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Your data matches 4 different statistics following compositions of up to 3 maps.
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Matching statistic: St001232
Mp00109: Permutations —descent word⟶ Binary words
Mp00097: Binary words —delta morphism⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00097: Binary words —delta morphism⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,2] => 0 => [1] => [1,0]
=> 0
[2,1] => 1 => [1] => [1,0]
=> 0
[1,2,3] => 00 => [2] => [1,1,0,0]
=> 0
[1,3,2] => 01 => [1,1] => [1,0,1,0]
=> 1
[2,1,3] => 10 => [1,1] => [1,0,1,0]
=> 1
[2,3,1] => 01 => [1,1] => [1,0,1,0]
=> 1
[3,1,2] => 10 => [1,1] => [1,0,1,0]
=> 1
[3,2,1] => 11 => [2] => [1,1,0,0]
=> 0
[1,2,3,4] => 000 => [3] => [1,1,1,0,0,0]
=> 0
[1,2,4,3] => 001 => [2,1] => [1,1,0,0,1,0]
=> 1
[1,3,4,2] => 001 => [2,1] => [1,1,0,0,1,0]
=> 1
[1,4,3,2] => 011 => [1,2] => [1,0,1,1,0,0]
=> 2
[2,1,3,4] => 100 => [1,2] => [1,0,1,1,0,0]
=> 2
[2,3,4,1] => 001 => [2,1] => [1,1,0,0,1,0]
=> 1
[2,4,3,1] => 011 => [1,2] => [1,0,1,1,0,0]
=> 2
[3,1,2,4] => 100 => [1,2] => [1,0,1,1,0,0]
=> 2
[3,2,1,4] => 110 => [2,1] => [1,1,0,0,1,0]
=> 1
[3,4,2,1] => 011 => [1,2] => [1,0,1,1,0,0]
=> 2
[4,1,2,3] => 100 => [1,2] => [1,0,1,1,0,0]
=> 2
[4,2,1,3] => 110 => [2,1] => [1,1,0,0,1,0]
=> 1
[4,3,1,2] => 110 => [2,1] => [1,1,0,0,1,0]
=> 1
[4,3,2,1] => 111 => [3] => [1,1,1,0,0,0]
=> 0
[1,2,3,4,5] => 0000 => [4] => [1,1,1,1,0,0,0,0]
=> 0
[1,2,3,5,4] => 0001 => [3,1] => [1,1,1,0,0,0,1,0]
=> 1
[1,2,4,5,3] => 0001 => [3,1] => [1,1,1,0,0,0,1,0]
=> 1
[1,2,5,4,3] => 0011 => [2,2] => [1,1,0,0,1,1,0,0]
=> 2
[1,3,4,5,2] => 0001 => [3,1] => [1,1,1,0,0,0,1,0]
=> 1
[1,3,5,4,2] => 0011 => [2,2] => [1,1,0,0,1,1,0,0]
=> 2
[1,4,3,2,5] => 0110 => [1,2,1] => [1,0,1,1,0,0,1,0]
=> 3
[1,4,5,3,2] => 0011 => [2,2] => [1,1,0,0,1,1,0,0]
=> 2
[1,5,3,2,4] => 0110 => [1,2,1] => [1,0,1,1,0,0,1,0]
=> 3
[1,5,4,2,3] => 0110 => [1,2,1] => [1,0,1,1,0,0,1,0]
=> 3
[1,5,4,3,2] => 0111 => [1,3] => [1,0,1,1,1,0,0,0]
=> 3
[2,1,3,4,5] => 1000 => [1,3] => [1,0,1,1,1,0,0,0]
=> 3
[2,1,3,5,4] => 1001 => [1,2,1] => [1,0,1,1,0,0,1,0]
=> 3
[2,1,4,5,3] => 1001 => [1,2,1] => [1,0,1,1,0,0,1,0]
=> 3
[2,3,4,5,1] => 0001 => [3,1] => [1,1,1,0,0,0,1,0]
=> 1
[2,3,5,4,1] => 0011 => [2,2] => [1,1,0,0,1,1,0,0]
=> 2
[2,4,3,1,5] => 0110 => [1,2,1] => [1,0,1,1,0,0,1,0]
=> 3
[2,4,5,3,1] => 0011 => [2,2] => [1,1,0,0,1,1,0,0]
=> 2
[2,5,3,1,4] => 0110 => [1,2,1] => [1,0,1,1,0,0,1,0]
=> 3
[2,5,4,1,3] => 0110 => [1,2,1] => [1,0,1,1,0,0,1,0]
=> 3
[2,5,4,3,1] => 0111 => [1,3] => [1,0,1,1,1,0,0,0]
=> 3
[3,1,2,4,5] => 1000 => [1,3] => [1,0,1,1,1,0,0,0]
=> 3
[3,1,2,5,4] => 1001 => [1,2,1] => [1,0,1,1,0,0,1,0]
=> 3
[3,1,4,5,2] => 1001 => [1,2,1] => [1,0,1,1,0,0,1,0]
=> 3
[3,2,1,4,5] => 1100 => [2,2] => [1,1,0,0,1,1,0,0]
=> 2
[3,2,4,5,1] => 1001 => [1,2,1] => [1,0,1,1,0,0,1,0]
=> 3
[3,4,2,1,5] => 0110 => [1,2,1] => [1,0,1,1,0,0,1,0]
=> 3
[3,4,5,2,1] => 0011 => [2,2] => [1,1,0,0,1,1,0,0]
=> 2
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
Matching statistic: St001227
Mp00109: Permutations —descent word⟶ Binary words
Mp00097: Binary words —delta morphism⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
St001227: Dyck paths ⟶ ℤResult quality: 26% ●values known / values provided: 26%●distinct values known / distinct values provided: 86%
Mp00097: Binary words —delta morphism⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
St001227: Dyck paths ⟶ ℤResult quality: 26% ●values known / values provided: 26%●distinct values known / distinct values provided: 86%
Values
[1,2] => 0 => [1] => [1,0]
=> 0
[2,1] => 1 => [1] => [1,0]
=> 0
[1,2,3] => 00 => [2] => [1,1,0,0]
=> 0
[1,3,2] => 01 => [1,1] => [1,0,1,0]
=> 1
[2,1,3] => 10 => [1,1] => [1,0,1,0]
=> 1
[2,3,1] => 01 => [1,1] => [1,0,1,0]
=> 1
[3,1,2] => 10 => [1,1] => [1,0,1,0]
=> 1
[3,2,1] => 11 => [2] => [1,1,0,0]
=> 0
[1,2,3,4] => 000 => [3] => [1,1,1,0,0,0]
=> 0
[1,2,4,3] => 001 => [2,1] => [1,1,0,0,1,0]
