,5,1,4,2,3] => ? = 0
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]
=> [2,1,4,5,3,6,7] => [2,1,7,6,5,4,3] => [7,6,5,1,4,2,3] => ? = 0
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]
=> [2,1,4,5,3,7,6] => [2,1,7,6,5,4,3] => [7,6,5,1,4,2,3] => ? = 0
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]
=> [2,1,4,5,6,3,7] => [2,1,7,6,5,4,3] => [7,6,5,1,4,2,3] => ? = 0
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]
=> [2,1,4,5,6,7,3] => [2,1,7,6,5,4,3] => [7,6,5,1,4,2,3] => ? = 0
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]
=> [2,1,4,5,7,3,6] => [2,1,7,6,5,4,3] => [7,6,5,1,4,2,3] => ? = 0
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]
=> [2,1,4,6,3,5,7] => [2,1,7,6,5,4,3] => [7,6,5,1,4,2,3] => ? = 0
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]
=> [2,1,4,6,3,7,5] => [2,1,7,6,5,4,3] => [7,6,5,1,4,2,3] => ? = 0
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]
=> [2,1,4,6,7,3,5] => [2,1,7,6,5,4,3] => [7,6,5,1,4,2,3] => ? = 0
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]
=> [2,1,4,7,3,5,6] => [2,1,7,6,5,4,3] => [7,6,5,1,4,2,3] => ? = 0
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]
=> [2,1,5,3,4,6,7] => [2,1,7,6,5,4,3] => [7,6,5,1,4,2,3] => ? = 0
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]
=> [2,1,5,3,4,7,6] => [2,1,7,6,5,4,3] => [7,6,5,1,4,2,3] => ? = 0
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]
=> [2,1,5,3,6,4,7] => [2,1,7,6,5,4,3] => [7,6,5,1,4,2,3] => ? = 0
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]
=> [2,1,5,3,6,7,4] => [2,1,7,6,5,4,3] => [7,6,5,1,4,2,3] => ? = 0
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]
=> [2,1,5,3,7,4,6] => [2,1,7,6,5,4,3] => [7,6,5,1,4,2,3] => ? = 0
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]
=> [2,1,5,6,3,4,7] => [2,1,7,6,5,4,3] => [7,6,5,1,4,2,3] => ? = 0
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]
=> [2,1,5,6,3,7,4] => [2,1,7,6,5,4,3] => [7,6,5,1,4,2,3] => ? = 0
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]
=> [2,1,5,6,7,3,4] => [2,1,7,6,5,4,3] => [7,6,5,1,4,2,3] => ? = 0
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]
=> [2,1,5,7,3,4,6] => [2,1,7,6,5,4,3] => [7,6,5,1,4,2,3] => ? = 0
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]
=> [2,1,6,3,4,5,7] => [2,1,7,6,5,4,3] => [7,6,5,1,4,2,3] => ? = 0
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]
=> [2,1,6,3,4,7,5] => [2,1,7,6,5,4,3] => [7,6,5,1,4,2,3] => ? = 0
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]
=> [2,1,6,3,7,4,5] => [2,1,7,6,5,4,3] => [7,6,5,1,4,2,3] => ? = 0
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]
=> [2,1,6,7,3,4,5] => [2,1,7,6,5,4,3] => [7,6,5,1,4,2,3] => ? = 0
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
=> [2,1,7,3,4,5,6] => [2,1,7,6,5,4,3] => [7,6,5,1,4,2,3] => ? = 0
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]
=> [2,3,1,4,6,5,7] => [2,7,1,6,5,4,3] => [7,6,5,1,3,4,2] => ? = 0
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]
=> [2,3,1,4,6,7,5] => [2,7,1,6,5,4,3] => [7,6,5,1,3,4,2] => ? = 0
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]
=> [2,3,1,4,7,5,6] => [2,7,1,6,5,4,3] => [7,6,5,1,3,4,2] => ? = 0
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]
=> [2,3,1,5,4,6,7] => [2,7,1,6,5,4,3] => [7,6,5,1,3,4,2] => ? = 0
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]
=> [2,3,1,5,4,7,6] => [2,7,1,6,5,4,3] => [7,6,5,1,3,4,2] => ? = 0
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]
=> [2,3,1,5,6,4,7] => [2,7,1,6,5,4,3] => [7,6,5,1,3,4,2] => ? = 0
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]
=> [2,3,1,5,6,7,4] => [2,7,1,6,5,4,3] => [7,6,5,1,3,4,2] => ? = 0
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]
=> [2,3,1,5,7,4,6] => [2,7,1,6,5,4,3] => [7,6,5,1,3,4,2] => ? = 0
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]
=> [2,3,1,6,4,5,7] => [2,7,1,6,5,4,3] => [7,6,5,1,3,4,2] => ? = 0
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]
=> [2,3,1,6,4,7,5] => [2,7,1,6,5,4,3] => [7,6,5,1,3,4,2] => ? = 0
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]
=> [2,3,1,6,7,4,5] => [2,7,1,6,5,4,3] => [7,6,5,1,3,4,2] => ? = 0
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]
=> [2,3,1,7,4,5,6] => [2,7,1,6,5,4,3] => [7,6,5,1,3,4,2] => ? = 0
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]
=> [2,3,4,1,5,6,7] => [2,7,6,1,5,4,3] => [7,6,4,5,1,3,2] => ? = 0
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]
=> [2,3,4,1,5,7,6] => [2,7,6,1,5,4,3] => [7,6,4,5,1,3,2] => ? = 0
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]
=> [2,3,4,1,6,5,7] => [2,7,6,1,5,4,3] => [7,6,4,5,1,3,2] => ? = 0
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]
=> [2,3,4,1,6,7,5] => [2,7,6,1,5,4,3] => [7,6,4,5,1,3,2] => ? = 0
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]
=> [2,3,4,1,7,5,6] => [2,7,6,1,5,4,3] => [7,6,4,5,1,3,2] => ? = 0
Description
The number of occurrences of the vincular pattern |12-3 in a permutation.
