Your data matches 8 different statistics following compositions of up to 3 maps.
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Matching statistic: St001232
(load all 4 compositions to match this statistic)
Mapping
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00315: Integer compositions —inverse Foata bijection⟶ 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] => [1] => [1] => [1,0]
 => 0
[1,2] => [2] => [2] => [1,1,0,0]
 => 0
[2,1] => [1,1] => [1,1] => [1,0,1,0]
 => 1
[1,2,3] => [3] => [3] => [1,1,1,0,0,0]
 => 0
[1,3,2] => [2,1] => [2,1] => [1,1,0,0,1,0]
 => 1
[2,1,3] => [1,2] => [1,2] => [1,0,1,1,0,0]
 => 2
[2,3,1] => [2,1] => [2,1] => [1,1,0,0,1,0]
 => 1
[3,1,2] => [1,2] => [1,2] => [1,0,1,1,0,0]
 => 2
[1,2,3,4] => [4] => [4] => [1,1,1,1,0,0,0,0]
 => 0
[1,2,4,3] => [3,1] => [3,1] => [1,1,1,0,0,0,1,0]
 => 1
[1,3,2,4] => [2,2] => [2,2] => [1,1,0,0,1,1,0,0]
 => 2
[1,3,4,2] => [3,1] => [3,1] => [1,1,1,0,0,0,1,0]
 => 1
[1,4,2,3] => [2,2] => [2,2] => [1,1,0,0,1,1,0,0]
 => 2
[1,4,3,2] => [2,1,1] => [1,2,1] => [1,0,1,1,0,0,1,0]
 => 3
[2,1,3,4] => [1,3] => [1,3] => [1,0,1,1,1,0,0,0]
 => 3
[2,3,1,4] => [2,2] => [2,2] => [1,1,0,0,1,1,0,0]
 => 2
[2,3,4,1] => [3,1] => [3,1] => [1,1,1,0,0,0,1,0]
 => 1
[2,4,1,3] => [2,2] => [2,2] => [1,1,0,0,1,1,0,0]
 => 2
[2,4,3,1] => [2,1,1] => [1,2,1] => [1,0,1,1,0,0,1,0]
 => 3
[3,1,2,4] => [1,3] => [1,3] => [1,0,1,1,1,0,0,0]
 => 3
[3,4,1,2] => [2,2] => [2,2] => [1,1,0,0,1,1,0,0]
 => 2
[3,4,2,1] => [2,1,1] => [1,2,1] => [1,0,1,1,0,0,1,0]
 => 3
[4,1,2,3] => [1,3] => [1,3] => [1,0,1,1,1,0,0,0]
 => 3
[1,2,3,4,5] => [5] => [5] => [1,1,1,1,1,0,0,0,0,0]
 => 0
[1,2,3,5,4] => [4,1] => [4,1] => [1,1,1,1,0,0,0,0,1,0]
 => 1
[1,2,4,3,5] => [3,2] => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => 2
[1,2,4,5,3] => [4,1] => [4,1] => [1,1,1,1,0,0,0,0,1,0]
 => 1
[1,2,5,3,4] => [3,2] => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => 2
[1,2,5,4,3] => [3,1,1] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0]
 => 4
[1,3,2,4,5] => [2,3] => [2,3] => [1,1,0,0,1,1,1,0,0,0]
 => 3
[1,3,2,5,4] => [2,2,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => 3
[1,3,4,2,5] => [3,2] => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => 2
[1,3,4,5,2] => [4,1] => [4,1] => [1,1,1,1,0,0,0,0,1,0]
 => 1
[1,3,5,2,4] => [3,2] => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => 2
[1,3,5,4,2] => [3,1,1] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0]
 => 4
[1,4,2,3,5] => [2,3] => [2,3] => [1,1,0,0,1,1,1,0,0,0]
 => 3
[1,4,2,5,3] => [2,2,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => 3
[1,4,3,5,2] => [2,2,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => 3
[1,4,5,2,3] => [3,2] => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => 2
[1,4,5,3,2] => [3,1,1] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0]
 => 4
[1,5,2,3,4] => [2,3] => [2,3] => [1,1,0,0,1,1,1,0,0,0]
 => 3
[1,5,2,4,3] => [2,2,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => 3
[1,5,3,4,2] => [2,2,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => 3
[2,1,3,4,5] => [1,4] => [1,4] => [1,0,1,1,1,1,0,0,0,0]
 => 4
[2,1,4,3,5] => [1,2,2] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0]
 => 4
[2,1,5,3,4] => [1,2,2] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0]
 => 4
[2,3,1,4,5] => [2,3] => [2,3] => [1,1,0,0,1,1,1,0,0,0]
 => 3
[2,3,1,5,4] => [2,2,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => 3
[2,3,4,1,5] => [3,2] => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => 2
[2,3,4,5,1] => [4,1] => [4,1] => [1,1,1,1,0,0,0,0,1,0]
 => 1
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
Matching statistic: St001227
Mapping
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00315: Integer compositions —inverse Foata bijection⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
St001227: Dyck paths ⟶ ℤResult quality: 18% ●values known / values provided: 18%●distinct values known / distinct values provided: 86%