=> 1
[1,3,4,2] => 001 => [2,1] => [1,1,0,0,1,0]
=> 1
[1,4,3,2] => 011 => [1,2] => [1,0,1,1,0,0]
=> 2
[2,1,3,4] => 100 => [1,2] => [1,0,1,1,0,0]
=> 2
[2,3,4,1] => 001 => [2,1] => [1,1,0,0,1,0]
=> 1
[2,4,3,1] => 011 => [1,2] => [1,0,1,1,0,0]
=> 2
[3,1,2,4] => 100 => [1,2] => [1,0,1,1,0,0]
=> 2
[3,2,1,4] => 110 => [2,1] => [1,1,0,0,1,0]
=> 1
[3,4,2,1] => 011 => [1,2] => [1,0,1,1,0,0]
=> 2
[4,1,2,3] => 100 => [1,2] => [1,0,1,1,0,0]
=> 2
[4,2,1,3] => 110 => [2,1] => [1,1,0,0,1,0]
=> 1
[4,3,1,2] => 110 => [2,1] => [1,1,0,0,1,0]
=> 1
[4,3,2,1] => 111 => [3] => [1,1,1,0,0,0]
=> 0
[1,2,3,4,5] => 0000 => [4] => [1,1,1,1,0,0,0,0]
=> 0
[1,2,3,5,4] => 0001 => [3,1] => [1,1,1,0,0,0,1,0]
=> 1
[1,2,4,5,3] => 0001 => [3,1] => [1,1,1,0,0,0,1,0]
=> 1
[1,2,5,4,3] => 0011 => [2,2] => [1,1,0,0,1,1,0,0]
=> 2
[1,3,4,5,2] => 0001 => [3,1] => [1,1,1,0,0,0,1,0]
=> 1
[1,3,5,4,2] => 0011 => [2,2] => [1,1,0,0,1,1,0,0]
=> 2
[1,4,3,2,5] => 0110 => [1,2,1] => [1,0,1,1,0,0,1,0]
=> 3
[1,4,5,3,2] => 0011 => [2,2] => [1,1,0,0,1,1,0,0]
=> 2
[1,5,3,2,4] => 0110 => [1,2,1] => [1,0,1,1,0,0,1,0]
=> 3
[1,5,4,2,3] => 0110 => [1,2,1] => [1,0,1,1,0,0,1,0]
=> 3
[1,5,4,3,2] => 0111 => [1,3] => [1,0,1,1,1,0,0,0]
=> 3
[2,1,3,4,5] => 1000 => [1,3] => [1,0,1,1,1,0,0,0]
=> 3
[2,1,3,5,4] => 1001 => [1,2,1] => [1,0,1,1,0,0,1,0]
=> 3
[2,1,4,5,3] => 1001 => [1,2,1] => [1,0,1,1,0,0,1,0]
=> 3
[2,3,4,5,1] => 0001 => [3,1] => [1,1,1,0,0,0,1,0]
=> 1
[2,3,5,4,1] => 0011 => [2,2] => [1,1,0,0,1,1,0,0]
=> 2
[2,4,3,1,5] => 0110 => [1,2,1] => [1,0,1,1,0,0,1,0]
=> 3
[2,4,5,3,1] => 0011 => [2,2] => [1,1,0,0,1,1,0,0]
=> 2
[2,5,3,1,4] => 0110 => [1,2,1] => [1,0,1,1,0,0,1,0]
=> 3
[2,5,4,1,3] => 0110 => [1,2,1] => [1,0,1,1,0,0,1,0]
=> 3
[2,5,4,3,1] => 0111 => [1,3] => [1,0,1,1,1,0,0,0]
=> 3
[3,1,2,4,5] => 1000 => [1,3] => [1,0,1,1,1,0,0,0]
=> 3
[3,1,2,5,4] => 1001 => [1,2,1] => [1,0,1,1,0,0,1,0]
=> 3
[3,1,4,5,2] => 1001 => [1,2,1] => [1,0,1,1,0,0,1,0]
=> 3
[3,2,1,4,5] => 1100 => [2,2] => [1,1,0,0,1,1,0,0]
=> 2
[3,2,4,5,1] => 1001 => [1,2,1] => [1,0,1,1,0,0,1,0]
=> 3
[3,4,2,1,5] => 0110 => [1,2,1] => [1,0,1,1,0,0,1,0]
=> 3
[3,4,5,2,1] => 0011 => [2,2] => [1,1,0,0,1,1,0,0]
=> 2
[8,7,6,5,4,3,2,1] => 1111111 => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 0
[7,8,6,5,4,3,2,1] => 0111111 => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 6
[6,7,8,5,4,3,2,1] => 0011111 => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0]
=> ? = 5
[8,5,6,7,4,3,2,1] => 1001111 => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0]
=> ? = 6
[7,5,6,8,4,3,2,1] => 1001111 => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0]
=> ? = 6
[6,5,7,8,4,3,2,1] => 1001111 => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0]
=> ? = 6
[5,6,7,8,4,3,2,1] => 0001111 => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
=> ? = 4
[8,7,4,5,6,3,2,1] => 1100111 => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0]
=> ? = 5
[8,6,4,5,7,3,2,1] => 1100111 => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0]
=> ? = 5
[8,5,4,6,7,3,2,1] => 1100111 => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0]
=> ? = 5
[8,4,5,6,7,3,2,1] => 1000111 => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0]
=> ? = 6
[7,6,4,5,8,3,2,1] => 1100111 => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0]
=> ? = 5
[7,5,4,6,8,3,2,1] => 1100111 => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0]
=> ? = 5
[7,4,5,6,8,3,2,1] => 1000111 => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0]
=> ? = 6
[6,5,4,7,8,3,2,1] => 1100111 => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0]
=> ? = 5
[6,4,5,7,8,3,2,1] => 1000111 => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0]
=> ? = 6
[5,4,6,7,8,3,2,1] => 1000111 => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0]
=> ? = 6
[4,5,6,7,8,3,2,1] => 0000111 => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
=> ? = 3
[8,7,6,3,4,5,2,1] => 1110011 => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0]
