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Your data matches 12 different statistics following compositions of up to 3 maps.
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Matching statistic: St000279
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St000279: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,2] => 2
[2,1] => 0
[1,2,3] => 4
[1,3,2] => 2
[2,1,3] => 0
[2,3,1] => 0
[3,1,2] => 0
[3,2,1] => 0
[1,2,3,4] => 8
[1,2,4,3] => 4
[1,3,2,4] => 4
[1,3,4,2] => 2
[1,4,2,3] => 4
[1,4,3,2] => 2
[2,1,3,4] => 0
[2,1,4,3] => 0
[2,3,1,4] => 0
[2,3,4,1] => 0
[2,4,1,3] => 0
[2,4,3,1] => 0
[3,1,2,4] => 0
[3,1,4,2] => 0
[3,2,1,4] => 0
[3,2,4,1] => 0
[3,4,1,2] => 0
[3,4,2,1] => 0
[4,1,2,3] => 0
[4,1,3,2] => 0
[4,2,1,3] => 0
[4,2,3,1] => 0
[4,3,1,2] => 0
[4,3,2,1] => 0
[1,2,3,4,5] => 16
[1,2,3,5,4] => 8
[1,2,4,3,5] => 8
[1,2,4,5,3] => 4
[1,2,5,3,4] => 8
[1,2,5,4,3] => 4
[1,3,2,4,5] => 8
[1,3,2,5,4] => 4
[1,3,4,2,5] => 4
[1,3,4,5,2] => 2
[1,3,5,2,4] => 4
[1,3,5,4,2] => 2
[1,4,2,3,5] => 8
[1,4,2,5,3] => 4
[1,4,3,2,5] => 4
[1,4,3,5,2] => 2
[1,4,5,2,3] => 4
[1,4,5,3,2] => 2
Description
The size of the preimage of the map 'cycle-as-one-line notation' from Permutations to Permutations.
Matching statistic: St001498
Mp00069: Permutations —complement⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
St001498: Dyck paths ⟶ ℤResult quality: 14% ●values known / values provided: 60%●distinct values known / distinct values provided: 14%
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
St001498: Dyck paths ⟶ ℤResult quality: 14% ●values known / values provided: 60%●distinct values known / distinct values provided: 14%
Values
[1,2] => [2,1] => [1,1,0,0]
=> [1,1,1,0,0,0]
=> ? = 2
[2,1] => [1,2] => [1,0,1,0]
=> [1,1,0,1,0,0]
=> 0
[1,2,3] => [3,2,1] => [1,1,1,0,0,0]
=> [1,1,1,1,0,0,0,0]
=> ? = 4
[1,3,2] => [3,1,2] => [1,1,1,0,0,0]
=> [1,1,1,1,0,0,0,0]
=> ? = 2
[2,1,3] => [2,3,1] => [1,1,0,1,0,0]
=> [1,1,1,0,1,0,0,0]
=> 0
[2,3,1] => [2,1,3] => [1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> 0
[3,1,2] => [1,3,2] => [1,0,1,1,0,0]
=> [1,1,0,1,1,0,0,0]
=> 0
[3,2,1] => [1,2,3] => [1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,0]
=> 0
[1,2,3,4] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 8
[1,2,4,3] => [4,3,1,2] => [1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 4
[1,3,2,4] => [4,2,3,1] => [1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 4
[1,3,4,2] => [4,2,1,3] => [1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 2
[1,4,2,3] => [4,1,3,2] => [1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 4
[1,4,3,2] => [4,1,2,3] => [1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 2
[2,1,3,4] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> 0
[2,1,4,3] => [3,4,1,2] => [1,1,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> 0
[2,3,1,4] => [3,2,4,1] => [1,1,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> 0
[2,3,4,1] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> 0
[2,4,1,3] => [3,1,4,2] => [1,1,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> 0
[2,4,3,1] => [3,1,2,4] => [1,1,1,0,0,0,1,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> 0
[3,1,2,4] => [2,4,3,1] => [1,1,0,1,1,0,0,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> 0
[3,1,4,2] => [2,4,1,3] => [1,1,0,1,1,0,0,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> 0
[3,2,1,4] => [2,3,4,1] => [1,1,0,1,0,1,0,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> 0
[3,2,4,1] => [2,3,1,4] => [1,1,0,1,0,0,1,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> 0
[3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,1,0,0,0]
=> 0
[3,4,2,1] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
=> [1,1,1,0,0,1,0,1,0,0]
=> 0
[4,1,2,3] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> 0
[4,1,3,2] => [1,4,2,3] => [1,0,1,1,1,0,0,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> 0
[4,2,1,3] => [1,3,4,2] => [1,0,1,1,0,1,0,0]
=> [1,1,0,1,1,0,1,0,0,0]
=> 0
[4,2,3,1] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,0,0,1,0,0]
=> 0
[4,3,1,2] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> 0
[4,3,2,1] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 0
[1,2,3,4,5] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 16
[1,2,3,5,4] => [5,4,3,1,2] => [1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 8
[1,2,4,3,5] => [5,4,2,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 8
[1,2,4,5,3] => [5,4,2,1,3] => [1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 4
[1,2,5,3,4] => [5,4,1,3,2] => [1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 8
[1,2,5,4,3] => [5,4,1,2,3] => [1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 4
[1,3,2,4,5] => [5,3,4,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 8
[1,3,2,5,4] => [5,3,4,1,2] => [1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 4
[1,3,4,2,5] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 4
[1,3,4,5,2] => [5,3,2,1,4] => [1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 2
[1,3,5,2,4] => [5,3,1,4,2] => [1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 4
[1,3,5,4,2] => [5,3,1,2,4] => [1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 2
[1,4,2,3,5] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 8
[1,4,2,5,3] => [5,2,4,1,3] => [1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 4
[1,4,3,2,5] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 4
[1,4,3,5,2] => [5,2,3,1,4] => [1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 2
[1,4,5,2,3] => [5,2,1,4,3] => [1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 4
[1,4,5,3,2] => [5,2,1,3,4] => [1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 2
[1,5,2,3,4] => [5,1,4,3,2] => [1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 8
[1,5,2,4,3] => [5,1,4,2,3] => [1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 4
[1,5,3,2,4] => [5,1,3,4,2] => [1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 4
[1,5,3,4,2] => [5,1,3,2,4] => [1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 2
[1,5,4,2,3] => [5,1,2,4,3] => [1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 4
[1,5,4,3,2] => [5,1,2,3,4] => [1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 2
[2,1,3,4,5] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> 0
[2,1,3,5,4] => [4,5,3,1,2] => [1,1,1,1,0,1,0,0,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> 0
[2,1,4,3,5] => [4,5,2,3,1] => [1,1,1,1,0,1,0,0,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> 0
[2,1,4,5,3] => [4,5,2,1,3] => [1,1,1,1,0,1,0,0,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> 0
[2,1,5,3,4] => [4,5,1,3,2] => [1,1,1,1,0,1,0,0,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> 0
[2,1,5,4,3] => [4,5,1,2,3] => [1,1,1,1,0,1,0,0,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> 0
[2,3,1,4,5] => [4,3,5,2,1] => [1,1,1,1,0,0,1,0,0,0]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 0
[2,3,1,5,4] => [4,3,5,1,2] => [1,1,1,1,0,0,1,0,0,0]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 0
[2,3,4,1,5] => [4,3,2,5,1] => [1,1,1,1,0,0,0,1,0,0]
=> [1,1,1,1,1,0,0,0,1,0,0,0]
=> 0
[2,3,4,5,1] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
=> [1,1,1,1,1,0,0,0,0,1,0,0]
=> 0
[2,3,5,1,4] => [4,3,1,5,2] => [1,1,1,1,0,0,0,1,0,0]
=> [1,1,1,1,1,0,0,0,1,0,0,0]
=> 0
[2,3,5,4,1] => [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0]
=> [1,1,1,1,1,0,0,0,0,1,0,0]
=> 0
[2,4,1,3,5] => [4,2,5,3,1] => [1,1,1,1,0,0,1,0,0,0]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 0
[2,4,1,5,3] => [4,2,5,1,3] => [1,1,1,1,0,0,1,0,0,0]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 0
[2,4,3,1,5] => [4,2,3,5,1] => [1,1,1,1,0,0,0,1,0,0]
=> [1,1,1,1,1,0,0,0,1,0,0,0]
=> 0
[2,4,3,5,1] => [4,2,3,1,5] => [1,1,1,1,0,0,0,0,1,0]
=> [1,1,1,1,1,0,0,0,0,1,0,0]
=> 0
[2,4,5,1,3] => [4,2,1,5,3] => [1,1,1,1,0,0,0,1,0,0]
=> [1,1,1,1,1,0,0,0,1,0,0,0]
=> 0
[2,4,5,3,1] => [4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0]
=> [1,1,1,1,1,0,0,0,0,1,0,0]
=> 0
[2,5,1,3,4] => [4,1,5,3,2] => [1,1,1,1,0,0,1,0,0,0]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 0
[2,5,1,4,3] => [4,1,5,2,3] => [1,1,1,1,0,0,1,0,0,0]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 0
[2,5,3,1,4] => [4,1,3,5,2] => [1,1,1,1,0,0,0,1,0,0]
=> [1,1,1,1,1,0,0,0,1,0,0,0]
=> 0
[2,5,3,4,1] => [4,1,3,2,5] => [1,1,1,1,0,0,0,0,1,0]
=> [1,1,1,1,1,0,0,0,0,1,0,0]
=> 0
[2,5,4,1,3] => [4,1,2,5,3] => [1,1,1,1,0,0,0,1,0,0]
=> [1,1,1,1,1,0,0,0,1,0,0,0]
=> 0
[2,5,4,3,1] => [4,1,2,3,5] => [1,1,1,1,0,0,0,0,1,0]
=> [1,1,1,1,1,0,0,0,0,1,0,0]
=> 0
[3,1,2,4,5] => [3,5,4,2,1] => [1,1,1,0,1,1,0,0,0,0]
=> [1,1,1,1,0,1,1,0,0,0,0,0]
=> 0
[3,1,2,5,4] => [3,5,4,1,2] => [1,1,1,0,1,1,0,0,0,0]
=> [1,1,1,1,0,1,1,0,0,0,0,0]
=> 0
[3,1,4,2,5] => [3,5,2,4,1] => [1,1,1,0,1,1,0,0,0,0]
=> [1,1,1,1,0,1,1,0,0,0,0,0]
=> 0
[1,2,3,4,5,6] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 32
[1,2,3,4,6,5] => [6,5,4,3,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 16
[1,2,3,5,4,6] => [6,5,4,2,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 16
[1,2,3,5,6,4] => [6,5,4,2,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 8
[1,2,3,6,4,5] => [6,5,4,1,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 16
[1,2,3,6,5,4] => [6,5,4,1,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 8
[1,2,4,3,5,6] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 16
[1,2,4,3,6,5] => [6,5,3,4,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 8
[1,2,4,5,3,6] => [6,5,3,2,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 8
[1,2,4,5,6,3] => [6,5,3,2,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 4
[1,2,4,6,3,5] => [6,5,3,1,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 8
[1,2,4,6,5,3] => [6,5,3,1,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 4
[1,2,5,3,4,6] => [6,5,2,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 16
[1,2,5,3,6,4] => [6,5,2,4,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 8
[1,2,5,4,3,6] => [6,5,2,3,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 8
[1,2,5,4,6,3] => [6,5,2,3,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 4
[1,2,5,6,3,4] => [6,5,2,1,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 8
Description
The normalised height of a Nakayama algebra with magnitude 1.
We use the bijection (see code) suggested by Christian Stump, to have a bijection between such Nakayama algebras with magnitude 1 and Dyck paths. The normalised height is the height of the (periodic) Dyck path given by the top of the Auslander-Reiten quiver. Thus when having a CNakayama algebra it is the Loewy length minus the number of simple modules and for the LNakayama algebras it is the usual height.