Values
[1] => [1] => [1] => [1,0]
 => 0
[1,2] => [2] => [2] => [1,1,0,0]
 => 0
[2,1] => [1,1] => [1,1] => [1,0,1,0]
 => 1
[1,2,3] => [3] => [3] => [1,1,1,0,0,0]
 => 0
[1,3,2] => [2,1] => [2,1] => [1,1,0,0,1,0]
 => 1
[2,1,3] => [1,2] => [1,2] => [1,0,1,1,0,0]
 => 2
[2,3,1] => [2,1] => [2,1] => [1,1,0,0,1,0]
 => 1
[3,1,2] => [1,2] => [1,2] => [1,0,1,1,0,0]
 => 2
[1,2,3,4] => [4] => [4] => [1,1,1,1,0,0,0,0]
 => 0
[1,2,4,3] => [3,1] => [3,1] => [1,1,1,0,0,0,1,0]
 => 1
[1,3,2,4] => [2,2] => [2,2] => [1,1,0,0,1,1,0,0]
 => 2
[1,3,4,2] => [3,1] => [3,1] => [1,1,1,0,0,0,1,0]
 => 1
[1,4,2,3] => [2,2] => [2,2] => [1,1,0,0,1,1,0,0]
 => 2
[1,4,3,2] => [2,1,1] => [1,2,1] => [1,0,1,1,0,0,1,0]
 => 3
[2,1,3,4] => [1,3] => [1,3] => [1,0,1,1,1,0,0,0]
 => 3
[2,3,1,4] => [2,2] => [2,2] => [1,1,0,0,1,1,0,0]
 => 2
[2,3,4,1] => [3,1] => [3,1] => [1,1,1,0,0,0,1,0]
 => 1
[2,4,1,3] => [2,2] => [2,2] => [1,1,0,0,1,1,0,0]
 => 2
[2,4,3,1] => [2,1,1] => [1,2,1] => [1,0,1,1,0,0,1,0]
 => 3
[3,1,2,4] => [1,3] => [1,3] => [1,0,1,1,1,0,0,0]
 => 3
[3,4,1,2] => [2,2] => [2,2] => [1,1,0,0,1,1,0,0]
 => 2
[3,4,2,1] => [2,1,1] => [1,2,1] => [1,0,1,1,0,0,1,0]
 => 3
[4,1,2,3] => [1,3] => [1,3] => [1,0,1,1,1,0,0,0]
 => 3
[1,2,3,4,5] => [5] => [5] => [1,1,1,1,1,0,0,0,0,0]
 => 0
[1,2,3,5,4] => [4,1] => [4,1] => [1,1,1,1,0,0,0,0,1,0]
 => 1
[1,2,4,3,5] => [3,2] => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => 2
[1,2,4,5,3] => [4,1] => [4,1] => [1,1,1,1,0,0,0,0,1,0]
 => 1
[1,2,5,3,4] => [3,2] => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => 2
[1,2,5,4,3] => [3,1,1] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0]
 => 4
[1,3,2,4,5] => [2,3] => [2,3] => [1,1,0,0,1,1,1,0,0,0]
 => 3
[1,3,2,5,4] => [2,2,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => 3
[1,3,4,2,5] => [3,2] => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => 2
[1,3,4,5,2] => [4,1] => [4,1] => [1,1,1,1,0,0,0,0,1,0]
 => 1
[1,3,5,2,4] => [3,2] => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => 2
[1,3,5,4,2] => [3,1,1] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0]
 => 4
[1,4,2,3,5] => [2,3] => [2,3] => [1,1,0,0,1,1,1,0,0,0]
 => 3
[1,4,2,5,3] => [2,2,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => 3
[1,4,3,5,2] => [2,2,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => 3
[1,4,5,2,3] => [3,2] => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => 2
[1,4,5,3,2] => [3,1,1] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0]
 => 4
[1,5,2,3,4] => [2,3] => [2,3] => [1,1,0,0,1,1,1,0,0,0]
 => 3
[1,5,2,4,3] => [2,2,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => 3
[1,5,3,4,2] => [2,2,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => 3
[2,1,3,4,5] => [1,4] => [1,4] => [1,0,1,1,1,1,0,0,0,0]
 => 4
[2,1,4,3,5] => [1,2,2] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0]
 => 4
[2,1,5,3,4] => [1,2,2] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0]
 => 4
[2,3,1,4,5] => [2,3] => [2,3] => [1,1,0,0,1,1,1,0,0,0]
 => 3
[2,3,1,5,4] => [2,2,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => 3
[2,3,4,1,5] => [3,2] => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => 2
[2,3,4,5,1] => [4,1] => [4,1] => [1,1,1,1,0,0,0,0,1,0]
 => 1
[1,2,3,4,5,6,7] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => ? = 0
[1,2,3,4,5,7,6] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => ? = 1
[1,2,3,4,6,5,7] => [5,2] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => ? = 2
[1,2,3,4,6,7,5] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => ? = 1
[1,2,3,4,7,5,6] => [5,2] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => ? = 2
[1,2,3,4,7,6,5] => [5,1,1] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => ? = 6
[1,2,3,5,4,6,7] => [4,3] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 3
[1,2,3,5,4,7,6] => [4,2,1] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
 => ? = 3