This is the number of occurrences of the pattern 123, where the first matched entry is the first entry of the permutation and the other two matched entries are consecutive.
In other words, this is the number of ascents whose bottom value is strictly larger than the first entry of the permutation.
Matching statistic: St000260
(load all 19 compositions to match this statistic)
(load all 19 compositions to match this statistic)
Mp00028: Dyck paths —reverse⟶ Dyck paths
Mp00102: Dyck paths —rise composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000260: Graphs ⟶ ℤResult quality: 22% ●values known / values provided: 22%●distinct values known / distinct values provided: 50%
Mp00102: Dyck paths —rise composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000260: Graphs ⟶ ℤResult quality: 22% ●values known / values provided: 22%●distinct values known / distinct values provided: 50%
Values
[1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 1 = 0 + 1
[1,0,1,0,1,1,0,0]
=> [1,1,0,0,1,0,1,0]
=> [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 1 = 0 + 1
[1,0,1,1,0,0,1,0]
=> [1,0,1,1,0,0,1,0]
=> [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 1 = 0 + 1
[1,0,1,1,0,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 1 = 0 + 1
[1,0,1,1,1,0,0,0]
=> [1,1,1,0,0,0,1,0]
=> [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1 = 0 + 1
[1,1,0,0,1,0,1,0]
=> [1,0,1,0,1,1,0,0]
=> [1,1,2] => ([(1,2),(1,3),(2,3)],4)
=> ? = 1 + 1
[1,1,0,0,1,1,0,0]
=> [1,1,0,0,1,1,0,0]
=> [2,2] => ([(1,3),(2,3)],4)
=> ? = 1 + 1
[1,0,1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1 = 0 + 1
[1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1 = 0 + 1
[1,0,1,0,1,1,0,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1 = 0 + 1
[1,0,1,0,1,1,0,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0]
=> [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1 = 0 + 1
[1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,0,0,0,1,0,1,0]
=> [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1 = 0 + 1
[1,0,1,1,0,0,1,0,1,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1 = 0 + 1
[1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,0,1,1,0,0,1,0]
=> [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1 = 0 + 1
[1,0,1,1,0,1,0,0,1,0]
=> [1,0,1,1,0,1,0,0,1,0]
=> [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1 = 0 + 1
[1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,0,1,0,0,1,0]
=> [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1 = 0 + 1
[1,0,1,1,0,1,1,0,0,0]
=> [1,1,1,0,0,1,0,0,1,0]
=> [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1 = 0 + 1
[1,0,1,1,1,0,0,0,1,0]
=> [1,0,1,1,1,0,0,0,1,0]
=> [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 1 = 0 + 1
[1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,0,0,0,1,0]
=> [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1 = 0 + 1
[1,0,1,1,1,0,1,0,0,0]
=> [1,1,1,0,1,0,0,0,1,0]
=> [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1 = 0 + 1
[1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0]
=> [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 0 + 1
[1,1,0,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,1,0,0]
=> [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 1
[1,1,0,0,1,0,1,1,0,0]
=> [1,1,0,0,1,0,1,1,0,0]
=> [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 1
[1,1,0,0,1,1,0,0,1,0]
=> [1,0,1,1,0,0,1,1,0,0]
=> [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 1
[1,1,0,0,1,1,0,1,0,0]
=> [1,1,0,1,0,0,1,1,0,0]
=> [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 1
[1,1,0,0,1,1,1,0,0,0]
=> [1,1,1,0,0,0,1,1,0,0]
=> [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 0 + 1
[1,1,0,1,0,0,1,0,1,0]
=> [1,0,1,0,1,1,0,1,0,0]
=> [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1 = 0 + 1
[1,1,0,1,0,0,1,1,0,0]
=> [1,1,0,0,1,1,0,1,0,0]
=> [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1 = 0 + 1
[1,1,0,1,0,1,0,0,1,0]
=> [1,0,1,1,0,1,0,1,0,0]
=> [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1 = 0 + 1
[1,1,0,1,0,1,0,1,0,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1 = 0 + 1
[1,1,0,1,0,1,1,0,0,0]