Matching statistic: St001199
Mp00069: Permutations —complement⟶ Permutations
Mp00068: Permutations —Simion-Schmidt map⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
St001199: Dyck paths ⟶ ℤResult quality: 14% ●values known / values provided: 60%●distinct values known / distinct values provided: 14%
Mp00068: Permutations —Simion-Schmidt map⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
St001199: Dyck paths ⟶ ℤResult quality: 14% ●values known / values provided: 60%●distinct values known / distinct values provided: 14%
Values
[1,2] => [2,1] => [2,1] => [1,1,0,0]
=> ? = 2 + 1
[2,1] => [1,2] => [1,2] => [1,0,1,0]
=> 1 = 0 + 1
[1,2,3] => [3,2,1] => [3,2,1] => [1,1,1,0,0,0]
=> ? = 4 + 1
[1,3,2] => [3,1,2] => [3,1,2] => [1,1,1,0,0,0]
=> ? = 2 + 1
[2,1,3] => [2,3,1] => [2,3,1] => [1,1,0,1,0,0]
=> 1 = 0 + 1
[2,3,1] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
=> 1 = 0 + 1
[3,1,2] => [1,3,2] => [1,3,2] => [1,0,1,1,0,0]
=> 1 = 0 + 1
[3,2,1] => [1,2,3] => [1,3,2] => [1,0,1,1,0,0]
=> 1 = 0 + 1
[1,2,3,4] => [4,3,2,1] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
=> ? = 8 + 1
[1,2,4,3] => [4,3,1,2] => [4,3,1,2] => [1,1,1,1,0,0,0,0]
=> ? = 4 + 1
[1,3,2,4] => [4,2,3,1] => [4,2,3,1] => [1,1,1,1,0,0,0,0]
=> ? = 4 + 1
[1,3,4,2] => [4,2,1,3] => [4,2,1,3] => [1,1,1,1,0,0,0,0]
=> ? = 2 + 1
[1,4,2,3] => [4,1,3,2] => [4,1,3,2] => [1,1,1,1,0,0,0,0]
=> ? = 4 + 1
[1,4,3,2] => [4,1,2,3] => [4,1,3,2] => [1,1,1,1,0,0,0,0]
=> ? = 2 + 1
[2,1,3,4] => [3,4,2,1] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
=> 1 = 0 + 1
[2,1,4,3] => [3,4,1,2] => [3,4,1,2] => [1,1,1,0,1,0,0,0]
=> 1 = 0 + 1
[2,3,1,4] => [3,2,4,1] => [3,2,4,1] => [1,1,1,0,0,1,0,0]
=> 1 = 0 + 1
[2,3,4,1] => [3,2,1,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
=> 1 = 0 + 1
[2,4,1,3] => [3,1,4,2] => [3,1,4,2] => [1,1,1,0,0,1,0,0]
=> 1 = 0 + 1
[2,4,3,1] => [3,1,2,4] => [3,1,4,2] => [1,1,1,0,0,1,0,0]
=> 1 = 0 + 1
[3,1,2,4] => [2,4,3,1] => [2,4,3,1] => [1,1,0,1,1,0,0,0]
=> 1 = 0 + 1
[3,1,4,2] => [2,4,1,3] => [2,4,1,3] => [1,1,0,1,1,0,0,0]
=> 1 = 0 + 1
[3,2,1,4] => [2,3,4,1] => [2,4,3,1] => [1,1,0,1,1,0,0,0]
=> 1 = 0 + 1
[3,2,4,1] => [2,3,1,4] => [2,4,1,3] => [1,1,0,1,1,0,0,0]
=> 1 = 0 + 1
[3,4,1,2] => [2,1,4,3] => [2,1,4,3] => [1,1,0,0,1,1,0,0]
=> 1 = 0 + 1
[3,4,2,1] => [2,1,3,4] => [2,1,4,3] => [1,1,0,0,1,1,0,0]
=> 1 = 0 + 1
[4,1,2,3] => [1,4,3,2] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
=> 1 = 0 + 1
[4,1,3,2] => [1,4,2,3] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
=> 1 = 0 + 1
[4,2,1,3] => [1,3,4,2] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
=> 1 = 0 + 1
[4,2,3,1] => [1,3,2,4] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
=> 1 = 0 + 1
[4,3,1,2] => [1,2,4,3] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
=> 1 = 0 + 1
[4,3,2,1] => [1,2,3,4] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
=> 1 = 0 + 1
[1,2,3,4,5] => [5,4,3,2,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 16 + 1
[1,2,3,5,4] => [5,4,3,1,2] => [5,4,3,1,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 8 + 1
[1,2,4,3,5] => [5,4,2,3,1] => [5,4,2,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 8 + 1
[1,2,4,5,3] => [5,4,2,1,3] => [5,4,2,1,3] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 4 + 1
[1,2,5,3,4] => [5,4,1,3,2] => [5,4,1,3,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 8 + 1
[1,2,5,4,3] => [5,4,1,2,3] => [5,4,1,3,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 4 + 1
[1,3,2,4,5] => [5,3,4,2,1] => [5,3,4,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 8 + 1
[1,3,2,5,4] => [5,3,4,1,2] => [5,3,4,1,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 4 + 1
[1,3,4,2,5] => [5,3,2,4,1] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 4 + 1
[1,3,4,5,2] => [5,3,2,1,4] => [5,3,2,1,4] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 + 1
[1,3,5,2,4] => [5,3,1,4,2] => [5,3,1,4,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 4 + 1
[1,3,5,4,2] => [5,3,1,2,4] => [5,3,1,4,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 + 1
[1,4,2,3,5] => [5,2,4,3,1] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 8 + 1
[1,4,2,5,3] => [5,2,4,1,3] => [5,2,4,1,3] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 4 + 1
[1,4,3,2,5] => [5,2,3,4,1] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 4 + 1
[1,4,3,5,2] => [5,2,3,1,4] => [5,2,4,1,3] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 + 1
[1,4,5,2,3] => [5,2,1,4,3] => [5,2,1,4,3] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 4 + 1
[1,4,5,3,2] => [5,2,1,3,4] => [5,2,1,4,3] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 + 1
[1,5,2,3,4] => [5,1,4,3,2] => [5,1,4,3,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 8 + 1
[1,5,2,4,3] => [5,1,4,2,3] => [5,1,4,3,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 4 + 1
[1,5,3,2,4] => [5,1,3,4,2] => [5,1,4,3,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 4 + 1
[1,5,3,4,2] => [5,1,3,2,4] => [5,1,4,3,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 + 1
[1,5,4,2,3] => [5,1,2,4,3] => [5,1,4,3,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 4 + 1
[1,5,4,3,2] => [5,1,2,3,4] => [5,1,4,3,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 + 1
[2,1,3,4,5] => [4,5,3,2,1] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
=> 1 = 0 + 1
[2,1,3,5,4] => [4,5,3,1,2] => [4,5,3,1,2] => [1,1,1,1,0,1,0,0,0,0]
=> 1 = 0 + 1
[2,1,4,3,5] => [4,5,2,3,1] => [4,5,2,3,1] => [1,1,1,1,0,1,0,0,0,0]
=> 1 = 0 + 1
[2,1,4,5,3] => [4,5,2,1,3] => [4,5,2,1,3] => [1,1,1,1,0,1,0,0,0,0]
=> 1 = 0 + 1
[2,1,5,3,4] => [4,5,1,3,2] => [4,5,1,3,2] => [1,1,1,1,0,1,0,0,0,0]
=> 1 = 0 + 1
[2,1,5,4,3] => [4,5,1,2,3] => [4,5,1,3,2] => [1,1,1,1,0,1,0,0,0,0]
=> 1 = 0 + 1
[2,3,1,4,5] => [4,3,5,2,1] => [4,3,5,2,1] => [1,1,1,1,0,0,1,0,0,0]
=> 1 = 0 + 1
[2,3,1,5,4] => [4,3,5,1,2] => [4,3,5,1,2] => [1,1,1,1,0,0,1,0,0,0]
=> 1 = 0 + 1
[2,3,4,1,5] => [4,3,2,5,1] => [4,3,2,5,1] => [1,1,1,1,0,0,0,1,0,0]
=> 1 = 0 + 1
[2,3,4,5,1] => [4,3,2,1,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
=> 1 = 0 + 1
[2,3,5,1,4] => [4,3,1,5,2] => [4,3,1,5,2] => [1,1,1,1,0,0,0,1,0,0]
=> 1 = 0 + 1
[2,3,5,4,1] => [4,3,1,2,5] => [4,3,1,5,2] => [1,1,1,1,0,0,0,1,0,0]
=> 1 = 0 + 1
[2,4,1,3,5] => [4,2,5,3,1] => [4,2,5,3,1] => [1,1,1,1,0,0,1,0,0,0]
=> 1 = 0 + 1
[2,4,1,5,3] => [4,2,5,1,3] => [4,2,5,1,3] => [1,1,1,1,0,0,1,0,0,0]
=> 1 = 0 + 1
[2,4,3,1,5] => [4,2,3,5,1] => [4,2,5,3,1] => [1,1,1,1,0,0,1,0,0,0]
=> 1 = 0 + 1
[2,4,3,5,1] => [4,2,3,1,5] => [4,2,5,1,3] => [1,1,1,1,0,0,1,0,0,0]
=> 1 = 0 + 1
[2,4,5,1,3] => [4,2,1,5,3] => [4,2,1,5,3] => [1,1,1,1,0,0,0,1,0,0]
=> 1 = 0 + 1
[2,4,5,3,1] => [4,2,1,3,5] => [4,2,1,5,3] => [1,1,1,1,0,0,0,1,0,0]
=> 1 = 0 + 1
[2,5,1,3,4] => [4,1,5,3,2] => [4,1,5,3,2] => [1,1,1,1,0,0,1,0,0,0]
=> 1 = 0 + 1
[2,5,1,4,3] => [4,1,5,2,3] => [4,1,5,3,2] => [1,1,1,1,0,0,1,0,0,0]
=> 1 = 0 + 1
[2,5,3,1,4] => [4,1,3,5,2] => [4,1,5,3,2] => [1,1,1,1,0,0,1,0,0,0]
=> 1 = 0 + 1
[2,5,3,4,1] => [4,1,3,2,5] => [4,1,5,3,2] => [1,1,1,1,0,0,1,0,0,0]
=> 1 = 0 + 1
[2,5,4,1,3] => [4,1,2,5,3] => [4,1,5,3,2] => [1,1,1,1,0,0,1,0,0,0]
=> 1 = 0 + 1
[2,5,4,3,1] => [4,1,2,3,5] => [4,1,5,3,2] => [1,1,1,1,0,0,1,0,0,0]
=> 1 = 0 + 1
[3,1,2,4,5] => [3,5,4,2,1] => [3,5,4,2,1] => [1,1,1,0,1,1,0,0,0,0]
=> 1 = 0 + 1
[3,1,2,5,4] => [3,5,4,1,2] => [3,5,4,1,2] => [1,1,1,0,1,1,0,0,0,0]
=> 1 = 0 + 1
[3,1,4,2,5] => [3,5,2,4,1] => [3,5,2,4,1] => [1,1,1,0,1,1,0,0,0,0]
=> 1 = 0 + 1
[1,2,3,4,5,6] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 32 + 1
[1,2,3,4,6,5] => [6,5,4,3,1,2] => [6,5,4,3,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 16 + 1
[1,2,3,5,4,6] => [6,5,4,2,3,1] => [6,5,4,2,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 16 + 1
[1,2,3,5,6,4] => [6,5,4,2,1,3] => [6,5,4,2,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 8 + 1
[1,2,3,6,4,5] => [6,5,4,1,3,2] => [6,5,4,1,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 16 + 1
[1,2,3,6,5,4] => [6,5,4,1,2,3] => [6,5,4,1,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 8 + 1
[1,2,4,3,5,6] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 16 + 1
[1,2,4,3,6,5] => [6,5,3,4,1,2] => [6,5,3,4,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 8 + 1
[1,2,4,5,3,6] => [6,5,3,2,4,1] => [6,5,3,2,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 8 + 1
[1,2,4,5,6,3] => [6,5,3,2,1,4] => [6,5,3,2,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 4 + 1
[1,2,4,6,3,5] => [6,5,3,1,4,2] => [6,5,3,1,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 8 + 1
[1,2,4,6,5,3] => [6,5,3,1,2,4] => [6,5,3,1,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 4 + 1
[1,2,5,3,4,6] => [6,5,2,4,3,1] => [6,5,2,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 16 + 1
[1,2,5,3,6,4] => [6,5,2,4,1,3] => [6,5,2,4,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 8 + 1
[1,2,5,4,3,6] => [6,5,2,3,4,1] => [6,5,2,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 8 + 1
[1,2,5,4,6,3] => [6,5,2,3,1,4] => [6,5,2,4,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 4 + 1
[1,2,5,6,3,4] => [6,5,2,1,4,3] => [6,5,2,1,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 8 + 1
Description
The dominant dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$.