[1,2,3,5,6,4,7] => [5,2] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => ? = 2
[1,2,3,5,6,7,4] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => ? = 1
[1,2,3,5,7,4,6] => [5,2] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => ? = 2
[1,2,3,5,7,6,4] => [5,1,1] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => ? = 6
[1,2,3,6,4,5,7] => [4,3] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 3
[1,2,3,6,4,7,5] => [4,2,1] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
 => ? = 3
[1,2,3,6,5,4,7] => [4,1,2] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0]
 => ? = 6
[1,2,3,6,5,7,4] => [4,2,1] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
 => ? = 3
[1,2,3,6,7,4,5] => [5,2] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => ? = 2
[1,2,3,6,7,5,4] => [5,1,1] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => ? = 6
[1,2,3,7,4,5,6] => [4,3] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 3
[1,2,3,7,4,6,5] => [4,2,1] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
 => ? = 3
[1,2,3,7,5,4,6] => [4,1,2] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0]
 => ? = 6
[1,2,3,7,5,6,4] => [4,2,1] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
 => ? = 3
[1,2,3,7,6,4,5] => [4,1,2] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0]
 => ? = 6
[1,2,4,3,5,6,7] => [3,4] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
 => ? = 4
[1,2,4,3,5,7,6] => [3,3,1] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0]
 => ? = 4
[1,2,4,3,6,5,7] => [3,2,2] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
 => ? = 5
[1,2,4,3,6,7,5] => [3,3,1] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0]
 => ? = 4
[1,2,4,3,7,5,6] => [3,2,2] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
 => ? = 5
[1,2,4,3,7,6,5] => [3,2,1,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0]
 => ? = 6
[1,2,4,5,3,6,7] => [4,3] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 3
[1,2,4,5,3,7,6] => [4,2,1] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
 => ? = 3
[1,2,4,5,6,3,7] => [5,2] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => ? = 2
[1,2,4,5,6,7,3] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => ? = 1
[1,2,4,5,7,3,6] => [5,2] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => ? = 2
[1,2,4,5,7,6,3] => [5,1,1] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => ? = 6
[1,2,4,6,3,5,7] => [4,3] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 3
[1,2,4,6,3,7,5] => [4,2,1] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
 => ? = 3
[1,2,4,6,5,3,7] => [4,1,2] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0]
 => ? = 6
[1,2,4,6,5,7,3] => [4,2,1] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
 => ? = 3
[1,2,4,6,7,3,5] => [5,2] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => ? = 2
[1,2,4,6,7,5,3] => [5,1,1] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => ? = 6
[1,2,4,7,3,5,6] => [4,3] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 3
[1,2,4,7,3,6,5] => [4,2,1] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
 => ? = 3
[1,2,4,7,5,3,6] => [4,1,2] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0]
 => ? = 6
[1,2,4,7,5,6,3] => [4,2,1] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
 => ? = 3
[1,2,4,7,6,3,5] => [4,1,2] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0]
 => ? = 6
[1,2,5,3,4,6,7] => [3,4] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
 => ? = 4
[1,2,5,3,4,7,6] => [3,3,1] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0]
 => ? = 4
[1,2,5,3,6,4,7] => [3,2,2] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
 => ? = 5
[1,2,5,3,6,7,4] => [3,3,1] => [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: St001879
Mapping
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001879: Posets ⟶ ℤResult quality: 5% ●values known / values provided: 5%●distinct values known / distinct values provided: 71%
Values
[1] => [1,0]
 => [1] => ([],1)
 => ? = 0
[1,2] => [1,0,1,0]