=> [1,1,1,0,0,1,0,1,0,0]
=> [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1 = 0 + 1
[1,1,0,1,1,0,0,0,1,0]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 1 = 0 + 1
[1,1,0,1,1,0,0,1,0,0]
=> [1,1,0,1,1,0,0,1,0,0]
=> [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1 = 0 + 1
[1,1,0,1,1,0,1,0,0,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1 = 0 + 1
[1,1,0,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 0 + 1
[1,1,1,0,0,0,1,0,1,0]
=> [1,0,1,0,1,1,1,0,0,0]
=> [1,1,3] => ([(2,3),(2,4),(3,4)],5)
=> ? = 1 + 1
[1,1,1,0,0,0,1,1,0,0]
=> [1,1,0,0,1,1,1,0,0,0]
=> [2,3] => ([(2,4),(3,4)],5)
=> ? = 1 + 1
[1,1,1,0,0,1,0,0,1,0]
=> [1,0,1,1,0,1,1,0,0,0]
=> [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 1 + 1
[1,1,1,0,0,1,0,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 1 + 1
[1,1,1,0,0,1,1,0,0,0]
=> [1,1,1,0,0,1,1,0,0,0]
=> [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 1 + 1
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1] => ([(0,1),(0,2),(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)
=> 1 = 0 + 1
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0]
=> [2,1,1,1,1] => ([(0,2),(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)
=> 1 = 0 + 1
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [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)
=> 1 = 0 + 1
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0,1,0]
=> [2,1,1,1,1] => ([(0,2),(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)
=> 1 = 0 + 1
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0]
=> [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1 = 0 + 1
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,2,1,1] => ([(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)
=> 1 = 0 + 1
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,0,1,1,0,0,1,0,1,0]
=> [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1 = 0 + 1
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,0,1,1,0,1,0,0,1,0,1,0]
=> [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)
=> 1 = 0 + 1
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,0,1,0,0,1,0,1,0]
=> [2,1,1,1,1] => ([(0,2),(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)
=> 1 = 0 + 1
[1,0,1,0,1,1,0,1,1,0,0,0]
=> [1,1,1,0,0,1,0,0,1,0,1,0]
=> [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1 = 0 + 1
[1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,0,1,1,1,0,0,0,1,0,1,0]
=> [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1 = 0 + 1
[1,0,1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,0,0,0,1,0,1,0]
=> [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1 = 0 + 1
[1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,1,1,0,1,0,0,0,1,0,1,0]
=> [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1 = 0 + 1
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1 = 0 + 1
[1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,2,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1 = 0 + 1
[1,0,1,1,0,0,1,0,1,1,0,0]
=> [1,1,0,0,1,0,1,1,0,0,1,0]
=> [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1 = 0 + 1
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1 = 0 + 1
[1,0,1,1,0,0,1,1,0,1,0,0]
=> [1,1,0,1,0,0,1,1,0,0,1,0]
=> [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1 = 0 + 1
[1,0,1,1,0,0,1,1,1,0,0,0]
=> [1,1,1,0,0,0,1,1,0,0,1,0]
=> [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1 = 0 + 1
[1,0,1,1,0,1,0,0,1,0,1,0]
=> [1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,1,2,1,1] => ([(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)
=> 1 = 0 + 1
[1,0,1,1,0,1,0,0,1,1,0,0]
=> [1,1,0,0,1,1,0,1,0,0,1,0]
=> [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1 = 0 + 1
[1,0,1,1,0,1,0,1,0,0,1,0]
=> [1,0,1,1,0,1,0,1,0,0,1,0]
=> [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)
=> 1 = 0 + 1
[1,1,0,0,1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 0 + 1
[1,1,0,0,1,0,1,0,1,1,0,0]
=> [1,1,0,0,1,0,1,0,1,1,0,0]
=> [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 0 + 1
[1,1,0,0,1,0,1,1,0,0,1,0]
=> [1,0,1,1,0,0,1,0,1,1,0,0]
=> [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 0 + 1