Matching statistic: St001198
(load all 4 compositions to match this statistic)
(load all 4 compositions to match this statistic)
Mp00069: Permutations —complement⟶ Permutations
Mp00068: Permutations —Simion-Schmidt map⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
St001198: Dyck paths ⟶ ℤResult quality: 14% ●values known / values provided: 60%●distinct values known / distinct values provided: 14%
Mp00068: Permutations —Simion-Schmidt map⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
St001198: Dyck paths ⟶ ℤResult quality: 14% ●values known / values provided: 60%●distinct values known / distinct values provided: 14%
Values
[1,2] => [2,1] => [2,1] => [1,1,0,0]
=> ? = 2 + 2
[2,1] => [1,2] => [1,2] => [1,0,1,0]
=> 2 = 0 + 2
[1,2,3] => [3,2,1] => [3,2,1] => [1,1,1,0,0,0]
=> ? = 4 + 2
[1,3,2] => [3,1,2] => [3,1,2] => [1,1,1,0,0,0]
=> ? = 2 + 2
[2,1,3] => [2,3,1] => [2,3,1] => [1,1,0,1,0,0]
=> 2 = 0 + 2
[2,3,1] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
=> 2 = 0 + 2
[3,1,2] => [1,3,2] => [1,3,2] => [1,0,1,1,0,0]
=> 2 = 0 + 2
[3,2,1] => [1,2,3] => [1,3,2] => [1,0,1,1,0,0]
=> 2 = 0 + 2
[1,2,3,4] => [4,3,2,1] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
=> ? = 8 + 2
[1,2,4,3] => [4,3,1,2] => [4,3,1,2] => [1,1,1,1,0,0,0,0]
=> ? = 4 + 2
[1,3,2,4] => [4,2,3,1] => [4,2,3,1] => [1,1,1,1,0,0,0,0]
=> ? = 4 + 2
[1,3,4,2] => [4,2,1,3] => [4,2,1,3] => [1,1,1,1,0,0,0,0]
=> ? = 2 + 2
[1,4,2,3] => [4,1,3,2] => [4,1,3,2] => [1,1,1,1,0,0,0,0]
=> ? = 4 + 2
[1,4,3,2] => [4,1,2,3] => [4,1,3,2] => [1,1,1,1,0,0,0,0]
=> ? = 2 + 2
[2,1,3,4] => [3,4,2,1] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
=> 2 = 0 + 2
[2,1,4,3] => [3,4,1,2] => [3,4,1,2] => [1,1,1,0,1,0,0,0]
=> 2 = 0 + 2
[2,3,1,4] => [3,2,4,1] => [3,2,4,1] => [1,1,1,0,0,1,0,0]
=> 2 = 0 + 2
[2,3,4,1] => [3,2,1,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
=> 2 = 0 + 2
[2,4,1,3] => [3,1,4,2] => [3,1,4,2] => [1,1,1,0,0,1,0,0]
=> 2 = 0 + 2
[2,4,3,1] => [3,1,2,4] => [3,1,4,2] => [1,1,1,0,0,1,0,0]
=> 2 = 0 + 2
[3,1,2,4] => [2,4,3,1] => [2,4,3,1] => [1,1,0,1,1,0,0,0]
=> 2 = 0 + 2
[3,1,4,2] => [2,4,1,3] => [2,4,1,3] => [1,1,0,1,1,0,0,0]
=> 2 = 0 + 2
[3,2,1,4] => [2,3,4,1] => [2,4,3,1] => [1,1,0,1,1,0,0,0]
=> 2 = 0 + 2
[3,2,4,1] => [2,3,1,4] => [2,4,1,3] => [1,1,0,1,1,0,0,0]
=> 2 = 0 + 2
[3,4,1,2] => [2,1,4,3] => [2,1,4,3] => [1,1,0,0,1,1,0,0]
=> 2 = 0 + 2
[3,4,2,1] => [2,1,3,4] => [2,1,4,3] => [1,1,0,0,1,1,0,0]
=> 2 = 0 + 2
[4,1,2,3] => [1,4,3,2] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
=> 2 = 0 + 2
[4,1,3,2] => [1,4,2,3] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
=> 2 = 0 + 2
[4,2,1,3] => [1,3,4,2] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
=> 2 = 0 + 2
[4,2,3,1] => [1,3,2,4] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
=> 2 = 0 + 2
[4,3,1,2] => [1,2,4,3] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
=> 2 = 0 + 2
[4,3,2,1] => [1,2,3,4] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
=> 2 = 0 + 2
[1,2,3,4,5] => [5,4,3,2,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 16 + 2
[1,2,3,5,4] => [5,4,3,1,2] => [5,4,3,1,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 8 + 2
[1,2,4,3,5] => [5,4,2,3,1] => [5,4,2,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 8 + 2
[1,2,4,5,3] => [5,4,2,1,3] => [5,4,2,1,3] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 4 + 2
[1,2,5,3,4] => [5,4,1,3,2] => [5,4,1,3,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 8 + 2
[1,2,5,4,3] => [5,4,1,2,3] => [5,4,1,3,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 4 + 2
[1,3,2,4,5] => [5,3,4,2,1] => [5,3,4,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 8 + 2
[1,3,2,5,4] => [5,3,4,1,2] => [5,3,4,1,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 4 + 2
[1,3,4,2,5] => [5,3,2,4,1] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 4 + 2
[1,3,4,5,2] => [5,3,2,1,4] => [5,3,2,1,4] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 + 2
[1,3,5,2,4] => [5,3,1,4,2] => [5,3,1,4,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 4 + 2
[1,3,5,4,2] => [5,3,1,2,4] => [5,3,1,4,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 + 2
[1,4,2,3,5] => [5,2,4,3,1] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 8 + 2
[1,4,2,5,3] => [5,2,4,1,3] => [5,2,4,1,3] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 4 + 2
[1,4,3,2,5] => [5,2,3,4,1] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 4 + 2
[1,4,3,5,2] => [5,2,3,1,4] => [5,2,4,1,3] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 + 2
[1,4,5,2,3] => [5,2,1,4,3] => [5,2,1,4,3] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 4 + 2
[1,4,5,3,2] => [5,2,1,3,4] => [5,2,1,4,3] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 + 2
[1,5,2,3,4] => [5,1,4,3,2] => [5,1,4,3,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 8 + 2
[1,5,2,4,3] => [5,1,4,2,3] => [5,1,4,3,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 4 + 2
[1,5,3,2,4] => [5,1,3,4,2] => [5,1,4,3,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 4 + 2
[1,5,3,4,2] => [5,1,3,2,4] => [5,1,4,3,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 + 2
[1,5,4,2,3] => [5,1,2,4,3] => [5,1,4,3,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 4 + 2
[1,5,4,3,2] => [5,1,2,3,4] => [5,1,4,3,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 + 2
[2,1,3,4,5] => [4,5,3,2,1] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
=> 2 = 0 + 2
[2,1,3,5,4] => [4,5,3,1,2] => [4,5,3,1,2] => [1,1,1,1,0,1,0,0,0,0]
=> 2 = 0 + 2
[2,1,4,3,5] => [4,5,2,3,1] => [4,5,2,3,1] => [1,1,1,1,0,1,0,0,0,0]
=> 2 = 0 + 2
[2,1,4,5,3] => [4,5,2,1,3] => [4,5,2,1,3] => [1,1,1,1,0,1,0,0,0,0]
=> 2 = 0 + 2
[2,1,5,3,4] => [4,5,1,3,2] => [4,5,1,3,2] => [1,1,1,1,0,1,0,0,0,0]
=> 2 = 0 + 2
[2,1,5,4,3] => [4,5,1,2,3] => [4,5,1,3,2] => [1,1,1,1,0,1,0,0,0,0]
=> 2 = 0 + 2
[2,3,1,4,5] => [4,3,5,2,1] => [4,3,5,2,1] => [1,1,1,1,0,0,1,0,0,0]
=> 2 = 0 + 2
[2,3,1,5,4] => [4,3,5,1,2] => [4,3,5,1,2] => [1,1,1,1,0,0,1,0,0,0]
=> 2 = 0 + 2
[2,3,4,1,5] => [4,3,2,5,1] => [4,3,2,5,1] => [1,1,1,1,0,0,0,1,0,0]
=> 2 = 0 + 2
[2,3,4,5,1] => [4,3,2,1,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
=> 2 = 0 + 2
[2,3,5,1,4] => [4,3,1,5,2] => [4,3,1,5,2] => [1,1,1,1,0,0,0,1,0,0]
=> 2 = 0 + 2
[2,3,5,4,1] => [4,3,1,2,5] => [4,3,1,5,2] => [1,1,1,1,0,0,0,1,0,0]
=> 2 = 0 + 2
[2,4,1,3,5] => [4,2,5,3,1] => [4,2,5,3,1] => [1,1,1,1,0,0,1,0,0,0]
=> 2 = 0 + 2
[2,4,1,5,3] => [4,2,5,1,3] => [4,2,5,1,3] => [1,1,1,1,0,0,1,0,0,0]
=> 2 = 0 + 2
[2,4,3,1,5] => [4,2,3,5,1] => [4,2,5,3,1] => [1,1,1,1,0,0,1,0,0,0]
=> 2 = 0 + 2
[2,4,3,5,1] => [4,2,3,1,5] => [4,2,5,1,3] => [1,1,1,1,0,0,1,0,0,0]
=> 2 = 0 + 2
[2,4,5,1,3] => [4,2,1,5,3] => [4,2,1,5,3] => [1,1,1,1,0,0,0,1,0,0]
=> 2 = 0 + 2
[2,4,5,3,1] => [4,2,1,3,5] => [4,2,1,5,3] => [1,1,1,1,0,0,0,1,0,0]
=> 2 = 0 + 2
[2,5,1,3,4] => [4,1,5,3,2] => [4,1,5,3,2] => [1,1,1,1,0,0,1,0,0,0]
=> 2 = 0 + 2
[2,5,1,4,3] => [4,1,5,2,3] => [4,1,5,3,2] => [1,1,1,1,0,0,1,0,0,0]
=> 2 = 0 + 2
[2,5,3,1,4] => [4,1,3,5,2] => [4,1,5,3,2] => [1,1,1,1,0,0,1,0,0,0]
=> 2 = 0 + 2
[2,5,3,4,1] => [4,1,3,2,5] => [4,1,5,3,2] => [1,1,1,1,0,0,1,0,0,0]
=> 2 = 0 + 2
[2,5,4,1,3] => [4,1,2,5,3] => [4,1,5,3,2] => [1,1,1,1,0,0,1,0,0,0]
=> 2 = 0 + 2
[2,5,4,3,1] => [4,1,2,3,5] => [4,1,5,3,2] => [1,1,1,1,0,0,1,0,0,0]
=> 2 = 0 + 2
[3,1,2,4,5] => [3,5,4,2,1] => [3,5,4,2,1] => [1,1,1,0,1,1,0,0,0,0]
=> 2 = 0 + 2
[3,1,2,5,4] => [3,5,4,1,2] => [3,5,4,1,2] => [1,1,1,0,1,1,0,0,0,0]
=> 2 = 0 + 2
[3,1,4,2,5] => [3,5,2,4,1] => [3,5,2,4,1] => [1,1,1,0,1,1,0,0,0,0]
=> 2 = 0 + 2
[1,2,3,4,5,6] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 32 + 2
[1,2,3,4,6,5] => [6,5,4,3,1,2] => [6,5,4,3,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 16 + 2
[1,2,3,5,4,6] => [6,5,4,2,3,1] => [6,5,4,2,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 16 + 2
[1,2,3,5,6,4] => [6,5,4,2,1,3] => [6,5,4,2,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 8 + 2
[1,2,3,6,4,5] => [6,5,4,1,3,2] => [6,5,4,1,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 16 + 2
[1,2,3,6,5,4] => [6,5,4,1,2,3] => [6,5,4,1,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 8 + 2
[1,2,4,3,5,6] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 16 + 2
[1,2,4,3,6,5] => [6,5,3,4,1,2] => [6,5,3,4,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 8 + 2
[1,2,4,5,3,6] => [6,5,3,2,4,1] => [6,5,3,2,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 8 + 2
[1,2,4,5,6,3] => [6,5,3,2,1,4] => [6,5,3,2,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 4 + 2
[1,2,4,6,3,5] => [6,5,3,1,4,2] => [6,5,3,1,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 8 + 2
[1,2,4,6,5,3] => [6,5,3,1,2,4] => [6,5,3,1,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 4 + 2
[1,2,5,3,4,6] => [6,5,2,4,3,1] => [6,5,2,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 16 + 2
[1,2,5,3,6,4] => [6,5,2,4,1,3] => [6,5,2,4,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 8 + 2
[1,2,5,4,3,6] => [6,5,2,3,4,1] => [6,5,2,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 8 + 2
[1,2,5,4,6,3] => [6,5,2,3,1,4] => [6,5,2,4,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 4 + 2
[1,2,5,6,3,4] => [6,5,2,1,4,3] => [6,5,2,1,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 8 + 2
Description
The 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 $eA$.