 => [2,1] => ([],2)
 => ? = 0
[2,1] => [1,1,0,0]
 => [1,2] => ([(0,1)],2)
 => ? = 1
[1,2,3] => [1,0,1,0,1,0]
 => [3,2,1] => ([],3)
 => ? = 0
[1,3,2] => [1,0,1,1,0,0]
 => [2,3,1] => ([(1,2)],3)
 => ? = 1
[2,1,3] => [1,1,0,0,1,0]
 => [3,1,2] => ([(1,2)],3)
 => ? = 2
[2,3,1] => [1,1,0,1,0,0]
 => [2,1,3] => ([(0,2),(1,2)],3)
 => ? = 1
[3,1,2] => [1,1,1,0,0,0]
 => [1,2,3] => ([(0,2),(2,1)],3)
 => 2
[1,2,3,4] => [1,0,1,0,1,0,1,0]
 => [4,3,2,1] => ([],4)
 => ? = 0
[1,2,4,3] => [1,0,1,0,1,1,0,0]
 => [3,4,2,1] => ([(2,3)],4)
 => ? = 1
[1,3,2,4] => [1,0,1,1,0,0,1,0]
 => [4,2,3,1] => ([(2,3)],4)
 => ? = 2
[1,3,4,2] => [1,0,1,1,0,1,0,0]
 => [3,2,4,1] => ([(1,3),(2,3)],4)
 => ? = 1
[1,4,2,3] => [1,0,1,1,1,0,0,0]
 => [2,3,4,1] => ([(1,2),(2,3)],4)
 => ? = 2
[1,4,3,2] => [1,0,1,1,1,0,0,0]
 => [2,3,4,1] => ([(1,2),(2,3)],4)
 => ? = 3
[2,1,3,4] => [1,1,0,0,1,0,1,0]
 => [4,3,1,2] => ([(2,3)],4)
 => ? = 3
[2,3,1,4] => [1,1,0,1,0,0,1,0]
 => [4,2,1,3] => ([(1,3),(2,3)],4)
 => ? = 2
[2,3,4,1] => [1,1,0,1,0,1,0,0]
 => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
 => ? = 1
[2,4,1,3] => [1,1,0,1,1,0,0,0]
 => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
 => ? = 2
[2,4,3,1] => [1,1,0,1,1,0,0,0]
 => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
 => ? = 3
[3,1,2,4] => [1,1,1,0,0,0,1,0]
 => [4,1,2,3] => ([(1,2),(2,3)],4)
 => ? = 3
[3,4,1,2] => [1,1,1,0,1,0,0,0]
 => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
 => ? = 2
[3,4,2,1] => [1,1,1,0,1,0,0,0]
 => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
 => ? = 3
[4,1,2,3] => [1,1,1,1,0,0,0,0]
 => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 3
[1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
 => [5,4,3,2,1] => ([],5)
 => ? = 0
[1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0]
 => [4,5,3,2,1] => ([(3,4)],5)
 => ? = 1
[1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0]
 => [5,3,4,2,1] => ([(3,4)],5)
 => ? = 2
[1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0]
 => [4,3,5,2,1] => ([(2,4),(3,4)],5)
 => ? = 1
[1,2,5,3,4] => [1,0,1,0,1,1,1,0,0,0]
 => [3,4,5,2,1] => ([(2,3),(3,4)],5)
 => ? = 2
[1,2,5,4,3] => [1,0,1,0,1,1,1,0,0,0]
 => [3,4,5,2,1] => ([(2,3),(3,4)],5)
 => ? = 4
[1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0]
 => [5,4,2,3,1] => ([(3,4)],5)
 => ? = 3
[1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0]
 => [4,5,2,3,1] => ([(1,4),(2,3)],5)
 => ? = 3
[1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0]
 => [5,3,2,4,1] => ([(2,4),(3,4)],5)
 => ? = 2
[1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0]
 => [4,3,2,5,1] => ([(1,4),(2,4),(3,4)],5)
 => ? = 1
[1,3,5,2,4] => [1,0,1,1,0,1,1,0,0,0]
 => [3,4,2,5,1] => ([(1,4),(2,3),(3,4)],5)
 => ? = 2
[1,3,5,4,2] => [1,0,1,1,0,1,1,0,0,0]
 => [3,4,2,5,1] => ([(1,4),(2,3),(3,4)],5)
 => ? = 4
[1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0]
 => [5,2,3,4,1] => ([(2,3),(3,4)],5)
 => ? = 3
[1,4,2,5,3] => [1,0,1,1,1,0,0,1,0,0]
 => [4,2,3,5,1] => ([(1,4),(2,3),(3,4)],5)
 => ? = 3
[1,4,3,5,2] => [1,0,1,1,1,0,0,1,0,0]
 => [4,2,3,5,1] => ([(1,4),(2,3),(3,4)],5)
 => ? = 3
[1,4,5,2,3] => [1,0,1,1,1,0,1,0,0,0]
 => [3,2,4,5,1] => ([(1,4),(2,4),(4,3)],5)
 => ? = 2
[1,4,5,3,2] => [1,0,1,1,1,0,1,0,0,0]
 => [3,2,4,5,1] => ([(1,4),(2,4),(4,3)],5)
 => ? = 4
[1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0]
 => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
 => ? = 3
[1,5,2,4,3] => [1,0,1,1,1,1,0,0,0,0]
 => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
 => ? = 3
[1,5,3,4,2] => [1,0,1,1,1,1,0,0,0,0]
 => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
 => ? = 3
[2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
 => [5,4,3,1,2] => ([(3,4)],5)
 => ? = 4
[2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0]
 => [5,3,4,1,2] => ([(1,4),(2,3)],5)
 => ? = 4
[2,1,5,3,4] => [1,1,0,0,1,1,1,0,0,0]
 => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
 => ? = 4