[1,1,0,0,1,0,1,1,0,1,0,0]
=> [1,1,0,1,0,0,1,0,1,1,0,0]
=> [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 0 + 1
[1,1,0,0,1,0,1,1,1,0,0,0]
=> [1,1,1,0,0,0,1,0,1,1,0,0]
=> [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 0 + 1
[1,1,0,0,1,1,0,0,1,0,1,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0]
=> [1,1,2,2] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 0 + 1
[1,1,0,0,1,1,0,0,1,1,0,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0]
=> [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 0 + 1
[1,1,0,0,1,1,0,1,0,0,1,0]
=> [1,0,1,1,0,1,0,0,1,1,0,0]
=> [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 0 + 1
[1,1,0,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,0,1,0,0,1,1,0,0]
=> [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 0 + 1
[1,1,0,0,1,1,0,1,1,0,0,0]
=> [1,1,1,0,0,1,0,0,1,1,0,0]
=> [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 0 + 1
[1,1,0,0,1,1,1,0,0,0,1,0]
=> [1,0,1,1,1,0,0,0,1,1,0,0]
=> [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 0 + 1
[1,1,0,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,0,0,0,1,1,0,0]
=> [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 0 + 1
[1,1,0,0,1,1,1,0,1,0,0,0]
=> [1,1,1,0,1,0,0,0,1,1,0,0]
=> [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 0 + 1
[1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 0 + 1
[1,1,1,0,0,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 0 + 1
[1,1,1,0,0,0,1,0,1,1,0,0]
=> [1,1,0,0,1,0,1,1,1,0,0,0]
=> [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 0 + 1
[1,1,1,0,0,0,1,1,0,0,1,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0]
=> [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 0 + 1
[1,1,1,0,0,0,1,1,0,1,0,0]
=> [1,1,0,1,0,0,1,1,1,0,0,0]
=> [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 0 + 1
[1,1,1,0,0,0,1,1,1,0,0,0]
=> [1,1,1,0,0,0,1,1,1,0,0,0]
=> [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 0 + 1
[1,1,1,0,0,1,0,0,1,0,1,0]
=> [1,0,1,0,1,1,0,1,1,0,0,0]
=> [1,1,2,2] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 0 + 1
[1,1,1,0,0,1,0,0,1,1,0,0]
=> [1,1,0,0,1,1,0,1,1,0,0,0]
=> [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 0 + 1
[1,1,1,0,0,1,0,1,0,0,1,0]
=> [1,0,1,1,0,1,0,1,1,0,0,0]
=> [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 0 + 1
[1,1,1,0,0,1,0,1,0,1,0,0]
=> [1,1,0,1,0,1,0,1,1,0,0,0]
=> [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 0 + 1
[1,1,1,0,0,1,0,1,1,0,0,0]
=> [1,1,1,0,0,1,0,1,1,0,0,0]
=> [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 0 + 1
[1,1,1,0,0,1,1,0,0,0,1,0]
=> [1,0,1,1,1,0,0,1,1,0,0,0]
=> [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 0 + 1
[1,1,1,0,0,1,1,0,0,1,0,0]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 0 + 1
[1,1,1,0,0,1,1,0,1,0,0,0]
=> [1,1,1,0,1,0,0,1,1,0,0,0]
=> [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 0 + 1
[1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 0 + 1
[1,1,1,1,0,0,0,0,1,0,1,0]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,4] => ([(3,4),(3,5),(4,5)],6)
=> ? = 1 + 1
[1,1,1,1,0,0,0,0,1,1,0,0]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> [2,4] => ([(3,5),(4,5)],6)
=> ? = 1 + 1
[1,1,1,1,0,0,0,1,0,0,1,0]
=> [1,0,1,1,0,1,1,1,0,0,0,0]
=> [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1 + 1
[1,1,1,1,0,0,0,1,0,1,0,0]
=> [1,1,0,1,0,1,1,1,0,0,0,0]
=> [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1 + 1
[1,1,1,1,0,0,0,1,1,0,0,0]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 1 + 1
[1,1,1,1,0,0,1,0,0,0,1,0]
=> [1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1 + 1
[1,1,1,1,0,0,1,0,0,1,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1 + 1
[1,1,1,1,0,0,1,0,1,0,0,0]
=> [1,1,1,0,1,0,1,1,0,0,0,0]
=> [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1 + 1
[1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 1 + 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]
=> [1,0,1,1,0,1,0,0,1,0,1,1,0,0]
=> [1,2,1,1,2] => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 0 + 1
Description
The radius of a connected graph.
This is the minimum eccentricity of any vertex.