Matching statistic: St001206
(load all 4 compositions to match this statistic)
(load all 4 compositions to match this statistic)
Mp00069: Permutations —complement⟶ Permutations
Mp00068: Permutations —Simion-Schmidt map⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
St001206: Dyck paths ⟶ ℤResult quality: 14% ●values known / values provided: 60%●distinct values known / distinct values provided: 14%
Mp00068: Permutations —Simion-Schmidt map⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
St001206: Dyck paths ⟶ ℤResult quality: 14% ●values known / values provided: 60%●distinct values known / distinct values provided: 14%
Values
[1,2] => [2,1] => [2,1] => [1,1,0,0]
=> ? = 2 + 2
[2,1] => [1,2] => [1,2] => [1,0,1,0]
=> 2 = 0 + 2
[1,2,3] => [3,2,1] => [3,2,1] => [1,1,1,0,0,0]
=> ? = 4 + 2
[1,3,2] => [3,1,2] => [3,1,2] => [1,1,1,0,0,0]
=> ? = 2 + 2
[2,1,3] => [2,3,1] => [2,3,1] => [1,1,0,1,0,0]
=> 2 = 0 + 2
[2,3,1] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
=> 2 = 0 + 2
[3,1,2] => [1,3,2] => [1,3,2] => [1,0,1,1,0,0]
=> 2 = 0 + 2
[3,2,1] => [1,2,3] => [1,3,2] => [1,0,1,1,0,0]
=> 2 = 0 + 2
[1,2,3,4] => [4,3,2,1] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
=> ? = 8 + 2
[1,2,4,3] => [4,3,1,2] => [4,3,1,2] => [1,1,1,1,0,0,0,0]
=> ? = 4 + 2
[1,3,2,4] => [4,2,3,1] => [4,2,3,1] => [1,1,1,1,0,0,0,0]
=> ? = 4 + 2
[1,3,4,2] => [4,2,1,3] => [4,2,1,3] => [1,1,1,1,0,0,0,0]
=> ? = 2 + 2
[1,4,2,3] => [4,1,3,2] => [4,1,3,2] => [1,1,1,1,0,0,0,0]
=> ? = 4 + 2
[1,4,3,2] => [4,1,2,3] => [4,1,3,2] => [1,1,1,1,0,0,0,0]
=> ? = 2 + 2
[2,1,3,4] => [3,4,2,1] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
=> 2 = 0 + 2
[2,1,4,3] => [3,4,1,2] => [3,4,1,2] => [1,1,1,0,1,0,0,0]
=> 2 = 0 + 2
[2,3,1,4] => [3,2,4,1] => [3,2,4,1] => [1,1,1,0,0,1,0,0]
=> 2 = 0 + 2
[2,3,4,1] => [3,2,1,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
=> 2 = 0 + 2
[2,4,1,3] => [3,1,4,2] => [3,1,4,2] => [1,1,1,0,0,1,0,0]
=> 2 = 0 + 2
[2,4,3,1] => [3,1,2,4] => [3,1,4,2] => [1,1,1,0,0,1,0,0]
=> 2 = 0 + 2
[3,1,2,4] => [2,4,3,1] => [2,4,3,1] => [1,1,0,1,1,0,0,0]
=> 2 = 0 + 2
[3,1,4,2] => [2,4,1,3] => [2,4,1,3] => [1,1,0,1,1,0,0,0]
=> 2 = 0 + 2
[3,2,1,4] => [2,3,4,1] => [2,4,3,1] => [1,1,0,1,1,0,0,0]
=> 2 = 0 + 2
[3,2,4,1] => [2,3,1,4] => [2,4,1,3] => [1,1,0,1,1,0,0,0]
=> 2 = 0 + 2
[3,4,1,2] => [2,1,4,3] => [2,1,4,3] => [1,1,0,0,1,1,0,0]
=> 2 = 0 + 2
[3,4,2,1] => [2,1,3,4] => [2,1,4,3] => [1,1,0,0,1,1,0,0]
=> 2 = 0 + 2
[4,1,2,3] => [1,4,3,2] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
=> 2 = 0 + 2
[4,1,3,2] => [1,4,2,3] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
=> 2 = 0 + 2
[4,2,1,3] => [1,3,4,2] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
=> 2 = 0 + 2
[4,2,3,1] => [1,3,2,4] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
=> 2 = 0 + 2
[4,3,1,2] => [1,2,4,3] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
=> 2 = 0 + 2
[4,3,2,1] => [1,2,3,4] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
=> 2 = 0 + 2
[1,2,3,4,5] => [5,4,3,2,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 16 + 2
[1,2,3,5,4] => [5,4,3,1,2] => [5,4,3,1,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 8 + 2
[1,2,4,3,5] => [5,4,2,3,1] => [5,4,2,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 8 + 2
[1,2,4,5,3] => [5,4,2,1,3] => [5,4,2,1,3] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 4 + 2
[1,2,5,3,4] => [5,4,1,3,2] => [5,4,1,3,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 8 + 2
[1,2,5,4,3] => [5,4,1,2,3] => [5,4,1,3,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 4 + 2
[1,3,2,4,5] => [5,3,4,2,1] => [5,3,4,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 8 + 2
[1,3,2,5,4] => [5,3,4,1,2] => [5,3,4,1,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 4 + 2
[1,3,4,2,5] => [5,3,2,4,1] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 4 + 2
[1,3,4,5,2] => [5,3,2,1,4] => [5,3,2,1,4] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 + 2
[1,3,5,2,4] => [5,3,1,4,2] => [5,3,1,4,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 4 + 2
[1,3,5,4,2] => [5,3,1,2,4] => [5,3,1,4,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 + 2
[1,4,2,3,5] => [5,2,4,3,1] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 8 + 2
[1,4,2,5,3] => [5,2,4,1,3] => [5,2,4,1,3] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 4 + 2
[1,4,3,2,5] => [5,2,3,4,1] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 4 + 2
[1,4,3,5,2] => [5,2,3,1,4] => [5,2,4,1,3] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 + 2
[1,4,5,2,3] => [5,2,1,4,3] => [5,2,1,4,3] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 4 + 2
[1,4,5,3,2] => [5,2,1,3,4] => [5,2,1,4,3] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 + 2
[1,5,2,3,4] => [5,1,4,3,2] => [5,1,4,3,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 8 + 2
[1,5,2,4,3] => [5,1,4,2,3] => [5,1,4,3,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 4 + 2
[1,5,3,2,4] => [5,1,3,4,2] => [5,1,4,3,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 4 + 2
[1,5,3,4,2] => [5,1,3,2,4] => [5,1,4,3,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 + 2
[1,5,4,2,3] => [5,1,2,4,3] => [5,1,4,3,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 4 + 2
[1,5,4,3,2] => [5,1,2,3,4] => [5,1,4,3,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 + 2
[2,1,3,4,5] => [4,5,3,2,1] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
=> 2 = 0 + 2
[2,1,3,5,4] => [4,5,3,1,2] => [4,5,3,1,2] => [1,1,1,1,0,1,0,0,0,0]
=> 2 = 0 + 2
[2,1,4,3,5] => [4,5,2,3,1] => [4,5,2,3,1] => [1,1,1,1,0,1,0,0,0,0]
=> 2 = 0 + 2
[2,1,4,5,3] => [4,5,2,1,3] => [4,5,2,1,3] => [1,1,1,1,0,1,0,0,0,0]
=> 2 = 0 + 2
[2,1,5,3,4] => [4,5,1,3,2] => [4,5,1,3,2] => [1,1,1,1,0,1,0,0,0,0]
=> 2 = 0 + 2
[2,1,5,4,3] => [4,5,1,2,3] => [4,5,1,3,2] => [1,1,1,1,0,1,0,0,0,0]
=> 2 = 0 + 2
[2,3,1,4,5] => [4,3,5,2,1] => [4,3,5,2,1] => [1,1,1,1,0,0,1,0,0,0]
=> 2 = 0 + 2
[2,3,1,5,4] => [4,3,5,1,2] => [4,3,5,1,2] => [1,1,1,1,0,0,1,0,0,0]
=> 2 = 0 + 2
[2,3,4,1,5] => [4,3,2,5,1] => [4,3,2,5,1] => [1,1,1,1,0,0,0,1,0,0]
=> 2 = 0 + 2
[2,3,4,5,1] => [4,3,2,1,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
=> 2 = 0 + 2
[2,3,5,1,4] => [4,3,1,5,2] => [4,3,1,5,2] => [1,1,1,1,0,0,0,1,0,0]
=> 2 = 0 + 2
[2,3,5,4,1] => [4,3,1,2,5] => [4,3,1,5,2] => [1,1,1,1,0,0,0,1,0,0]
=> 2 = 0 + 2
[2,4,1,3,5] => [4,2,5,3,1] => [4,2,5,3,1] => [1,1,1,1,0,0,1,0,0,0]
=> 2 = 0 + 2
[2,4,1,5,3] => [4,2,5,1,3] => [4,2,5,1,3] => [1,1,1,1,0,0,1,0,0,0]
=> 2 = 0 + 2
[2,4,3,1,5] => [4,2,3,5,1] => [4,2,5,3,1] => [1,1,1,1,0,0,1,0,0,0]
=> 2 = 0 + 2
[2,4,3,5,1] => [4,2,3,1,5] => [4,2,5,1,3] => [1,1,1,1,0,0,1,0,0,0]
=> 2 = 0 + 2
[2,4,5,1,3] => [4,2,1,5,3] => [4,2,1,5,3] => [1,1,1,1,0,0,0,1,0,0]
=> 2 = 0 + 2
[2,4,5,3,1] => [4,2,1,3,5] => [4,2,1,5,3] => [1,1,1,1,0,0,0,1,0,0]
=> 2 = 0 + 2
[2,5,1,3,4] => [4,1,5,3,2] => [4,1,5,3,2] => [1,1,1,1,0,0,1,0,0,0]
=> 2 = 0 + 2
[2,5,1,4,3] => [4,1,5,2,3] => [4,1,5,3,2] => [1,1,1,1,0,0,1,0,0,0]
=> 2 = 0 + 2
[2,5,3,1,4] => [4,1,3,5,2] => [4,1,5,3,2] => [1,1,1,1,0,0,1,0,0,0]
=> 2 = 0 + 2
[2,5,3,4,1] => [4,1,3,2,5] => [4,1,5,3,2] => [1,1,1,1,0,0,1,0,0,0]
=> 2 = 0 + 2
[2,5,4,1,3] => [4,1,2,5,3] => [4,1,5,3,2] => [1,1,1,1,0,0,1,0,0,0]
=> 2 = 0 + 2
[2,5,4,3,1] => [4,1,2,3,5] => [4,1,5,3,2] => [1,1,1,1,0,0,1,0,0,0]
=> 2 = 0 + 2
[3,1,2,4,5] => [3,5,4,2,1] => [3,5,4,2,1] => [1,1,1,0,1,1,0,0,0,0]
=> 2 = 0 + 2
[3,1,2,5,4] => [3,5,4,1,2] => [3,5,4,1,2] => [1,1,1,0,1,1,0,0,0,0]
=> 2 = 0 + 2
[3,1,4,2,5] => [3,5,2,4,1] => [3,5,2,4,1] => [1,1,1,0,1,1,0,0,0,0]
=> 2 = 0 + 2
[1,2,3,4,5,6] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 32 + 2
[1,2,3,4,6,5] => [6,5,4,3,1,2] => [6,5,4,3,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 16 + 2
[1,2,3,5,4,6] => [6,5,4,2,3,1] => [6,5,4,2,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 16 + 2
[1,2,3,5,6,4] => [6,5,4,2,1,3] => [6,5,4,2,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 8 + 2
[1,2,3,6,4,5] => [6,5,4,1,3,2] => [6,5,4,1,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 16 + 2
[1,2,3,6,5,4] => [6,5,4,1,2,3] => [6,5,4,1,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 8 + 2
[1,2,4,3,5,6] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 16 + 2
[1,2,4,3,6,5] => [6,5,3,4,1,2] => [6,5,3,4,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 8 + 2
[1,2,4,5,3,6] => [6,5,3,2,4,1] => [6,5,3,2,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 8 + 2
[1,2,4,5,6,3] => [6,5,3,2,1,4] => [6,5,3,2,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 4 + 2
[1,2,4,6,3,5] => [6,5,3,1,4,2] => [6,5,3,1,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 8 + 2
[1,2,4,6,5,3] => [6,5,3,1,2,4] => [6,5,3,1,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 4 + 2
[1,2,5,3,4,6] => [6,5,2,4,3,1] => [6,5,2,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 16 + 2
[1,2,5,3,6,4] => [6,5,2,4,1,3] => [6,5,2,4,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 8 + 2
[1,2,5,4,3,6] => [6,5,2,3,4,1] => [6,5,2,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 8 + 2
[1,2,5,4,6,3] => [6,5,2,3,1,4] => [6,5,2,4,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 4 + 2
[1,2,5,6,3,4] => [6,5,2,1,4,3] => [6,5,2,1,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 8 + 2
Description
The 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 $eA$.