=> ? = 4
[7,8,6,3,4,5,2,1] => 0110011 => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
=> ? = 6
[8,7,5,3,4,6,2,1] => 1110011 => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0]
=> ? = 4
[7,8,5,3,4,6,2,1] => 0110011 => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
=> ? = 6
[8,7,4,3,5,6,2,1] => 1110011 => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0]
=> ? = 4
[8,7,3,4,5,6,2,1] => 1100011 => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
=> ? = 5
[8,6,4,3,5,7,2,1] => 1110011 => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0]
=> ? = 4
[8,5,4,3,6,7,2,1] => 1110011 => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0]
=> ? = 4
[8,5,3,4,6,7,2,1] => 1100011 => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
=> ? = 5
[8,4,3,5,6,7,2,1] => 1100011 => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
=> ? = 5
[8,3,4,5,6,7,2,1] => 1000011 => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0]
=> ? = 6
[7,6,5,3,4,8,2,1] => 1110011 => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0]
=> ? = 4
[7,6,4,3,5,8,2,1] => 1110011 => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0]
=> ? = 4
[7,6,3,4,5,8,2,1] => 1100011 => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
=> ? = 5
[7,5,4,3,6,8,2,1] => 1110011 => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0]
=> ? = 4
[7,5,3,4,6,8,2,1] => 1100011 => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
=> ? = 5
[7,3,4,5,6,8,2,1] => 1000011 => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0]
=> ? = 6
[6,5,4,3,7,8,2,1] => 1110011 => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0]
=> ? = 4
[6,5,3,4,7,8,2,1] => 1100011 => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
=> ? = 5
[6,3,4,5,7,8,2,1] => 1000011 => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0]
=> ? = 6
[5,4,3,6,7,8,2,1] => 1100011 => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
=> ? = 5
[5,3,4,6,7,8,2,1] => 1000011 => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0]
=> ? = 6
[4,3,5,6,7,8,2,1] => 1000011 => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0]
=> ? = 6
[3,4,5,6,7,8,2,1] => 0000011 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
=> ? = 2
[8,7,6,5,2,3,4,1] => 1111001 => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
=> ? = 3
[6,7,8,5,2,3,4,1] => 0011001 => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
=> ? = 5
[8,7,6,4,2,3,5,1] => 1111001 => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
=> ? = 3
[6,7,8,4,2,3,5,1] => 0011001 => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
=> ? = 5
[8,7,6,3,2,4,5,1] => 1111001 => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
=> ? = 3
[7,8,6,3,2,4,5,1] => 0111001 => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0]
=> ? = 6
[6,7,8,3,2,4,5,1] => 0011001 => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
=> ? = 5
[8,7,6,2,3,4,5,1] => 1110001 => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0]
=> ? = 4
Description
The vector space dimension of the first extension group between the socle of the regular module and the Jacobson radical of the corresponding Nakayama algebra.
Matching statistic: St001742
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00064: Permutations —reverse⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St001742: Graphs ⟶ ℤResult quality: 6% ●values known / values provided: 6%●distinct values known / distinct values provided: 71%
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St001742: Graphs ⟶ ℤResult quality: 6% ●values known / values provided: 6%●distinct values known / distinct values provided: 71%
Values
[1,2] => [2,1] => [1,1] => ([(0,1)],2)
=> 0
[2,1] => [1,2] => [2] => ([],2)
=> 0
[1,2,3] => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 0
[1,3,2] => [2,3,1] => [2,1] => ([(0,2),(1,2)],3)
=> 1
[2,1,3] => [3,1,2] => [1,2] => ([(1,2)],3)
=> 1
[2,3,1] => [1,3,2] => [2,1] => ([(0,2),(1,2)],3)
=> 1
[3,1,2] => [2,1,3] => [1,2] => ([(1,2)],3)