Matching statistic: St001199
(load all 4 compositions to match this statistic)
(load all 4 compositions to match this statistic)
Mp00129: Dyck paths —to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶ Permutations
Mp00069: Permutations —complement⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
St001199: Dyck paths ⟶ ℤResult quality: 22% ●values known / values provided: 22%●distinct values known / distinct values provided: 50%
Mp00069: Permutations —complement⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
St001199: Dyck paths ⟶ ℤResult quality: 22% ●values known / values provided: 22%●distinct values known / distinct values provided: 50%
Values
[1,0,1,0,1,0,1,0]
=> [2,3,4,1] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
=> 1 = 0 + 1
[1,0,1,0,1,1,0,0]
=> [2,3,1,4] => [3,2,4,1] => [1,1,1,0,0,1,0,0]
=> 1 = 0 + 1
[1,0,1,1,0,0,1,0]
=> [2,1,4,3] => [3,4,1,2] => [1,1,1,0,1,0,0,0]
=> 1 = 0 + 1
[1,0,1,1,0,1,0,0]
=> [2,4,1,3] => [3,1,4,2] => [1,1,1,0,0,1,0,0]
=> 1 = 0 + 1
[1,0,1,1,1,0,0,0]
=> [2,1,3,4] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
=> 1 = 0 + 1
[1,1,0,0,1,0,1,0]
=> [1,3,4,2] => [4,2,1,3] => [1,1,1,1,0,0,0,0]
=> ? = 1 + 1
[1,1,0,0,1,1,0,0]
=> [1,3,2,4] => [4,2,3,1] => [1,1,1,1,0,0,0,0]
=> ? = 1 + 1
[1,0,1,0,1,0,1,0,1,0]
=> [2,3,4,5,1] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
=> 1 = 0 + 1
[1,0,1,0,1,0,1,1,0,0]
=> [2,3,4,1,5] => [4,3,2,5,1] => [1,1,1,1,0,0,0,1,0,0]
=> 1 = 0 + 1
[1,0,1,0,1,1,0,0,1,0]
=> [2,3,1,5,4] => [4,3,5,1,2] => [1,1,1,1,0,0,1,0,0,0]
=> 1 = 0 + 1
[1,0,1,0,1,1,0,1,0,0]
=> [2,3,5,1,4] => [4,3,1,5,2] => [1,1,1,1,0,0,0,1,0,0]
=> 1 = 0 + 1
[1,0,1,0,1,1,1,0,0,0]
=> [2,3,1,4,5] => [4,3,5,2,1] => [1,1,1,1,0,0,1,0,0,0]
=> 1 = 0 + 1
[1,0,1,1,0,0,1,0,1,0]
=> [2,1,4,5,3] => [4,5,2,1,3] => [1,1,1,1,0,1,0,0,0,0]
=> 1 = 0 + 1
[1,0,1,1,0,0,1,1,0,0]
=> [2,1,4,3,5] => [4,5,2,3,1] => [1,1,1,1,0,1,0,0,0,0]
=> 1 = 0 + 1
[1,0,1,1,0,1,0,0,1,0]
=> [2,4,1,5,3] => [4,2,5,1,3] => [1,1,1,1,0,0,1,0,0,0]
=> 1 = 0 + 1
[1,0,1,1,0,1,0,1,0,0]
=> [2,4,5,1,3] => [4,2,1,5,3] => [1,1,1,1,0,0,0,1,0,0]
=> 1 = 0 + 1
[1,0,1,1,0,1,1,0,0,0]
=> [2,4,1,3,5] => [4,2,5,3,1] => [1,1,1,1,0,0,1,0,0,0]
=> 1 = 0 + 1
[1,0,1,1,1,0,0,0,1,0]
=> [2,1,3,5,4] => [4,5,3,1,2] => [1,1,1,1,0,1,0,0,0,0]
=> 1 = 0 + 1
[1,0,1,1,1,0,0,1,0,0]
=> [2,1,5,3,4] => [4,5,1,3,2] => [1,1,1,1,0,1,0,0,0,0]
=> 1 = 0 + 1
[1,0,1,1,1,0,1,0,0,0]
=> [2,5,1,3,4] => [4,1,5,3,2] => [1,1,1,1,0,0,1,0,0,0]
=> 1 = 0 + 1
[1,0,1,1,1,1,0,0,0,0]
=> [2,1,3,4,5] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
=> 1 = 0 + 1
[1,1,0,0,1,0,1,0,1,0]
=> [1,3,4,5,2] => [5,3,2,1,4] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,0,0,1,0,1,1,0,0]
=> [1,3,4,2,5] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,0,0,1,1,0,0,1,0]
=> [1,3,2,5,4] => [5,3,4,1,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,0,0,1,1,0,1,0,0]
=> [1,3,5,2,4] => [5,3,1,4,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,0,0,1,1,1,0,0,0]
=> [1,3,2,4,5] => [5,3,4,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,0,1,0,0,1,0,1,0]
=> [3,1,4,5,2] => [3,5,2,1,4] => [1,1,1,0,1,1,0,0,0,0]
=> 1 = 0 + 1
[1,1,0,1,0,0,1,1,0,0]
=> [3,1,4,2,5] => [3,5,2,4,1] => [1,1,1,0,1,1,0,0,0,0]
=> 1 = 0 + 1
[1,1,0,1,0,1,0,0,1,0]
=> [3,4,1,5,2] => [3,2,5,1,4] => [1,1,1,0,0,1,1,0,0,0]
=> 1 = 0 + 1
[1,1,0,1,0,1,0,1,0,0]
=> [3,4,5,1,2] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0]
=> 1 = 0 + 1
[1,1,0,1,0,1,1,0,0,0]
=> [3,4,1,2,5] => [3,2,5,4,1] => [1,1,1,0,0,1,1,0,0,0]
=> 1 = 0 + 1
[1,1,0,1,1,0,0,0,1,0]
=> [3,1,2,5,4] => [3,5,4,1,2] => [1,1,1,0,1,1,0,0,0,0]
=> 1 = 0 + 1
[1,1,0,1,1,0,0,1,0,0]
=> [3,1,5,2,4] => [3,5,1,4,2] => [1,1,1,0,1,1,0,0,0,0]
=> 1 = 0 + 1
[1,1,0,1,1,0,1,0,0,0]
=> [3,5,1,2,4] => [3,1,5,4,2] => [1,1,1,0,0,1,1,0,0,0]
=> 1 = 0 + 1
[1,1,0,1,1,1,0,0,0,0]
=> [3,1,2,4,5] => [3,5,4,2,1] => [1,1,1,0,1,1,0,0,0,0]
=> 1 = 0 + 1