Matching statistic: St000260
(load all 9 compositions to match this statistic)
(load all 9 compositions to match this statistic)
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00023: Dyck paths —to non-crossing permutation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000260: Graphs ⟶ ℤResult quality: 14% ●values known / values provided: 46%●distinct values known / distinct values provided: 14%
Mp00023: Dyck paths —to non-crossing permutation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000260: Graphs ⟶ ℤResult quality: 14% ●values known / values provided: 46%●distinct values known / distinct values provided: 14%
Values
[1,2] => [1,0,1,0]
=> [1,2] => ([],2)
=> ? = 2 + 1
[2,1] => [1,1,0,0]
=> [2,1] => ([(0,1)],2)
=> 1 = 0 + 1
[1,2,3] => [1,0,1,0,1,0]
=> [1,2,3] => ([],3)
=> ? = 4 + 1
[1,3,2] => [1,0,1,1,0,0]
=> [1,3,2] => ([(1,2)],3)
=> ? = 2 + 1
[2,1,3] => [1,1,0,0,1,0]
=> [2,1,3] => ([(1,2)],3)
=> ? = 0 + 1
[2,3,1] => [1,1,0,1,0,0]
=> [2,3,1] => ([(0,2),(1,2)],3)
=> 1 = 0 + 1
[3,1,2] => [1,1,1,0,0,0]
=> [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> 1 = 0 + 1
[3,2,1] => [1,1,1,0,0,0]
=> [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> 1 = 0 + 1
[1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [1,2,3,4] => ([],4)
=> ? = 8 + 1
[1,2,4,3] => [1,0,1,0,1,1,0,0]
=> [1,2,4,3] => ([(2,3)],4)
=> ? = 4 + 1
[1,3,2,4] => [1,0,1,1,0,0,1,0]
=> [1,3,2,4] => ([(2,3)],4)
=> ? = 4 + 1
[1,3,4,2] => [1,0,1,1,0,1,0,0]
=> [1,3,4,2] => ([(1,3),(2,3)],4)
=> ? = 2 + 1
[1,4,2,3] => [1,0,1,1,1,0,0,0]
=> [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ? = 4 + 1
[1,4,3,2] => [1,0,1,1,1,0,0,0]
=> [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ? = 2 + 1
[2,1,3,4] => [1,1,0,0,1,0,1,0]
=> [2,1,3,4] => ([(2,3)],4)
=> ? = 0 + 1
[2,1,4,3] => [1,1,0,0,1,1,0,0]
=> [2,1,4,3] => ([(0,3),(1,2)],4)
=> ? = 0 + 1
[2,3,1,4] => [1,1,0,1,0,0,1,0]
=> [2,3,1,4] => ([(1,3),(2,3)],4)
=> ? = 0 + 1
[2,3,4,1] => [1,1,0,1,0,1,0,0]
=> [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
=> 1 = 0 + 1
[2,4,1,3] => [1,1,0,1,1,0,0,0]
=> [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 1 = 0 + 1
[2,4,3,1] => [1,1,0,1,1,0,0,0]
=> [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 1 = 0 + 1
[3,1,2,4] => [1,1,1,0,0,0,1,0]
=> [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ? = 0 + 1
[3,1,4,2] => [1,1,1,0,0,1,0,0]
=> [3,2,4,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 1 = 0 + 1
[3,2,1,4] => [1,1,1,0,0,0,1,0]
=> [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ? = 0 + 1
[3,2,4,1] => [1,1,1,0,0,1,0,0]
=> [3,2,4,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 1 = 0 + 1
[3,4,1,2] => [1,1,1,0,1,0,0,0]
=> [4,2,3,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 1 = 0 + 1
[3,4,2,1] => [1,1,1,0,1,0,0,0]
=> [4,2,3,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 1 = 0 + 1
[4,1,2,3] => [1,1,1,1,0,0,0,0]
=> [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 1 = 0 + 1
[4,1,3,2] => [1,1,1,1,0,0,0,0]
=> [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 1 = 0 + 1
[4,2,1,3] => [1,1,1,1,0,0,0,0]
=> [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 1 = 0 + 1
[4,2,3,1] => [1,1,1,1,0,0,0,0]
=> [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 1 = 0 + 1
[4,3,1,2] => [1,1,1,1,0,0,0,0]
=> [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 1 = 0 + 1
[4,3,2,1] => [1,1,1,1,0,0,0,0]
=> [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 1 = 0 + 1
[1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
=> [1,2,3,4,5] => ([],5)
=> ? = 16 + 1
[1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0]
=> [1,2,3,5,4] => ([(3,4)],5)
=> ? = 8 + 1
[1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0]
=> [1,2,4,3,5] => ([(3,4)],5)
=> ? = 8 + 1
[1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0]
=> [1,2,4,5,3] => ([(2,4),(3,4)],5)
=> ? = 4 + 1
[1,2,5,3,4] => [1,0,1,0,1,1,1,0,0,0]
=> [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
=> ? = 8 + 1
[1,2,5,4,3] => [1,0,1,0,1,1,1,0,0,0]
=> [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
=> ? = 4 + 1
[1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0]
=> [1,3,2,4,5] => ([(3,4)],5)
=> ? = 8 + 1
[1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0]
=> [1,3,2,5,4] => ([(1,4),(2,3)],5)
=> ? = 4 + 1
[1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0]
=> [1,3,4,2,5] => ([(2,4),(3,4)],5)
=> ? = 4 + 1
[1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0]
=> [1,3,4,5,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 2 + 1
[1,3,5,2,4] => [1,0,1,1,0,1,1,0,0,0]
=> [1,3,5,4,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 + 1
[1,3,5,4,2] => [1,0,1,1,0,1,1,0,0,0]
=> [1,3,5,4,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 2 + 1
[1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0]
=> [1,4,3,2,5] => ([(2,3),(2,4),(3,4)],5)
=> ? = 8 + 1
[1,4,2,5,3] => [1,0,1,1,1,0,0,1,0,0]
=> [1,4,3,5,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 + 1
[1,4,3,2,5] => [1,0,1,1,1,0,0,0,1,0]
=> [1,4,3,2,5] => ([(2,3),(2,4),(3,4)],5)
=> ? = 4 + 1
[1,4,3,5,2] => [1,0,1,1,1,0,0,1,0,0]
=> [1,4,3,5,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 2 + 1
[1,4,5,2,3] => [1,0,1,1,1,0,1,0,0,0]
=> [1,5,3,4,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 + 1
[1,4,5,3,2] => [1,0,1,1,1,0,1,0,0,0]
=> [1,5,3,4,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 2 + 1
[1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0]
=> [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 8 + 1
[1,5,2,4,3] => [1,0,1,1,1,1,0,0,0,0]
=> [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 + 1
[1,5,3,2,4] => [1,0,1,1,1,1,0,0,0,0]
=> [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 + 1
[1,5,3,4,2] => [1,0,1,1,1,1,0,0,0,0]
=> [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 2 + 1
[1,5,4,2,3] => [1,0,1,1,1,1,0,0,0,0]
=> [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 + 1
[1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0]
=> [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 2 + 1
[2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
=> [2,1,3,4,5] => ([(3,4)],5)
=> ? = 0 + 1
[2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0]
=> [2,1,3,5,4] => ([(1,4),(2,3)],5)
=> ? = 0 + 1
[2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0]
=> [2,1,4,3,5] => ([(1,4),(2,3)],5)
=> ? = 0 + 1
[2,1,4,5,3] => [1,1,0,0,1,1,0,1,0,0]
=> [2,1,4,5,3] => ([(0,1),(2,4),(3,4)],5)
=> ? = 0 + 1
[2,1,5,3,4] => [1,1,0,0,1,1,1,0,0,0]
=> [2,1,5,4,3] => ([(0,1),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 1
[2,1,5,4,3] => [1,1,0,0,1,1,1,0,0,0]
=> [2,1,5,4,3] => ([(0,1),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 1
[2,3,1,4,5] => [1,1,0,1,0,0,1,0,1,0]
=> [2,3,1,4,5] => ([(2,4),(3,4)],5)
=> ? = 0 + 1
[2,3,1,5,4] => [1,1,0,1,0,0,1,1,0,0]
=> [2,3,1,5,4] => ([(0,1),(2,4),(3,4)],5)
=> ? = 0 + 1
[2,3,4,1,5] => [1,1,0,1,0,1,0,0,1,0]
=> [2,3,4,1,5] => ([(1,4),(2,4),(3,4)],5)
=> ? = 0 + 1
[2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0]
=> [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 0 + 1
[2,3,5,1,4] => [1,1,0,1,0,1,1,0,0,0]
=> [2,3,5,4,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 1 = 0 + 1
[2,3,5,4,1] => [1,1,0,1,0,1,1,0,0,0]
=> [2,3,5,4,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 1 = 0 + 1
[2,4,1,3,5] => [1,1,0,1,1,0,0,0,1,0]
=> [2,4,3,1,5] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 1
[2,4,1,5,3] => [1,1,0,1,1,0,0,1,0,0]
=> [2,4,3,5,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 1 = 0 + 1
[2,4,3,1,5] => [1,1,0,1,1,0,0,0,1,0]
=> [2,4,3,1,5] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 1
[2,4,3,5,1] => [1,1,0,1,1,0,0,1,0,0]
=> [2,4,3,5,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 1 = 0 + 1
[2,4,5,1,3] => [1,1,0,1,1,0,1,0,0,0]
=> [2,5,3,4,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1 = 0 + 1
[2,4,5,3,1] => [1,1,0,1,1,0,1,0,0,0]
=> [2,5,3,4,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1 = 0 + 1
[2,5,1,3,4] => [1,1,0,1,1,1,0,0,0,0]
=> [2,5,4,3,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1 = 0 + 1
[2,5,1,4,3] => [1,1,0,1,1,1,0,0,0,0]
=> [2,5,4,3,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1 = 0 + 1
[2,5,3,1,4] => [1,1,0,1,1,1,0,0,0,0]
=> [2,5,4,3,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1 = 0 + 1
[2,5,3,4,1] => [1,1,0,1,1,1,0,0,0,0]
=> [2,5,4,3,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1 = 0 + 1
[2,5,4,1,3] => [1,1,0,1,1,1,0,0,0,0]
=> [2,5,4,3,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1 = 0 + 1
[2,5,4,3,1] => [1,1,0,1,1,1,0,0,0,0]
=> [2,5,4,3,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1 = 0 + 1
[3,1,4,5,2] => [1,1,1,0,0,1,0,1,0,0]
=> [3,2,4,5,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 1 = 0 + 1
[3,1,5,2,4] => [1,1,1,0,0,1,1,0,0,0]
=> [3,2,5,4,1] => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> 1 = 0 + 1
[3,1,5,4,2] => [1,1,1,0,0,1,1,0,0,0]
=> [3,2,5,4,1] => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> 1 = 0 + 1
[3,2,4,5,1] => [1,1,1,0,0,1,0,1,0,0]
=> [3,2,4,5,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 1 = 0 + 1
[3,2,5,1,4] => [1,1,1,0,0,1,1,0,0,0]
=> [3,2,5,4,1] => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> 1 = 0 + 1
[3,2,5,4,1] => [1,1,1,0,0,1,1,0,0,0]
=> [3,2,5,4,1] => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> 1 = 0 + 1
[3,4,1,5,2] => [1,1,1,0,1,0,0,1,0,0]
=> [4,2,3,5,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1 = 0 + 1
[3,4,2,5,1] => [1,1,1,0,1,0,0,1,0,0]
=> [4,2,3,5,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1 = 0 + 1
[3,4,5,1,2] => [1,1,1,0,1,0,1,0,0,0]
=> [5,2,3,4,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1 = 0 + 1
[3,4,5,2,1] => [1,1,1,0,1,0,1,0,0,0]
=> [5,2,3,4,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1 = 0 + 1
[3,5,1,2,4] => [1,1,1,0,1,1,0,0,0,0]
=> [5,2,4,3,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1 = 0 + 1
[3,5,1,4,2] => [1,1,1,0,1,1,0,0,0,0]
=> [5,2,4,3,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1 = 0 + 1
[3,5,2,1,4] => [1,1,1,0,1,1,0,0,0,0]
=> [5,2,4,3,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1 = 0 + 1
[3,5,2,4,1] => [1,1,1,0,1,1,0,0,0,0]
=> [5,2,4,3,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1 = 0 + 1
[3,5,4,1,2] => [1,1,1,0,1,1,0,0,0,0]
=> [5,2,4,3,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1 = 0 + 1
[3,5,4,2,1] => [1,1,1,0,1,1,0,0,0,0]
=> [5,2,4,3,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1 = 0 + 1
[4,1,2,5,3] => [1,1,1,1,0,0,0,1,0,0]
=> [4,3,2,5,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1 = 0 + 1
[4,1,3,5,2] => [1,1,1,1,0,0,0,1,0,0]
=> [4,3,2,5,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1 = 0 + 1
[4,1,5,2,3] => [1,1,1,1,0,0,1,0,0,0]
=> [5,3,2,4,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1 = 0 + 1
[4,1,5,3,2] => [1,1,1,1,0,0,1,0,0,0]
=> [5,3,2,4,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1 = 0 + 1
Description
The radius of a connected graph.
This is the minimum eccentricity of any vertex.