=> 1
[3,2,1] => [1,2,3] => [3] => ([],3)
=> 0
[1,2,3,4] => [4,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 0
[1,2,4,3] => [3,4,2,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 1
[1,3,4,2] => [2,4,3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 1
[1,4,3,2] => [2,3,4,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2
[2,1,3,4] => [4,3,1,2] => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
=> 2
[2,3,4,1] => [1,4,3,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 1
[2,4,3,1] => [1,3,4,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2
[3,1,2,4] => [4,2,1,3] => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
=> 2
[3,2,1,4] => [4,1,2,3] => [1,3] => ([(2,3)],4)
=> 1
[3,4,2,1] => [1,2,4,3] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2
[4,1,2,3] => [3,2,1,4] => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
=> 2
[4,2,1,3] => [3,1,2,4] => [1,3] => ([(2,3)],4)
=> 1
[4,3,1,2] => [2,1,3,4] => [1,3] => ([(2,3)],4)
=> 1
[4,3,2,1] => [1,2,3,4] => [4] => ([],4)
=> 0
[1,2,3,4,5] => [5,4,3,2,1] => [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)
=> 0
[1,2,3,5,4] => [4,5,3,2,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
[1,2,4,5,3] => [3,5,4,2,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
[1,2,5,4,3] => [3,4,5,2,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[1,3,4,5,2] => [2,5,4,3,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
[1,3,5,4,2] => [2,4,5,3,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[1,4,3,2,5] => [5,2,3,4,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[1,4,5,3,2] => [2,3,5,4,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[1,5,3,2,4] => [4,2,3,5,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[1,5,4,2,3] => [3,2,4,5,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[1,5,4,3,2] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3
[2,1,3,4,5] => [5,4,3,1,2] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[2,1,3,5,4] => [4,5,3,1,2] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[2,1,4,5,3] => [3,5,4,1,2] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[2,3,4,5,1] => [1,5,4,3,2] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
[2,3,5,4,1] => [1,4,5,3,2] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[2,4,3,1,5] => [5,1,3,4,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[2,4,5,3,1] => [1,3,5,4,2] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[2,5,3,1,4] => [4,1,3,5,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[2,5,4,1,3] => [3,1,4,5,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[2,5,4,3,1] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3
[3,1,2,4,5] => [5,4,2,1,3] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[3,1,2,5,4] => [4,5,2,1,3] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[3,1,4,5,2] => [2,5,4,1,3] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[3,2,1,4,5] => [5,4,1,2,3] => [1,1,3] => ([(2,3),(2,4),(3,4)],5)
=> 2
[3,2,4,5,1] => [1,5,4,2,3] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[3,4,2,1,5] => [5,1,2,4,3] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[3,4,5,2,1] => [1,2,5,4,3] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[1,2,3,4,5,6,7] => [7,6,5,4,3,2,1] => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(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
[1,2,3,4,5,7,6] => [6,7,5,4,3,2,1] => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(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)
=> ? = 1
[1,2,3,4,6,7,5] => [5,7,6,4,3,2,1] => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(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)
=> ? = 1
[1,2,3,4,7,6,5] => [5,6,7,4,3,2,1] => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(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)
=> ? = 2
[1,2,3,5,6,7,4] => [4,7,6,5,3,2,1] => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(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)