[1,1,1,0,0,0,1,0,1,0]
=> [1,2,4,5,3] => [5,4,2,1,3] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 1 + 1
[1,1,1,0,0,0,1,1,0,0]
=> [1,2,4,3,5] => [5,4,2,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 1 + 1
[1,1,1,0,0,1,0,0,1,0]
=> [1,4,2,5,3] => [5,2,4,1,3] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 1 + 1
[1,1,1,0,0,1,0,1,0,0]
=> [1,4,5,2,3] => [5,2,1,4,3] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 1 + 1
[1,1,1,0,0,1,1,0,0,0]
=> [1,4,2,3,5] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 1 + 1
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [2,3,4,5,6,1] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
=> 1 = 0 + 1
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [2,3,4,5,1,6] => [5,4,3,2,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0]
=> 1 = 0 + 1
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [2,3,4,1,6,5] => [5,4,3,6,1,2] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 1 = 0 + 1
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [2,3,4,6,1,5] => [5,4,3,1,6,2] => [1,1,1,1,1,0,0,0,0,1,0,0]
=> 1 = 0 + 1
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [2,3,4,1,5,6] => [5,4,3,6,2,1] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 1 = 0 + 1
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [2,3,1,5,6,4] => [5,4,6,2,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1 = 0 + 1
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [2,3,1,5,4,6] => [5,4,6,2,3,1] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1 = 0 + 1
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [2,3,5,1,6,4] => [5,4,2,6,1,3] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 1 = 0 + 1
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [2,3,5,6,1,4] => [5,4,2,1,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0]
=> 1 = 0 + 1
[1,0,1,0,1,1,0,1,1,0,0,0]
=> [2,3,5,1,4,6] => [5,4,2,6,3,1] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 1 = 0 + 1
[1,0,1,0,1,1,1,0,0,0,1,0]
=> [2,3,1,4,6,5] => [5,4,6,3,1,2] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1 = 0 + 1
[1,0,1,0,1,1,1,0,0,1,0,0]
=> [2,3,1,6,4,5] => [5,4,6,1,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1 = 0 + 1
[1,0,1,0,1,1,1,0,1,0,0,0]
=> [2,3,6,1,4,5] => [5,4,1,6,3,2] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 1 = 0 + 1
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [2,3,1,4,5,6] => [5,4,6,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1 = 0 + 1
[1,0,1,1,0,0,1,0,1,0,1,0]
=> [2,1,4,5,6,3] => [5,6,3,2,1,4] => [1,1,1,1,1,0,1,0,0,0,0,0]
=> 1 = 0 + 1
[1,0,1,1,0,0,1,0,1,1,0,0]
=> [2,1,4,5,3,6] => [5,6,3,2,4,1] => [1,1,1,1,1,0,1,0,0,0,0,0]
=> 1 = 0 + 1
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [2,1,4,3,6,5] => [5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
=> 1 = 0 + 1
[1,0,1,1,0,0,1,1,0,1,0,0]
=> [2,1,4,6,3,5] => [5,6,3,1,4,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
=> 1 = 0 + 1
[1,0,1,1,0,0,1,1,1,0,0,0]
=> [2,1,4,3,5,6] => [5,6,3,4,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0]
=> 1 = 0 + 1
[1,0,1,1,0,1,0,0,1,0,1,0]
=> [2,4,1,5,6,3] => [5,3,6,2,1,4] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1 = 0 + 1
[1,0,1,1,0,1,0,0,1,1,0,0]
=> [2,4,1,5,3,6] => [5,3,6,2,4,1] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1 = 0 + 1
[1,0,1,1,0,1,0,1,0,0,1,0]
=> [2,4,5,1,6,3] => [5,3,2,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 1 = 0 + 1
[1,1,0,0,1,0,1,0,1,0,1,0]
=> [1,3,4,5,6,2] => [6,4,3,2,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 0 + 1
[1,1,0,0,1,0,1,0,1,1,0,0]
=> [1,3,4,5,2,6] => [6,4,3,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 0 + 1
[1,1,0,0,1,0,1,1,0,0,1,0]
=> [1,3,4,2,6,5] => [6,4,3,5,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 0 + 1
[1,1,0,0,1,0,1,1,0,1,0,0]
=> [1,3,4,6,2,5] => [6,4,3,1,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 0 + 1