Matching statistic: St000264
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00068: Permutations —Simion-Schmidt map⟶ Permutations
Mp00064: Permutations —reverse⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000264: Graphs ⟶ ℤResult quality: 14% ●values known / values provided: 26%●distinct values known / distinct values provided: 14%
Mp00064: Permutations —reverse⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000264: Graphs ⟶ ℤResult quality: 14% ●values known / values provided: 26%●distinct values known / distinct values provided: 14%
Values
[1,2] => [1,2] => [2,1] => ([(0,1)],2)
=> ? = 2 + 4
[2,1] => [2,1] => [1,2] => ([],2)
=> ? = 0 + 4
[1,2,3] => [1,3,2] => [2,3,1] => ([(0,2),(1,2)],3)
=> ? = 4 + 4
[1,3,2] => [1,3,2] => [2,3,1] => ([(0,2),(1,2)],3)
=> ? = 2 + 4
[2,1,3] => [2,1,3] => [3,1,2] => ([(0,2),(1,2)],3)
=> ? = 0 + 4
[2,3,1] => [2,3,1] => [1,3,2] => ([(1,2)],3)
=> ? = 0 + 4
[3,1,2] => [3,1,2] => [2,1,3] => ([(1,2)],3)
=> ? = 0 + 4
[3,2,1] => [3,2,1] => [1,2,3] => ([],3)
=> ? = 0 + 4
[1,2,3,4] => [1,4,3,2] => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
=> ? = 8 + 4
[1,2,4,3] => [1,4,3,2] => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
=> ? = 4 + 4
[1,3,2,4] => [1,4,3,2] => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
=> ? = 4 + 4
[1,3,4,2] => [1,4,3,2] => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
=> ? = 2 + 4
[1,4,2,3] => [1,4,3,2] => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
=> ? = 4 + 4
[1,4,3,2] => [1,4,3,2] => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
=> ? = 2 + 4
[2,1,3,4] => [2,1,4,3] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> 4 = 0 + 4
[2,1,4,3] => [2,1,4,3] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> 4 = 0 + 4
[2,3,1,4] => [2,4,1,3] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
=> ? = 0 + 4
[2,3,4,1] => [2,4,3,1] => [1,3,4,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 4
[2,4,1,3] => [2,4,1,3] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
=> ? = 0 + 4
[2,4,3,1] => [2,4,3,1] => [1,3,4,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 4
[3,1,2,4] => [3,1,4,2] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
=> ? = 0 + 4
[3,1,4,2] => [3,1,4,2] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
=> ? = 0 + 4
[3,2,1,4] => [3,2,1,4] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4)
=> ? = 0 + 4
[3,2,4,1] => [3,2,4,1] => [1,4,2,3] => ([(1,3),(2,3)],4)
=> ? = 0 + 4
[3,4,1,2] => [3,4,1,2] => [2,1,4,3] => ([(0,3),(1,2)],4)
=> ? = 0 + 4
[3,4,2,1] => [3,4,2,1] => [1,2,4,3] => ([(2,3)],4)
=> ? = 0 + 4
[4,1,2,3] => [4,1,3,2] => [2,3,1,4] => ([(1,3),(2,3)],4)
=> ? = 0 + 4
[4,1,3,2] => [4,1,3,2] => [2,3,1,4] => ([(1,3),(2,3)],4)
=> ? = 0 + 4
[4,2,1,3] => [4,2,1,3] => [3,1,2,4] => ([(1,3),(2,3)],4)
=> ? = 0 + 4
[4,2,3,1] => [4,2,3,1] => [1,3,2,4] => ([(2,3)],4)
=> ? = 0 + 4
[4,3,1,2] => [4,3,1,2] => [2,1,3,4] => ([(2,3)],4)
=> ? = 0 + 4
[4,3,2,1] => [4,3,2,1] => [1,2,3,4] => ([],4)
=> ? = 0 + 4
[1,2,3,4,5] => [1,5,4,3,2] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? = 16 + 4
[1,2,3,5,4] => [1,5,4,3,2] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? = 8 + 4
[1,2,4,3,5] => [1,5,4,3,2] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? = 8 + 4
[1,2,4,5,3] => [1,5,4,3,2] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? = 4 + 4
[1,2,5,3,4] => [1,5,4,3,2] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? = 8 + 4
[1,2,5,4,3] => [1,5,4,3,2] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? = 4 + 4
[1,3,2,4,5] => [1,5,4,3,2] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? = 8 + 4
[1,3,2,5,4] => [1,5,4,3,2] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? = 4 + 4
[1,3,4,2,5] => [1,5,4,3,2] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? = 4 + 4
[1,3,4,5,2] => [1,5,4,3,2] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? = 2 + 4
[1,3,5,2,4] => [1,5,4,3,2] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? = 4 + 4
[1,3,5,4,2] => [1,5,4,3,2] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? = 2 + 4
[1,4,2,3,5] => [1,5,4,3,2] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? = 8 + 4
[1,4,2,5,3] => [1,5,4,3,2] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? = 4 + 4
[1,4,3,2,5] => [1,5,4,3,2] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? = 4 + 4
[1,4,3,5,2] => [1,5,4,3,2] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? = 2 + 4
[1,4,5,2,3] => [1,5,4,3,2] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? = 4 + 4
[1,4,5,3,2] => [1,5,4,3,2] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? = 2 + 4
[1,5,2,3,4] => [1,5,4,3,2] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? = 8 + 4
[1,5,2,4,3] => [1,5,4,3,2] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? = 4 + 4
[2,1,3,4,5] => [2,1,5,4,3] => [3,4,5,1,2] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> 4 = 0 + 4
[2,1,3,5,4] => [2,1,5,4,3] => [3,4,5,1,2] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> 4 = 0 + 4
[2,1,4,3,5] => [2,1,5,4,3] => [3,4,5,1,2] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> 4 = 0 + 4
[2,1,4,5,3] => [2,1,5,4,3] => [3,4,5,1,2] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> 4 = 0 + 4
[2,1,5,3,4] => [2,1,5,4,3] => [3,4,5,1,2] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> 4 = 0 + 4
[2,1,5,4,3] => [2,1,5,4,3] => [3,4,5,1,2] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> 4 = 0 + 4
[2,3,1,4,5] => [2,5,1,4,3] => [3,4,1,5,2] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 4 = 0 + 4
[2,3,1,5,4] => [2,5,1,4,3] => [3,4,1,5,2] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 4 = 0 + 4
[2,4,1,3,5] => [2,5,1,4,3] => [3,4,1,5,2] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 4 = 0 + 4
[2,4,1,5,3] => [2,5,1,4,3] => [3,4,1,5,2] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 4 = 0 + 4
[2,5,1,3,4] => [2,5,1,4,3] => [3,4,1,5,2] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 4 = 0 + 4
[2,5,1,4,3] => [2,5,1,4,3] => [3,4,1,5,2] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 4 = 0 + 4
[3,1,2,4,5] => [3,1,5,4,2] => [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 4 = 0 + 4
[3,1,2,5,4] => [3,1,5,4,2] => [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 4 = 0 + 4
[3,1,4,2,5] => [3,1,5,4,2] => [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 4 = 0 + 4
[3,1,4,5,2] => [3,1,5,4,2] => [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 4 = 0 + 4
[3,1,5,2,4] => [3,1,5,4,2] => [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 4 = 0 + 4
[3,1,5,4,2] => [3,1,5,4,2] => [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 4 = 0 + 4
[3,2,1,4,5] => [3,2,1,5,4] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> 4 = 0 + 4
[3,2,1,5,4] => [3,2,1,5,4] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> 4 = 0 + 4
[3,2,4,1,5] => [3,2,5,1,4] => [4,1,5,2,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 4 = 0 + 4
[3,2,4,5,1] => [3,2,5,4,1] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> 4 = 0 + 4
[3,2,5,1,4] => [3,2,5,1,4] => [4,1,5,2,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 4 = 0 + 4
[3,2,5,4,1] => [3,2,5,4,1] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> 4 = 0 + 4
[4,2,1,3,5] => [4,2,1,5,3] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 4 = 0 + 4
[4,2,1,5,3] => [4,2,1,5,3] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 4 = 0 + 4
[5,2,1,3,4] => [5,2,1,4,3] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> 4 = 0 + 4
[5,2,1,4,3] => [5,2,1,4,3] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> 4 = 0 + 4
[2,1,3,4,5,6] => [2,1,6,5,4,3] => [3,4,5,6,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4 = 0 + 4
[2,1,3,4,6,5] => [2,1,6,5,4,3] => [3,4,5,6,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4 = 0 + 4
[2,1,3,5,4,6] => [2,1,6,5,4,3] => [3,4,5,6,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4 = 0 + 4
[2,1,3,5,6,4] => [2,1,6,5,4,3] => [3,4,5,6,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4 = 0 + 4
[2,1,3,6,4,5] => [2,1,6,5,4,3] => [3,4,5,6,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4 = 0 + 4
[2,1,3,6,5,4] => [2,1,6,5,4,3] => [3,4,5,6,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4 = 0 + 4
[2,1,4,3,5,6] => [2,1,6,5,4,3] => [3,4,5,6,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4 = 0 + 4
[2,1,4,3,6,5] => [2,1,6,5,4,3] => [3,4,5,6,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4 = 0 + 4
[2,1,4,5,3,6] => [2,1,6,5,4,3] => [3,4,5,6,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4 = 0 + 4
[2,1,4,5,6,3] => [2,1,6,5,4,3] => [3,4,5,6,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4 = 0 + 4
[2,1,4,6,3,5] => [2,1,6,5,4,3] => [3,4,5,6,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4 = 0 + 4
[2,1,4,6,5,3] => [2,1,6,5,4,3] => [3,4,5,6,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4 = 0 + 4
[2,1,5,3,4,6] => [2,1,6,5,4,3] => [3,4,5,6,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4 = 0 + 4
[2,1,5,3,6,4] => [2,1,6,5,4,3] => [3,4,5,6,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4 = 0 + 4
[2,1,5,4,3,6] => [2,1,6,5,4,3] => [3,4,5,6,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4 = 0 + 4
[2,1,5,4,6,3] => [2,1,6,5,4,3] => [3,4,5,6,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4 = 0 + 4
[2,1,5,6,3,4] => [2,1,6,5,4,3] => [3,4,5,6,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4 = 0 + 4
[2,1,5,6,4,3] => [2,1,6,5,4,3] => [3,4,5,6,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4 = 0 + 4
[2,1,6,3,4,5] => [2,1,6,5,4,3] => [3,4,5,6,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4 = 0 + 4
[2,1,6,3,5,4] => [2,1,6,5,4,3] => [3,4,5,6,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4 = 0 + 4
Description
The girth of a graph, which is not a tree.
This is the length of the shortest cycle in the graph.
Matching statistic: St000456
(load all 4 compositions to match this statistic)
(load all 4 compositions to match this statistic)
Values
[1,2] => ([],2)
=> ([],2)
=> ? = 2 + 1
[2,1] => ([(0,1)],2)
=> ([],1)
=> ? = 0 + 1
[1,2,3] => ([],3)
=> ([],3)
=> ? = 4 + 1
[1,3,2] => ([(1,2)],3)
=> ([],2)
=> ? = 2 + 1
[2,1,3] => ([(1,2)],3)
=> ([],2)
=> ? = 0 + 1
[2,3,1] => ([(0,2),(1,2)],3)
=> ([(0,2),(1,2)],3)
=> 1 = 0 + 1
[3,1,2] => ([(0,2),(1,2)],3)
=> ([(0,2),(1,2)],3)
=> 1 = 0 + 1
[3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([],1)
=> ? = 0 + 1
[1,2,3,4] => ([],4)
=> ([],4)
=> ? = 8 + 1
[1,2,4,3] => ([(2,3)],4)
=> ([],3)
=> ? = 4 + 1
[1,3,2,4] => ([(2,3)],4)
=> ([],3)
=> ? = 4 + 1
[1,3,4,2] => ([(1,3),(2,3)],4)
=> ([(1,3),(2,3)],4)
=> ? = 2 + 1
[1,4,2,3] => ([(1,3),(2,3)],4)
=> ([(1,3),(2,3)],4)
=> ? = 4 + 1
[1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([],2)
=> ? = 2 + 1
[2,1,3,4] => ([(2,3)],4)
=> ([],3)
=> ? = 0 + 1
[2,1,4,3] => ([(0,3),(1,2)],4)
=> ([],2)
=> ? = 0 + 1
[2,3,1,4] => ([(1,3),(2,3)],4)
=> ([(1,3),(2,3)],4)
=> ? = 0 + 1
[2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
=> ([(0,3),(1,3),(2,3)],4)
=> 1 = 0 + 1
[2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 1 = 0 + 1
[2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,2),(1,2)],3)
=> 1 = 0 + 1
[3,1,2,4] => ([(1,3),(2,3)],4)
=> ([(1,3),(2,3)],4)
=> ? = 0 + 1
[3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 1 = 0 + 1
[3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([],2)
=> ? = 0 + 1
[3,2,4,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,2),(1,2)],3)
=> 1 = 0 + 1
[3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([],1)
=> ? = 0 + 1
[3,4,2,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],1)
=> ? = 0 + 1
[4,1,2,3] => ([(0,3),(1,3),(2,3)],4)
=> ([(0,3),(1,3),(2,3)],4)
=> 1 = 0 + 1
[4,1,3,2] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,2),(1,2)],3)
=> 1 = 0 + 1
[4,2,1,3] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,2),(1,2)],3)
=> 1 = 0 + 1
[4,2,3,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],1)
=> ? = 0 + 1
[4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],1)
=> ? = 0 + 1
[4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],1)
=> ? = 0 + 1
[1,2,3,4,5] => ([],5)
=> ([],5)
=> ? = 16 + 1
[1,2,3,5,4] => ([(3,4)],5)
=> ([],4)
=> ? = 8 + 1
[1,2,4,3,5] => ([(3,4)],5)
=> ([],4)
=> ? = 8 + 1
[1,2,4,5,3] => ([(2,4),(3,4)],5)
=> ([(2,4),(3,4)],5)
=> ? = 4 + 1
[1,2,5,3,4] => ([(2,4),(3,4)],5)
=> ([(2,4),(3,4)],5)
=> ? = 8 + 1
[1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
=> ([],3)
=> ? = 4 + 1
[1,3,2,4,5] => ([(3,4)],5)
=> ([],4)
=> ? = 8 + 1
[1,3,2,5,4] => ([(1,4),(2,3)],5)
=> ([],3)
=> ? = 4 + 1
[1,3,4,2,5] => ([(2,4),(3,4)],5)
=> ([(2,4),(3,4)],5)
=> ? = 4 + 1
[1,3,4,5,2] => ([(1,4),(2,4),(3,4)],5)
=> ([(1,4),(2,4),(3,4)],5)
=> ? = 2 + 1
[1,3,5,2,4] => ([(1,4),(2,3),(3,4)],5)