[2,3,1,4,5] => [1,1,0,1,0,0,1,0,1,0]
 => [5,4,2,1,3] => ([(2,4),(3,4)],5)
 => ? = 3
[2,3,1,5,4] => [1,1,0,1,0,0,1,1,0,0]
 => [4,5,2,1,3] => ([(0,4),(1,4),(2,3)],5)
 => ? = 3
[2,3,4,1,5] => [1,1,0,1,0,1,0,0,1,0]
 => [5,3,2,1,4] => ([(1,4),(2,4),(3,4)],5)
 => ? = 2
[2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0]
 => [4,3,2,1,5] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ? = 1
[2,3,5,1,4] => [1,1,0,1,0,1,1,0,0,0]
 => [3,4,2,1,5] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ? = 2
[2,3,5,4,1] => [1,1,0,1,0,1,1,0,0,0]
 => [3,4,2,1,5] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ? = 4
[5,1,2,3,4] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[5,1,3,2,4] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[5,1,4,2,3] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[5,2,3,1,4] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[5,2,4,1,3] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[5,3,4,1,2] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[6,1,2,3,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[6,1,3,2,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[6,1,4,2,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[6,1,5,2,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[6,2,3,1,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[6,2,4,1,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[6,2,5,1,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[6,3,4,1,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[6,3,5,1,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[6,4,5,1,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[7,1,2,3,4,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6
[7,1,2,4,3,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6
[7,1,2,5,3,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6
[7,1,2,6,3,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6
[7,1,3,2,4,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6
[7,1,3,2,5,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6
[7,1,3,2,6,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6
[7,1,3,4,2,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6
[7,1,3,5,2,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6
[7,1,3,6,2,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6
[7,1,4,2,3,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6
[7,1,4,2,5,3,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6
[7,1,4,2,6,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6
[7,1,4,3,5,2,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6
[7,1,4,3,6,2,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6
[7,1,4,5,2,3,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6
[7,1,4,6,2,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6
[7,1,5,2,3,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6
[7,1,5,2,4,3,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6
[7,1,5,2,6,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6
[7,1,5,3,4,2,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6
[7,1,5,3,6,2,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6
[7,1,5,4,6,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6
[7,1,5,6,2,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6
[7,1,6,2,3,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6
[7,1,6,2,4,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6
[7,1,6,2,5,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6
[7,1,6,3,4,2,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6
[7,1,6,3,5,2,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6
[7,1,6,4,5,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6
[7,2,3,1,4,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6
[7,2,3,1,5,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6
Description
The number of indecomposable summands of the top of the first syzygy of the dual of the regular module in the incidence algebra of the lattice.