=> ? = 1
[1,2,3,5,7,6,4] => [4,6,7,5,3,2,1] => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(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)
=> ? = 2
[1,2,3,6,5,4,7] => [7,4,5,6,3,2,1] => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(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)
=> ? = 3
[1,2,3,6,7,5,4] => [4,5,7,6,3,2,1] => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(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)
=> ? = 2
[1,2,3,7,5,4,6] => [6,4,5,7,3,2,1] => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(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)
=> ? = 3
[1,2,3,7,6,4,5] => [5,4,6,7,3,2,1] => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(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)
=> ? = 3
[1,2,3,7,6,5,4] => [4,5,6,7,3,2,1] => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 3
[1,2,4,5,6,7,3] => [3,7,6,5,4,2,1] => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(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)
=> ? = 1
[1,2,4,5,7,6,3] => [3,6,7,5,4,2,1] => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(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)
=> ? = 2
[1,2,4,6,5,3,7] => [7,3,5,6,4,2,1] => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(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)
=> ? = 3
[1,2,4,6,7,5,3] => [3,5,7,6,4,2,1] => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(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)
=> ? = 2
[1,2,4,7,5,3,6] => [6,3,5,7,4,2,1] => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(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)
=> ? = 3
[1,2,4,7,6,3,5] => [5,3,6,7,4,2,1] => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(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)
=> ? = 3
[1,2,4,7,6,5,3] => [3,5,6,7,4,2,1] => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 3
[1,2,5,4,3,6,7] => [7,6,3,4,5,2,1] => [1,1,3,1,1] => ([(0,5),(0,6),(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)
=> ? = 4
[1,2,5,6,4,3,7] => [7,3,4,6,5,2,1] => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(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)
=> ? = 3
[1,2,5,6,7,4,3] => [3,4,7,6,5,2,1] => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(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)
=> ? = 2
[1,2,5,7,4,3,6] => [6,3,4,7,5,2,1] => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(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)
=> ? = 3
[1,2,5,7,6,3,4] => [4,3,6,7,5,2,1] => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(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)
=> ? = 3
[1,2,5,7,6,4,3] => [3,4,6,7,5,2,1] => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 3
[1,2,6,4,3,5,7] => [7,5,3,4,6,2,1] => [1,1,3,1,1] => ([(0,5),(0,6),(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)
=> ? = 4
[1,2,6,5,3,4,7] => [7,4,3,5,6,2,1] => [1,1,3,1,1] => ([(0,5),(0,6),(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)
=> ? = 4
[1,2,6,5,4,3,7] => [7,3,4,5,6,2,1] => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 4
[1,2,6,7,4,3,5] => [5,3,4,7,6,2,1] => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(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)
=> ? = 3
[1,2,6,7,5,3,4] => [4,3,5,7,6,2,1] => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(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)
=> ? = 3
[1,2,6,7,5,4,3] => [3,4,5,7,6,2,1] => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 3
[1,2,7,4,3,5,6] => [6,5,3,4,7,2,1] => [1,1,3,1,1] => ([(0,5),(0,6),(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)
=> ? = 4
[1,2,7,5,3,4,6] => [6,4,3,5,7,2,1] => [1,1,3,1,1] => ([(0,5),(0,6),(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)
=> ? = 4
[1,2,7,5,4,3,6] => [6,3,4,5,7,2,1] => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 4
[1,2,7,6,3,4,5] => [5,4,3,6,7,2,1] => [1,1,3,1,1] => ([(0,5),(0,6),(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)