=> ([(1,5),(2,4),(3,4),(3,5)],6)
=> ? = 4 + 1
[1,3,5,4,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,3),(2,3)],4)
=> ? = 2 + 1
[1,4,2,3,5] => ([(2,4),(3,4)],5)
=> ([(2,4),(3,4)],5)
=> ? = 8 + 1
[1,4,2,5,3] => ([(1,4),(2,3),(3,4)],5)
=> ([(1,5),(2,4),(3,4),(3,5)],6)
=> ? = 4 + 1
[1,4,3,2,5] => ([(2,3),(2,4),(3,4)],5)
=> ([],3)
=> ? = 4 + 1
[1,4,3,5,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,3),(2,3)],4)
=> ? = 2 + 1
[1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([],2)
=> ? = 4 + 1
[1,4,5,3,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],2)
=> ? = 2 + 1
[1,5,2,3,4] => ([(1,4),(2,4),(3,4)],5)
=> ([(1,4),(2,4),(3,4)],5)
=> ? = 8 + 1
[1,5,2,4,3] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,3),(2,3)],4)
=> ? = 4 + 1
[1,5,3,2,4] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,3),(2,3)],4)
=> ? = 4 + 1
[1,5,3,4,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],2)
=> ? = 2 + 1
[1,5,4,2,3] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],2)
=> ? = 4 + 1
[1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],2)
=> ? = 2 + 1
[2,1,3,4,5] => ([(3,4)],5)
=> ([],4)
=> ? = 0 + 1
[2,1,3,5,4] => ([(1,4),(2,3)],5)
=> ([],3)
=> ? = 0 + 1
[2,1,4,3,5] => ([(1,4),(2,3)],5)
=> ([],3)
=> ? = 0 + 1
[2,1,4,5,3] => ([(0,1),(2,4),(3,4)],5)
=> ([(1,3),(2,3)],4)
=> ? = 0 + 1
[2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 0 + 1
[2,3,5,1,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> 1 = 0 + 1
[2,3,5,4,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(1,3),(2,3)],4)
=> 1 = 0 + 1
[2,4,1,5,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
=> 1 = 0 + 1
[2,4,3,5,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(1,3),(2,3)],4)
=> 1 = 0 + 1
[2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 1 = 0 + 1
[2,4,5,3,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 1 = 0 + 1
[2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> 1 = 0 + 1
[2,5,1,4,3] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 1 = 0 + 1
[2,5,3,1,4] => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 1 = 0 + 1
[2,5,3,4,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 1 = 0 + 1
[2,5,4,1,3] => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 1 = 0 + 1
[2,5,4,3,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 1 = 0 + 1
[3,1,4,5,2] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> 1 = 0 + 1
[3,1,5,2,4] => ([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
=> 1 = 0 + 1
[3,1,5,4,2] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 1 = 0 + 1
[3,2,4,5,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(1,3),(2,3)],4)
=> 1 = 0 + 1
[3,2,5,1,4] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 1 = 0 + 1
[3,2,5,4,1] => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 1 = 0 + 1
[3,4,1,5,2] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 1 = 0 + 1
[3,4,2,5,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 1 = 0 + 1
[3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 1 = 0 + 1
[3,5,2,1,4] => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 1 = 0 + 1
[4,1,2,5,3] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> 1 = 0 + 1
[4,1,3,5,2] => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 1 = 0 + 1
[4,1,5,2,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 1 = 0 + 1
[4,1,5,3,2] => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 1 = 0 + 1
[4,2,1,5,3] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 1 = 0 + 1
[4,2,3,5,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 1 = 0 + 1
[4,3,1,5,2] => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 1 = 0 + 1
[4,3,2,5,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 1 = 0 + 1
[5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 0 + 1
[5,1,2,4,3] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(1,3),(2,3)],4)
=> 1 = 0 + 1
[5,1,3,2,4] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(1,3),(2,3)],4)
=> 1 = 0 + 1
[5,1,3,4,2] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 1 = 0 + 1
[5,1,4,2,3] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 1 = 0 + 1
[5,1,4,3,2] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 1 = 0 + 1
[5,2,1,3,4] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(1,3),(2,3)],4)
=> 1 = 0 + 1
[5,2,1,4,3] => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 1 = 0 + 1
[5,2,3,1,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 1 = 0 + 1
Description
The monochromatic index of a connected graph.
This is the maximal number of colours such that there is a colouring of the edges where any two vertices can be joined by a monochromatic path.
For example, a circle graph other than the triangle can be coloured with at most two colours: one edge blue, all the others red.
Matching statistic: St000259
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Mp00175: Permutations —inverse Foata bijection⟶ Permutations
Mp00248: Permutations —DEX composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000259: Graphs ⟶ ℤResult quality: 14% ●values known / values provided: 24%●distinct values known / distinct values provided: 14%
Mp00248: Permutations —DEX composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000259: Graphs ⟶ ℤResult quality: 14% ●values known / values provided: 24%●distinct values known / distinct values provided: 14%
Values
[1,2] => [1,2] => [2] => ([],2)
=> ? = 2 + 2
[2,1] => [2,1] => [2] => ([],2)
=> ? = 0 + 2
[1,2,3] => [1,2,3] => [3] => ([],3)
=> ? = 4 + 2
[1,3,2] => [3,1,2] => [3] => ([],3)
=> ? = 2 + 2
[2,1,3] => [2,1,3] => [3] => ([],3)
=> ? = 0 + 2
[2,3,1] => [2,3,1] => [3] => ([],3)
=> ? = 0 + 2
[3,1,2] => [1,3,2] => [1,2] => ([(1,2)],3)
=> ? = 0 + 2
[3,2,1] => [3,2,1] => [2,1] => ([(0,2),(1,2)],3)
=> 2 = 0 + 2
[1,2,3,4] => [1,2,3,4] => [4] => ([],4)
=> ? = 8 + 2
[1,2,4,3] => [4,1,2,3] => [4] => ([],4)
=> ? = 4 + 2
[1,3,2,4] => [3,1,2,4] => [4] => ([],4)
=> ? = 4 + 2
[1,3,4,2] => [3,4,1,2] => [4] => ([],4)
=> ? = 2 + 2
[1,4,2,3] => [1,4,2,3] => [1,3] => ([(2,3)],4)
=> ? = 4 + 2
[1,4,3,2] => [4,3,1,2] => [1,3] => ([(2,3)],4)
=> ? = 2 + 2
[2,1,3,4] => [2,1,3,4] => [4] => ([],4)
=> ? = 0 + 2
[2,1,4,3] => [2,4,1,3] => [4] => ([],4)
=> ? = 0 + 2
[2,3,1,4] => [2,3,1,4] => [4] => ([],4)
=> ? = 0 + 2
[2,3,4,1] => [2,3,4,1] => [4] => ([],4)
=> ? = 0 + 2
[2,4,1,3] => [4,2,1,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 2
[2,4,3,1] => [4,2,3,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 0 + 2
[3,1,2,4] => [1,3,2,4] => [1,3] => ([(2,3)],4)
=> ? = 0 + 2
[3,1,4,2] => [1,3,4,2] => [1,3] => ([(2,3)],4)
=> ? = 0 + 2
[3,2,1,4] => [3,2,1,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 2
[3,2,4,1] => [3,2,4,1] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 2
[3,4,1,2] => [3,1,4,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 2
[3,4,2,1] => [3,4,2,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 0 + 2
[4,1,2,3] => [1,2,4,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 2
[4,1,3,2] => [4,1,3,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 0 + 2
[4,2,1,3] => [2,1,4,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 2
[4,2,3,1] => [2,4,3,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 0 + 2
[4,3,1,2] => [1,4,3,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 2 = 0 + 2
[4,3,2,1] => [4,3,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 2 = 0 + 2
[1,2,3,4,5] => [1,2,3,4,5] => [5] => ([],5)
=> ? = 16 + 2
[1,2,3,5,4] => [5,1,2,3,4] => [5] => ([],5)
=> ? = 8 + 2
[1,2,4,3,5] => [4,1,2,3,5] => [5] => ([],5)
=> ? = 8 + 2
[1,2,4,5,3] => [4,5,1,2,3] => [5] => ([],5)
=> ? = 4 + 2
[1,2,5,3,4] => [1,5,2,3,4] => [1,4] => ([(3,4)],5)
=> ? = 8 + 2
[1,2,5,4,3] => [5,4,1,2,3] => [1,4] => ([(3,4)],5)
=> ? = 4 + 2
[1,3,2,4,5] => [3,1,2,4,5] => [5] => ([],5)
=> ? = 8 + 2
[1,3,2,5,4] => [3,5,1,2,4] => [5] => ([],5)
=> ? = 4 + 2
[1,3,4,2,5] => [3,4,1,2,5] => [5] => ([],5)
=> ? = 4 + 2
[1,3,4,5,2] => [3,4,5,1,2] => [5] => ([],5)
=> ? = 2 + 2
[1,3,5,2,4] => [5,3,1,2,4] => [1,4] => ([(3,4)],5)
=> ? = 4 + 2
[1,3,5,4,2] => [5,3,4,1,2] => [1,4] => ([(3,4)],5)
=> ? = 2 + 2
[1,4,2,3,5] => [1,4,2,3,5] => [1,4] => ([(3,4)],5)
=> ? = 8 + 2
[1,4,2,5,3] => [1,4,5,2,3] => [1,4] => ([(3,4)],5)
=> ? = 4 + 2
[1,4,3,2,5] => [4,3,1,2,5] => [1,4] => ([(3,4)],5)
=> ? = 4 + 2
[1,4,3,5,2] => [4,3,5,1,2] => [1,4] => ([(3,4)],5)
=> ? = 2 + 2
[1,4,5,2,3] => [4,1,5,2,3] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 4 + 2
[1,4,5,3,2] => [4,5,3,1,2] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 2 + 2
[1,5,2,3,4] => [1,2,5,3,4] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 8 + 2
[1,5,2,4,3] => [5,1,4,2,3] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 4 + 2
[1,5,3,2,4] => [5,1,3,2,4] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 4 + 2
[1,5,3,4,2] => [3,5,4,1,2] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 2 + 2
[1,5,4,2,3] => [1,5,4,2,3] => [1,1,3] => ([(2,3),(2,4),(3,4)],5)
=> ? = 4 + 2
[1,5,4,3,2] => [5,4,3,1,2] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 2 + 2
[2,1,3,4,5] => [2,1,3,4,5] => [5] => ([],5)
=> ? = 0 + 2
[2,3,5,4,1] => [5,2,3,4,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[2,4,5,3,1] => [4,5,2,3,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[2,5,3,4,1] => [2,5,3,4,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[2,5,4,3,1] => [5,4,2,3,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 0 + 2
[3,1,5,4,2] => [5,1,3,4,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[3,2,5,4,1] => [3,5,2,4,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[3,4,5,2,1] => [3,4,5,2,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[3,5,1,4,2] => [3,5,1,4,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[3,5,2,4,1] => [5,3,2,4,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 0 + 2
[3,5,4,1,2] => [5,3,1,4,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 0 + 2
[3,5,4,2,1] => [5,3,4,2,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 0 + 2
[4,1,5,3,2] => [4,5,1,3,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[4,2,5,3,1] => [2,4,5,3,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[4,3,5,2,1] => [4,3,5,2,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 0 + 2
[4,5,1,3,2] => [1,4,5,3,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 0 + 2
[4,5,2,3,1] => [4,2,5,3,1] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 0 + 2
[4,5,3,1,2] => [4,1,5,3,2] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 0 + 2
[4,5,3,2,1] => [4,5,3,2,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 0 + 2
[5,1,2,4,3] => [5,1,2,4,3] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[5,1,3,4,2] => [1,5,3,4,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 0 + 2
[5,1,4,2,3] => [1,5,2,4,3] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 0 + 2
[5,1,4,3,2] => [5,4,1,3,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 0 + 2
[5,2,1,4,3] => [2,5,1,4,3] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[5,2,3,4,1] => [2,3,5,4,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[5,2,4,1,3] => [5,2,1,4,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 0 + 2
[5,2,4,3,1] => [5,2,4,3,1] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 0 + 2
[5,3,1,4,2] => [1,3,5,4,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 0 + 2
[5,3,2,4,1] => [3,2,5,4,1] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 0 + 2
[5,3,4,1,2] => [3,1,5,4,2] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 0 + 2
[5,3,4,2,1] => [3,5,4,2,1] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 0 + 2
[5,4,1,2,3] => [1,2,5,4,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 0 + 2
[5,4,1,3,2] => [5,1,4,3,2] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 0 + 2
[5,4,2,1,3] => [2,1,5,4,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 0 + 2
[5,4,2,3,1] => [2,5,4,3,1] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 0 + 2
[5,4,3,1,2] => [1,5,4,3,2] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 0 + 2
[5,4,3,2,1] => [5,4,3,2,1] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 0 + 2
[2,3,4,6,5,1] => [6,2,3,4,5,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 0 + 2
[2,3,5,6,4,1] => [5,6,2,3,4,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 0 + 2
[2,3,6,4,5,1] => [2,6,3,4,5,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 0 + 2
[2,3,6,5,4,1] => [6,5,2,3,4,1] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> 2 = 0 + 2
[2,4,3,6,5,1] => [4,6,2,3,5,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 0 + 2
[2,4,5,6,3,1] => [4,5,6,2,3,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 0 + 2
[2,4,6,3,5,1] => [6,4,2,3,5,1] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> 2 = 0 + 2
Description
The diameter of a connected graph.