[1,1,0,0,1,0,1,1,1,0,0,0]
=> [1,3,4,2,5,6] => [6,4,3,5,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 0 + 1
[1,1,0,0,1,1,0,0,1,0,1,0]
=> [1,3,2,5,6,4] => [6,4,5,2,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 0 + 1
[1,1,0,0,1,1,0,0,1,1,0,0]
=> [1,3,2,5,4,6] => [6,4,5,2,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 0 + 1
[1,1,0,0,1,1,0,1,0,0,1,0]
=> [1,3,5,2,6,4] => [6,4,2,5,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 0 + 1
[1,1,0,0,1,1,0,1,0,1,0,0]
=> [1,3,5,6,2,4] => [6,4,2,1,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 0 + 1
[1,1,0,0,1,1,0,1,1,0,0,0]
=> [1,3,5,2,4,6] => [6,4,2,5,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 0 + 1
[1,1,0,0,1,1,1,0,0,0,1,0]
=> [1,3,2,4,6,5] => [6,4,5,3,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 0 + 1
[1,1,0,0,1,1,1,0,0,1,0,0]
=> [1,3,2,6,4,5] => [6,4,5,1,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 0 + 1
[1,1,0,0,1,1,1,0,1,0,0,0]
=> [1,3,6,2,4,5] => [6,4,1,5,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 0 + 1
[1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,3,2,4,5,6] => [6,4,5,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,0,0,1,0,1,0,1,0]
=> [1,2,4,5,6,3] => [6,5,3,2,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,0,0,1,0,1,1,0,0]
=> [1,2,4,5,3,6] => [6,5,3,2,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,0,0,1,1,0,0,1,0]
=> [1,2,4,3,6,5] => [6,5,3,4,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,0,0,1,1,0,1,0,0]
=> [1,2,4,6,3,5] => [6,5,3,1,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,0,0,1,1,1,0,0,0]
=> [1,2,4,3,5,6] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,0,1,0,0,1,0,1,0]
=> [1,4,2,5,6,3] => [6,3,5,2,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,0,1,0,0,1,1,0,0]
=> [1,4,2,5,3,6] => [6,3,5,2,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,0,1,0,1,0,0,1,0]
=> [1,4,5,2,6,3] => [6,3,2,5,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,0,1,0,1,0,1,0,0]
=> [1,4,5,6,2,3] => [6,3,2,1,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,0,1,0,1,1,0,0,0]
=> [1,4,5,2,3,6] => [6,3,2,5,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,0,1,1,0,0,0,1,0]
=> [1,4,2,3,6,5] => [6,3,5,4,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,0,1,1,0,0,1,0,0]
=> [1,4,2,6,3,5] => [6,3,5,1,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,0,1,1,0,1,0,0,0]
=> [1,4,6,2,3,5] => [6,3,1,5,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,4,2,3,5,6] => [6,3,5,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,1,0,0,0,0,1,0,1,0]
=> [1,2,3,5,6,4] => [6,5,4,2,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 + 1
[1,1,1,1,0,0,0,0,1,1,0,0]
=> [1,2,3,5,4,6] => [6,5,4,2,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 + 1
[1,1,1,1,0,0,0,1,0,0,1,0]
=> [1,2,5,3,6,4] => [6,5,2,4,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 + 1
[1,1,1,1,0,0,0,1,0,1,0,0]
=> [1,2,5,6,3,4] => [6,5,2,1,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 + 1
[1,1,1,1,0,0,0,1,1,0,0,0]
=> [1,2,5,3,4,6] => [6,5,2,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 + 1
[1,1,1,1,0,0,1,0,0,0,1,0]
=> [1,5,2,3,6,4] => [6,2,5,4,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 + 1
[1,1,1,1,0,0,1,0,0,1,0,0]
=> [1,5,2,6,3,4] => [6,2,5,1,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 + 1
[1,1,1,1,0,0,1,0,1,0,0,0]
=> [1,5,6,2,3,4] => [6,2,1,5,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 + 1
[1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,5,2,3,4,6] => [6,2,5,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 + 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]
=> [1,3,4,6,2,7,5] => [7,5,4,2,6,1,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 0 + 1
Description
The dominant dimension of eAe for the corresponding Nakayama algebra A with minimal faithful projective-injective module eA.