=> ? = 4
[1,2,7,6,4,3,5] => [5,3,4,6,7,2,1] => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 4
[1,2,7,6,5,3,4] => [4,3,5,6,7,2,1] => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 4
[1,2,7,6,5,4,3] => [3,4,5,6,7,2,1] => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 4
[1,3,4,5,6,7,2] => [2,7,6,5,4,3,1] => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(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)
=> ? = 1
[1,3,4,5,7,6,2] => [2,6,7,5,4,3,1] => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(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)
=> ? = 2
[1,3,4,6,5,2,7] => [7,2,5,6,4,3,1] => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(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)
=> ? = 3
[1,3,4,6,7,5,2] => [2,5,7,6,4,3,1] => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(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)
=> ? = 2
[1,3,4,7,5,2,6] => [6,2,5,7,4,3,1] => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(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)
=> ? = 3
[1,3,4,7,6,2,5] => [5,2,6,7,4,3,1] => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(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)
=> ? = 3
[1,3,4,7,6,5,2] => [2,5,6,7,4,3,1] => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 3
[1,3,5,4,2,6,7] => [7,6,2,4,5,3,1] => [1,1,3,1,1] => ([(0,5),(0,6),(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)
=> ? = 4
[1,3,5,6,4,2,7] => [7,2,4,6,5,3,1] => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(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)
=> ? = 3
[1,3,5,6,7,4,2] => [2,4,7,6,5,3,1] => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(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)
=> ? = 2
[1,3,5,7,4,2,6] => [6,2,4,7,5,3,1] => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(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)
=> ? = 3
[1,3,5,7,6,2,4] => [4,2,6,7,5,3,1] => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(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)
=> ? = 3
[1,3,5,7,6,4,2] => [2,4,6,7,5,3,1] => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 3
Description
The difference of the maximal and the minimal degree in a graph.
The graph is regular if and only if this statistic is zero.
Matching statistic: St000264
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Mp00070: Permutations —Robinson-Schensted recording tableau⟶ Standard tableaux
Mp00295: Standard tableaux —valley composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000264: Graphs ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 14%
Mp00295: Standard tableaux —valley composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000264: Graphs ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 14%
Values
[1,2] => [[1,2]]
=> [2] => ([],2)
=> ? = 0 - 2
[2,1] => [[1],[2]]
=> [2] => ([],2)
=> ? = 0 - 2
[1,2,3] => [[1,2,3]]
=> [3] => ([],3)
=> ? = 0 - 2
[1,3,2] => [[1,2],[3]]
=> [3] => ([],3)
=> ? = 1 - 2
[2,1,3] => [[1,3],[2]]
=> [2,1] => ([(0,2),(1,2)],3)
=> ? = 1 - 2
[2,3,1] => [[1,2],[3]]
=> [3] => ([],3)
=> ? = 1 - 2
[3,1,2] => [[1,3],[2]]
=> [2,1] => ([(0,2),(1,2)],3)
=> ? = 1 - 2
[3,2,1] => [[1],[2],[3]]
=> [3] => ([],3)
=> ? = 0 - 2
[1,2,3,4] => [[1,2,3,4]]
=> [4] => ([],4)
=> ? = 0 - 2
[1,2,4,3] => [[1,2,3],[4]]
=> [4] => ([],4)
=> ? = 1 - 2
[1,3,4,2] => [[1,2,3],[4]]
=> [4] => ([],4)
=> ? = 1 - 2
[1,4,3,2] => [[1,2],[3],[4]]
=> [4] => ([],4)
=> ? = 2 - 2
[2,1,3,4] => [[1,3,4],[2]]
=> [2,2] => ([(1,3),(2,3)],4)
=> ? = 2 - 2
[2,3,4,1] => [[1,2,3],[4]]
=> [4] => ([],4)
=> ? = 1 - 2
[2,4,3,1] => [[1,2],[3],[4]]
=> [4] => ([],4)
=> ? = 2 - 2
[3,1,2,4] => [[1,3,4],[2]]
=> [2,2] => ([(1,3),(2,3)],4)
=> ? = 2 - 2
[3,2,1,4] => [[1,4],[2],[3]]
=> [3,1] => ([(0,3),(1,3),(2,3)],4)
=> ? = 1 - 2
[3,4,2,1] => [[1,2],[3],[4]]
=> [4] => ([],4)
=> ? = 2 - 2
[4,1,2,3] => [[1,3,4],[2]]
=> [2,2] => ([(1,3),(2,3)],4)