Matching statistic: St001880
Mapping
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001880: Posets ⟶ ℤResult quality: 5% ●values known / values provided: 5%●distinct values known / distinct values provided: 71%
Values
[1] => [1,0]
 => [1] => ([],1)
 => ? = 0 + 1
[1,2] => [1,0,1,0]
 => [2,1] => ([],2)
 => ? = 0 + 1
[2,1] => [1,1,0,0]
 => [1,2] => ([(0,1)],2)
 => ? = 1 + 1
[1,2,3] => [1,0,1,0,1,0]
 => [3,2,1] => ([],3)
 => ? = 0 + 1
[1,3,2] => [1,0,1,1,0,0]
 => [2,3,1] => ([(1,2)],3)
 => ? = 1 + 1
[2,1,3] => [1,1,0,0,1,0]
 => [3,1,2] => ([(1,2)],3)
 => ? = 2 + 1
[2,3,1] => [1,1,0,1,0,0]
 => [2,1,3] => ([(0,2),(1,2)],3)
 => ? = 1 + 1
[3,1,2] => [1,1,1,0,0,0]
 => [1,2,3] => ([(0,2),(2,1)],3)
 => 3 = 2 + 1
[1,2,3,4] => [1,0,1,0,1,0,1,0]
 => [4,3,2,1] => ([],4)
 => ? = 0 + 1
[1,2,4,3] => [1,0,1,0,1,1,0,0]
 => [3,4,2,1] => ([(2,3)],4)
 => ? = 1 + 1
[1,3,2,4] => [1,0,1,1,0,0,1,0]
 => [4,2,3,1] => ([(2,3)],4)
 => ? = 2 + 1
[1,3,4,2] => [1,0,1,1,0,1,0,0]
 => [3,2,4,1] => ([(1,3),(2,3)],4)
 => ? = 1 + 1
[1,4,2,3] => [1,0,1,1,1,0,0,0]
 => [2,3,4,1] => ([(1,2),(2,3)],4)
 => ? = 2 + 1
[1,4,3,2] => [1,0,1,1,1,0,0,0]
 => [2,3,4,1] => ([(1,2),(2,3)],4)
 => ? = 3 + 1
[2,1,3,4] => [1,1,0,0,1,0,1,0]
 => [4,3,1,2] => ([(2,3)],4)
 => ? = 3 + 1
[2,3,1,4] => [1,1,0,1,0,0,1,0]
 => [4,2,1,3] => ([(1,3),(2,3)],4)
 => ? = 2 + 1
[2,3,4,1] => [1,1,0,1,0,1,0,0]
 => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
 => ? = 1 + 1
[2,4,1,3] => [1,1,0,1,1,0,0,0]
 => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
 => ? = 2 + 1
[2,4,3,1] => [1,1,0,1,1,0,0,0]
 => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
 => ? = 3 + 1
[3,1,2,4] => [1,1,1,0,0,0,1,0]
 => [4,1,2,3] => ([(1,2),(2,3)],4)
 => ? = 3 + 1
[3,4,1,2] => [1,1,1,0,1,0,0,0]
 => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
 => ? = 2 + 1
[3,4,2,1] => [1,1,1,0,1,0,0,0]
 => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
 => ? = 3 + 1
[4,1,2,3] => [1,1,1,1,0,0,0,0]
 => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
[1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
 => [5,4,3,2,1] => ([],5)
 => ? = 0 + 1
[1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0]
 => [4,5,3,2,1] => ([(3,4)],5)
 => ? = 1 + 1
[1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0]
 => [5,3,4,2,1] => ([(3,4)],5)
 => ? = 2 + 1
[1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0]
 => [4,3,5,2,1] => ([(2,4),(3,4)],5)
 => ? = 1 + 1
[1,2,5,3,4] => [1,0,1,0,1,1,1,0,0,0]