The following 88 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St000234The number of global ascents of a permutation. St001498The normalised height of a Nakayama algebra with magnitude 1. St000731The number of double exceedences of a permutation. St000352The Elizalde-Pak rank of a permutation. St000772The multiplicity of the largest distance Laplacian eigenvalue in a connected graph. St000259The diameter of a connected graph. St000221The number of strong fixed points of a permutation. St000804The number of occurrences of the vincular pattern |123 in a permutation. St000056The decomposition (or block) number of a permutation. St001876The number of 2-regular simple modules in the incidence algebra of the lattice. St001877Number of indecomposable injective modules with projective dimension 2. St001878The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L. St001198The number of simple modules in the algebra eAe with projective dimension at most 1 in the corresponding Nakayama algebra A with minimal faithful projective-injective module eA. St001206The maximal dimension of an indecomposable projective eAe-module (that is the height of the corresponding Dyck path) of the corresponding Nakayama algebra with minimal faithful projective-injective module eA. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St001545The second Elser number of a connected graph. St001330The hat guessing number of a graph. St000842The breadth of a permutation. St000382The first part of an integer composition. St000741The Colin de Verdière graph invariant. St001630The global dimension of the incidence algebra of the lattice over the rational numbers. St000002The number of occurrences of the pattern 123 in a permutation. St000022The number of fixed points of a permutation. St000359The number of occurrences of the pattern 23-1. St000404The number of occurrences of the pattern 3241 or of the pattern 4231 in a permutation. St000405The number of occurrences of the pattern 1324 in a permutation. St000408The number of occurrences of the pattern 4231 in a permutation. St000440The number of occurrences of the pattern 4132 or of the pattern 4231 in a permutation. St000441The number of successions of a permutation. St000534The number of 2-rises of a permutation. St000546The number of global descents of a permutation. St000647The number of big descents of a permutation. St000648The number of 2-excedences of a permutation. St000665The number of rafts of a permutation. St001084The number of occurrences of the vincular pattern |1-23 in a permutation. St001394The genus of a permutation. St000028The number of stack-sorts needed to sort a permutation. St000036The evaluation at 1 of the Kazhdan-Lusztig polynomial with parameters given by the identity and the permutation. St000245The number of ascents of a permutation. St000669The number of permutations obtained by switching ascents or descents of size 2. St000672The number of minimal elements in Bruhat order not less than the permutation. St000696The number of cycles in the breakpoint graph of a permutation. St000834The number of right outer peaks of a permutation. St000871The number of very big ascents of a permutation. St000884The number of isolated descents of a permutation. St001085The number of occurrences of the vincular pattern |21-3 in a permutation. St001086The number of occurrences of the consecutive pattern 132 in a permutation. St001090The number of pop-stack-sorts needed to sort a permutation. St000035The number of left outer peaks of a permutation. St000054The first entry of the permutation. St000153The number of adjacent cycles of a permutation. St000237The number of small exceedances. St000374The number of exclusive right-to-left minima of a permutation. St000402Half the size of the symmetry class of a permutation. St000451The length of the longest pattern of the form k 1 2. St000483The number of times a permutation switches from increasing to decreasing or decreasing to increasing. St000725The smallest label of a leaf of the increasing binary tree associated to a permutation. St000742The number of big ascents of a permutation after prepending zero. St000862The number of parts of the shifted shape of a permutation. St000996The number of exclusive left-to-right maxima of a permutation. St001052The length of the exterior of a permutation. St001096The size of the overlap set of a permutation. St001465The number of adjacent transpositions in the cycle decomposition of a permutation. St001004The number of indices that are either left-to-right maxima or right-to-left minima. St001875The number of simple modules with projective dimension at most 1. St000454The largest eigenvalue of a graph if it is integral. St001964The interval resolution global dimension of a poset. St001632The number of indecomposable injective modules I with dimExt1(I,A)=1 for the incidence algebra A of a poset. St000455The second largest eigenvalue of a graph if it is integral. St000058The order of a permutation. St000873The aix statistic of a permutation. St001162The minimum jump of a permutation. 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]/(xn). St001344The neighbouring number of a permutation. St001820The size of the image of the pop stack sorting operator. St001615The number of join prime elements of a lattice. St001846The number of elements which do not have a complement in the lattice. St001613The binary logarithm of the size of the center of a lattice. St001719The number of shortest chains of small intervals from the bottom to the top in a lattice. St001881The number of factors of a lattice as a Cartesian product of lattices. St001616The number of neutral elements in a lattice. St001720The minimal length of a chain of small intervals in a lattice. St001200The number of simple modules in eAe with projective dimension at most 2 in the corresponding Nakayama algebra A with minimal faithful projective-injective module eA. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. St000297The number of leading ones in a binary word. St000768The number of peaks in an integer composition. St001868The number of alignments of type NE of a signed permutation. St001870The number of positive entries followed by a negative entry in a signed permutation.
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