=> ? = 2 - 2
[4,2,1,3] => [[1,4],[2],[3]]
=> [3,1] => ([(0,3),(1,3),(2,3)],4)
=> ? = 1 - 2
[4,3,1,2] => [[1,4],[2],[3]]
=> [3,1] => ([(0,3),(1,3),(2,3)],4)
=> ? = 1 - 2
[4,3,2,1] => [[1],[2],[3],[4]]
=> [4] => ([],4)
=> ? = 0 - 2
[1,2,3,4,5] => [[1,2,3,4,5]]
=> [5] => ([],5)
=> ? = 0 - 2
[1,2,3,5,4] => [[1,2,3,4],[5]]
=> [5] => ([],5)
=> ? = 1 - 2
[1,2,4,5,3] => [[1,2,3,4],[5]]
=> [5] => ([],5)
=> ? = 1 - 2
[1,2,5,4,3] => [[1,2,3],[4],[5]]
=> [5] => ([],5)
=> ? = 2 - 2
[1,3,4,5,2] => [[1,2,3,4],[5]]
=> [5] => ([],5)
=> ? = 1 - 2
[1,3,5,4,2] => [[1,2,3],[4],[5]]
=> [5] => ([],5)
=> ? = 2 - 2
[1,4,3,2,5] => [[1,2,5],[3],[4]]
=> [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? = 3 - 2
[1,4,5,3,2] => [[1,2,3],[4],[5]]
=> [5] => ([],5)
=> ? = 2 - 2
[1,5,3,2,4] => [[1,2,5],[3],[4]]
=> [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? = 3 - 2
[1,5,4,2,3] => [[1,2,5],[3],[4]]
=> [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? = 3 - 2
[1,5,4,3,2] => [[1,2],[3],[4],[5]]
=> [5] => ([],5)
=> ? = 3 - 2
[2,1,3,4,5] => [[1,3,4,5],[2]]
=> [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 2
[2,1,3,5,4] => [[1,3,4],[2,5]]
=> [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 2
[2,1,4,5,3] => [[1,3,4],[2,5]]
=> [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 2
[2,3,4,5,1] => [[1,2,3,4],[5]]
=> [5] => ([],5)
=> ? = 1 - 2
[2,3,5,4,1] => [[1,2,3],[4],[5]]
=> [5] => ([],5)
=> ? = 2 - 2
[2,4,3,1,5] => [[1,2,5],[3],[4]]
=> [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? = 3 - 2
[2,4,5,3,1] => [[1,2,3],[4],[5]]
=> [5] => ([],5)
=> ? = 2 - 2
[2,5,3,1,4] => [[1,2,5],[3],[4]]
=> [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? = 3 - 2
[2,5,4,1,3] => [[1,2],[3,5],[4]]
=> [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? = 3 - 2
[2,5,4,3,1] => [[1,2],[3],[4],[5]]
=> [5] => ([],5)
=> ? = 3 - 2
[3,1,2,4,5] => [[1,3,4,5],[2]]
=> [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 2
[3,1,2,5,4] => [[1,3,4],[2,5]]
=> [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 2
[3,1,4,5,2] => [[1,3,4],[2,5]]
=> [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 2
[3,2,1,4,5] => [[1,4,5],[2],[3]]
=> [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 2 - 2
[3,2,4,5,1] => [[1,3,4],[2],[5]]
=> [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 2
[3,4,2,1,5] => [[1,2,5],[3],[4]]
=> [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? = 3 - 2
[3,4,5,2,1] => [[1,2,3],[4],[5]]
=> [5] => ([],5)
=> ? = 2 - 2
[2,1,3,6,5,4,7] => [[1,3,4,7],[2,5],[6]]
=> [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 5 - 2
[2,1,3,7,5,4,6] => [[1,3,4,7],[2,5],[6]]
=> [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 5 - 2
[2,1,3,7,6,4,5] => [[1,3,4,7],[2,5],[6]]
=> [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 5 - 2
[2,1,4,6,5,3,7] => [[1,3,4,7],[2,5],[6]]
=> [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 5 - 2
[2,1,4,7,5,3,6] => [[1,3,4,7],[2,5],[6]]
=> [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 5 - 2
[2,1,4,7,6,3,5] => [[1,3,4],[2,5,7],[6]]
=> [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 5 - 2
[2,1,5,6,4,3,7] => [[1,3,4,7],[2,5],[6]]
=> [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 5 - 2
[2,1,5,7,4,3,6] => [[1,3,4],[2,5,7],[6]]
=> [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 5 - 2
[2,1,5,7,6,3,4] => [[1,3,4],[2,5,7],[6]]
=> [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 5 - 2
[2,1,6,7,4,3,5] => [[1,3,4],[2,5,7],[6]]
=> [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 5 - 2
[2,1,6,7,5,3,4] => [[1,3,4],[2,5,7],[6]]
=> [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 5 - 2
[3,1,2,6,5,4,7] => [[1,3,4,7],[2,5],[6]]
=> [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 5 - 2
[3,1,2,7,5,4,6] => [[1,3,4,7],[2,5],[6]]
=> [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 5 - 2
[3,1,2,7,6,4,5] => [[1,3,4,7],[2,5],[6]]
=> [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 5 - 2