This is the greatest distance between any pair of vertices.
Matching statistic: St001200
Mp00069: Permutations —complement⟶ Permutations
Mp00068: Permutations —Simion-Schmidt map⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
St001200: Dyck paths ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 14%
Mp00068: Permutations —Simion-Schmidt map⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
St001200: Dyck paths ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 14%
Values
[1,2] => [2,1] => [2,1] => [1,1,0,0]
=> ? = 2 + 2
[2,1] => [1,2] => [1,2] => [1,0,1,0]
=> 2 = 0 + 2
[1,2,3] => [3,2,1] => [3,2,1] => [1,1,1,0,0,0]
=> ? = 4 + 2
[1,3,2] => [3,1,2] => [3,1,2] => [1,1,1,0,0,0]
=> ? = 2 + 2
[2,1,3] => [2,3,1] => [2,3,1] => [1,1,0,1,0,0]
=> 2 = 0 + 2
[2,3,1] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
=> 2 = 0 + 2
[3,1,2] => [1,3,2] => [1,3,2] => [1,0,1,1,0,0]
=> 2 = 0 + 2
[3,2,1] => [1,2,3] => [1,3,2] => [1,0,1,1,0,0]
=> 2 = 0 + 2
[1,2,3,4] => [4,3,2,1] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
=> ? = 8 + 2
[1,2,4,3] => [4,3,1,2] => [4,3,1,2] => [1,1,1,1,0,0,0,0]
=> ? = 4 + 2
[1,3,2,4] => [4,2,3,1] => [4,2,3,1] => [1,1,1,1,0,0,0,0]
=> ? = 4 + 2
[1,3,4,2] => [4,2,1,3] => [4,2,1,3] => [1,1,1,1,0,0,0,0]
=> ? = 2 + 2
[1,4,2,3] => [4,1,3,2] => [4,1,3,2] => [1,1,1,1,0,0,0,0]
=> ? = 4 + 2
[1,4,3,2] => [4,1,2,3] => [4,1,3,2] => [1,1,1,1,0,0,0,0]
=> ? = 2 + 2
[2,1,3,4] => [3,4,2,1] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
=> 2 = 0 + 2
[2,1,4,3] => [3,4,1,2] => [3,4,1,2] => [1,1,1,0,1,0,0,0]
=> 2 = 0 + 2
[2,3,1,4] => [3,2,4,1] => [3,2,4,1] => [1,1,1,0,0,1,0,0]
=> 2 = 0 + 2
[2,3,4,1] => [3,2,1,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
=> 2 = 0 + 2
[2,4,1,3] => [3,1,4,2] => [3,1,4,2] => [1,1,1,0,0,1,0,0]
=> 2 = 0 + 2
[2,4,3,1] => [3,1,2,4] => [3,1,4,2] => [1,1,1,0,0,1,0,0]
=> 2 = 0 + 2
[3,1,2,4] => [2,4,3,1] => [2,4,3,1] => [1,1,0,1,1,0,0,0]
=> 2 = 0 + 2
[3,1,4,2] => [2,4,1,3] => [2,4,1,3] => [1,1,0,1,1,0,0,0]
=> 2 = 0 + 2
[3,2,1,4] => [2,3,4,1] => [2,4,3,1] => [1,1,0,1,1,0,0,0]
=> 2 = 0 + 2
[3,2,4,1] => [2,3,1,4] => [2,4,1,3] => [1,1,0,1,1,0,0,0]
=> 2 = 0 + 2
[3,4,1,2] => [2,1,4,3] => [2,1,4,3] => [1,1,0,0,1,1,0,0]
=> 2 = 0 + 2
[3,4,2,1] => [2,1,3,4] => [2,1,4,3] => [1,1,0,0,1,1,0,0]
=> 2 = 0 + 2
[4,1,2,3] => [1,4,3,2] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
=> 2 = 0 + 2
[4,1,3,2] => [1,4,2,3] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
=> 2 = 0 + 2
[4,2,1,3] => [1,3,4,2] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
=> 2 = 0 + 2
[4,2,3,1] => [1,3,2,4] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
=> 2 = 0 + 2
[4,3,1,2] => [1,2,4,3] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
=> 2 = 0 + 2
[4,3,2,1] => [1,2,3,4] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
=> 2 = 0 + 2
[1,2,3,4,5] => [5,4,3,2,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 16 + 2
[1,2,3,5,4] => [5,4,3,1,2] => [5,4,3,1,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 8 + 2
[1,2,4,3,5] => [5,4,2,3,1] => [5,4,2,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 8 + 2
[1,2,4,5,3] => [5,4,2,1,3] => [5,4,2,1,3] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 4 + 2
[1,2,5,3,4] => [5,4,1,3,2] => [5,4,1,3,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 8 + 2
[1,2,5,4,3] => [5,4,1,2,3] => [5,4,1,3,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 4 + 2
[1,3,2,4,5] => [5,3,4,2,1] => [5,3,4,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 8 + 2
[1,3,2,5,4] => [5,3,4,1,2] => [5,3,4,1,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 4 + 2
[1,3,4,2,5] => [5,3,2,4,1] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 4 + 2
[1,3,4,5,2] => [5,3,2,1,4] => [5,3,2,1,4] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 + 2
[1,3,5,2,4] => [5,3,1,4,2] => [5,3,1,4,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 4 + 2
[1,3,5,4,2] => [5,3,1,2,4] => [5,3,1,4,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 + 2
[1,4,2,3,5] => [5,2,4,3,1] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 8 + 2
[1,4,2,5,3] => [5,2,4,1,3] => [5,2,4,1,3] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 4 + 2
[1,4,3,2,5] => [5,2,3,4,1] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 4 + 2
[1,4,3,5,2] => [5,2,3,1,4] => [5,2,4,1,3] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 + 2
[1,4,5,2,3] => [5,2,1,4,3] => [5,2,1,4,3] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 4 + 2
[1,4,5,3,2] => [5,2,1,3,4] => [5,2,1,4,3] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 + 2
[1,5,2,3,4] => [5,1,4,3,2] => [5,1,4,3,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 8 + 2
[1,5,2,4,3] => [5,1,4,2,3] => [5,1,4,3,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 4 + 2
[1,5,3,2,4] => [5,1,3,4,2] => [5,1,4,3,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 4 + 2
[1,5,3,4,2] => [5,1,3,2,4] => [5,1,4,3,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 + 2
[1,5,4,2,3] => [5,1,2,4,3] => [5,1,4,3,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 4 + 2
[1,5,4,3,2] => [5,1,2,3,4] => [5,1,4,3,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 + 2
[2,1,3,4,5] => [4,5,3,2,1] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
=> 2 = 0 + 2
[2,1,3,5,4] => [4,5,3,1,2] => [4,5,3,1,2] => [1,1,1,1,0,1,0,0,0,0]
=> 2 = 0 + 2
[2,1,4,3,5] => [4,5,2,3,1] => [4,5,2,3,1] => [1,1,1,1,0,1,0,0,0,0]
=> 2 = 0 + 2
[2,1,4,5,3] => [4,5,2,1,3] => [4,5,2,1,3] => [1,1,1,1,0,1,0,0,0,0]
=> 2 = 0 + 2
[2,1,5,3,4] => [4,5,1,3,2] => [4,5,1,3,2] => [1,1,1,1,0,1,0,0,0,0]
=> 2 = 0 + 2
[2,1,5,4,3] => [4,5,1,2,3] => [4,5,1,3,2] => [1,1,1,1,0,1,0,0,0,0]
=> 2 = 0 + 2
[2,3,1,4,5] => [4,3,5,2,1] => [4,3,5,2,1] => [1,1,1,1,0,0,1,0,0,0]
=> 2 = 0 + 2
[2,3,1,5,4] => [4,3,5,1,2] => [4,3,5,1,2] => [1,1,1,1,0,0,1,0,0,0]
=> 2 = 0 + 2
[2,3,4,1,5] => [4,3,2,5,1] => [4,3,2,5,1] => [1,1,1,1,0,0,0,1,0,0]
=> 2 = 0 + 2
[2,3,4,5,1] => [4,3,2,1,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
=> 2 = 0 + 2
[2,3,5,1,4] => [4,3,1,5,2] => [4,3,1,5,2] => [1,1,1,1,0,0,0,1,0,0]
=> 2 = 0 + 2
[2,3,5,4,1] => [4,3,1,2,5] => [4,3,1,5,2] => [1,1,1,1,0,0,0,1,0,0]
=> 2 = 0 + 2
[2,4,1,3,5] => [4,2,5,3,1] => [4,2,5,3,1] => [1,1,1,1,0,0,1,0,0,0]
=> 2 = 0 + 2
[2,4,1,5,3] => [4,2,5,1,3] => [4,2,5,1,3] => [1,1,1,1,0,0,1,0,0,0]
=> 2 = 0 + 2
[2,4,3,1,5] => [4,2,3,5,1] => [4,2,5,3,1] => [1,1,1,1,0,0,1,0,0,0]
=> 2 = 0 + 2
[2,4,3,5,1] => [4,2,3,1,5] => [4,2,5,1,3] => [1,1,1,1,0,0,1,0,0,0]
=> 2 = 0 + 2
[2,4,5,1,3] => [4,2,1,5,3] => [4,2,1,5,3] => [1,1,1,1,0,0,0,1,0,0]
=> 2 = 0 + 2
[2,4,5,3,1] => [4,2,1,3,5] => [4,2,1,5,3] => [1,1,1,1,0,0,0,1,0,0]
=> 2 = 0 + 2
[2,5,1,3,4] => [4,1,5,3,2] => [4,1,5,3,2] => [1,1,1,1,0,0,1,0,0,0]
=> 2 = 0 + 2
[2,5,1,4,3] => [4,1,5,2,3] => [4,1,5,3,2] => [1,1,1,1,0,0,1,0,0,0]
=> 2 = 0 + 2
[2,5,3,1,4] => [4,1,3,5,2] => [4,1,5,3,2] => [1,1,1,1,0,0,1,0,0,0]
=> 2 = 0 + 2
[2,5,3,4,1] => [4,1,3,2,5] => [4,1,5,3,2] => [1,1,1,1,0,0,1,0,0,0]
=> 2 = 0 + 2
[2,5,4,1,3] => [4,1,2,5,3] => [4,1,5,3,2] => [1,1,1,1,0,0,1,0,0,0]
=> 2 = 0 + 2
[2,5,4,3,1] => [4,1,2,3,5] => [4,1,5,3,2] => [1,1,1,1,0,0,1,0,0,0]
=> 2 = 0 + 2
[3,1,2,4,5] => [3,5,4,2,1] => [3,5,4,2,1] => [1,1,1,0,1,1,0,0,0,0]
=> 2 = 0 + 2
[3,1,2,5,4] => [3,5,4,1,2] => [3,5,4,1,2] => [1,1,1,0,1,1,0,0,0,0]
=> 2 = 0 + 2
[3,1,4,2,5] => [3,5,2,4,1] => [3,5,2,4,1] => [1,1,1,0,1,1,0,0,0,0]
=> 2 = 0 + 2
[1,2,3,4,5,6] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 32 + 2
[1,2,3,4,6,5] => [6,5,4,3,1,2] => [6,5,4,3,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 16 + 2
[1,2,3,5,4,6] => [6,5,4,2,3,1] => [6,5,4,2,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 16 + 2
[1,2,3,5,6,4] => [6,5,4,2,1,3] => [6,5,4,2,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 8 + 2
[1,2,3,6,4,5] => [6,5,4,1,3,2] => [6,5,4,1,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 16 + 2
[1,2,3,6,5,4] => [6,5,4,1,2,3] => [6,5,4,1,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 8 + 2
[1,2,4,3,5,6] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 16 + 2
[1,2,4,3,6,5] => [6,5,3,4,1,2] => [6,5,3,4,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 8 + 2
[1,2,4,5,3,6] => [6,5,3,2,4,1] => [6,5,3,2,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 8 + 2
[1,2,4,5,6,3] => [6,5,3,2,1,4] => [6,5,3,2,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 4 + 2
[1,2,4,6,3,5] => [6,5,3,1,4,2] => [6,5,3,1,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 8 + 2
[1,2,4,6,5,3] => [6,5,3,1,2,4] => [6,5,3,1,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 4 + 2
[1,2,5,3,4,6] => [6,5,2,4,3,1] => [6,5,2,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 16 + 2
[1,2,5,3,6,4] => [6,5,2,4,1,3] => [6,5,2,4,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 8 + 2
[1,2,5,4,3,6] => [6,5,2,3,4,1] => [6,5,2,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 8 + 2
[1,2,5,4,6,3] => [6,5,2,3,1,4] => [6,5,2,4,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 4 + 2
[1,2,5,6,3,4] => [6,5,2,1,4,3] => [6,5,2,1,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 8 + 2
Description
The number of simple modules in $eAe$ with projective dimension at most 2 in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$.
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