[3,1,4,6,5,2,7] => [[1,3,4,7],[2,5],[6]]
=> [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 5 - 2
[3,1,4,7,5,2,6] => [[1,3,4,7],[2,5],[6]]
=> [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 5 - 2
[3,1,4,7,6,2,5] => [[1,3,4],[2,5,7],[6]]
=> [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 5 - 2
[3,1,5,6,4,2,7] => [[1,3,4,7],[2,5],[6]]
=> [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 5 - 2
[3,1,5,7,4,2,6] => [[1,3,4],[2,5,7],[6]]
=> [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 5 - 2
[3,1,5,7,6,2,4] => [[1,3,4],[2,5,7],[6]]
=> [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 5 - 2
[3,1,6,7,4,2,5] => [[1,3,4],[2,5,7],[6]]
=> [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 5 - 2
[3,1,6,7,5,2,4] => [[1,3,4],[2,5,7],[6]]
=> [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 5 - 2
[3,2,4,6,5,1,7] => [[1,3,4,7],[2,5],[6]]
=> [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 5 - 2
[3,2,4,7,5,1,6] => [[1,3,4,7],[2,5],[6]]
=> [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 5 - 2
[3,2,4,7,6,1,5] => [[1,3,4],[2,5],[6,7]]
=> [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 5 - 2
[3,2,5,6,4,1,7] => [[1,3,4,7],[2,5],[6]]
=> [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 5 - 2
[3,2,5,7,4,1,6] => [[1,3,4],[2,5,7],[6]]
=> [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 5 - 2
[3,2,5,7,6,1,4] => [[1,3,4],[2,5],[6,7]]
=> [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 5 - 2
[3,2,6,7,4,1,5] => [[1,3,4],[2,5,7],[6]]
=> [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 5 - 2
[3,2,6,7,5,1,4] => [[1,3,4],[2,5],[6,7]]
=> [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 5 - 2
[4,1,2,6,5,3,7] => [[1,3,4,7],[2,5],[6]]
=> [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 5 - 2
[4,1,2,7,5,3,6] => [[1,3,4,7],[2,5],[6]]
=> [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 5 - 2
[4,1,2,7,6,3,5] => [[1,3,4,7],[2,5],[6]]
=> [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 5 - 2
[4,1,3,6,5,2,7] => [[1,3,4,7],[2,5],[6]]
=> [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 5 - 2
[4,1,3,7,5,2,6] => [[1,3,4,7],[2,5],[6]]
=> [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 5 - 2
[4,1,3,7,6,2,5] => [[1,3,4],[2,5],[6,7]]
=> [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 5 - 2
[4,1,5,6,3,2,7] => [[1,3,4,7],[2,5],[6]]
=> [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 5 - 2
[4,1,5,7,3,2,6] => [[1,3,4],[2,5,7],[6]]
=> [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 5 - 2
[4,1,5,7,6,2,3] => [[1,3,4],[2,5,7],[6]]
=> [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 5 - 2
[4,1,6,7,3,2,5] => [[1,3,4],[2,5,7],[6]]
=> [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 5 - 2
[4,1,6,7,5,2,3] => [[1,3,4],[2,5,7],[6]]
=> [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 5 - 2
[4,2,3,6,5,1,7] => [[1,3,4,7],[2,5],[6]]
=> [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 5 - 2
[4,2,3,7,5,1,6] => [[1,3,4,7],[2,5],[6]]
=> [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 5 - 2
[4,2,3,7,6,1,5] => [[1,3,4],[2,5],[6,7]]
=> [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 5 - 2
[4,2,5,6,3,1,7] => [[1,3,4,7],[2,5],[6]]
=> [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 5 - 2
[4,2,5,7,3,1,6] => [[1,3,4],[2,5,7],[6]]
=> [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 5 - 2
[4,2,5,7,6,1,3] => [[1,3,4],[2,5],[6,7]]
=> [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 5 - 2
[4,2,6,7,3,1,5] => [[1,3,4],[2,5,7],[6]]
=> [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 5 - 2
[4,2,6,7,5,1,3] => [[1,3,4],[2,5],[6,7]]
=> [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 5 - 2
[4,3,5,6,2,1,7] => [[1,3,4,7],[2],[5],[6]]
=> [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 5 - 2
Description
The girth of a graph, which is not a tree.
This is the length of the shortest cycle in the graph.
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