 => [3,4,5,2,1] => ([(2,3),(3,4)],5)
 => ? = 2 + 1
[1,2,5,4,3] => [1,0,1,0,1,1,1,0,0,0]
 => [3,4,5,2,1] => ([(2,3),(3,4)],5)
 => ? = 4 + 1
[1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0]
 => [5,4,2,3,1] => ([(3,4)],5)
 => ? = 3 + 1
[1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0]
 => [4,5,2,3,1] => ([(1,4),(2,3)],5)
 => ? = 3 + 1
[1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0]
 => [5,3,2,4,1] => ([(2,4),(3,4)],5)
 => ? = 2 + 1
[1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0]
 => [4,3,2,5,1] => ([(1,4),(2,4),(3,4)],5)
 => ? = 1 + 1
[1,3,5,2,4] => [1,0,1,1,0,1,1,0,0,0]
 => [3,4,2,5,1] => ([(1,4),(2,3),(3,4)],5)
 => ? = 2 + 1
[1,3,5,4,2] => [1,0,1,1,0,1,1,0,0,0]
 => [3,4,2,5,1] => ([(1,4),(2,3),(3,4)],5)
 => ? = 4 + 1
[1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0]
 => [5,2,3,4,1] => ([(2,3),(3,4)],5)
 => ? = 3 + 1
[1,4,2,5,3] => [1,0,1,1,1,0,0,1,0,0]
 => [4,2,3,5,1] => ([(1,4),(2,3),(3,4)],5)
 => ? = 3 + 1
[1,4,3,5,2] => [1,0,1,1,1,0,0,1,0,0]
 => [4,2,3,5,1] => ([(1,4),(2,3),(3,4)],5)
 => ? = 3 + 1
[1,4,5,2,3] => [1,0,1,1,1,0,1,0,0,0]
 => [3,2,4,5,1] => ([(1,4),(2,4),(4,3)],5)
 => ? = 2 + 1
[1,4,5,3,2] => [1,0,1,1,1,0,1,0,0,0]
 => [3,2,4,5,1] => ([(1,4),(2,4),(4,3)],5)
 => ? = 4 + 1
[1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0]
 => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
 => ? = 3 + 1
[1,5,2,4,3] => [1,0,1,1,1,1,0,0,0,0]
 => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
 => ? = 3 + 1
[1,5,3,4,2] => [1,0,1,1,1,1,0,0,0,0]
 => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
 => ? = 3 + 1
[2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
 => [5,4,3,1,2] => ([(3,4)],5)
 => ? = 4 + 1
[2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0]
 => [5,3,4,1,2] => ([(1,4),(2,3)],5)
 => ? = 4 + 1
[2,1,5,3,4] => [1,1,0,0,1,1,1,0,0,0]
 => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
 => ? = 4 + 1
[2,3,1,4,5] => [1,1,0,1,0,0,1,0,1,0]
 => [5,4,2,1,3] => ([(2,4),(3,4)],5)
 => ? = 3 + 1
[2,3,1,5,4] => [1,1,0,1,0,0,1,1,0,0]
 => [4,5,2,1,3] => ([(0,4),(1,4),(2,3)],5)
 => ? = 3 + 1
[2,3,4,1,5] => [1,1,0,1,0,1,0,0,1,0]
 => [5,3,2,1,4] => ([(1,4),(2,4),(3,4)],5)
 => ? = 2 + 1
[2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0]
 => [4,3,2,1,5] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ? = 1 + 1
[2,3,5,1,4] => [1,1,0,1,0,1,1,0,0,0]
 => [3,4,2,1,5] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ? = 2 + 1
[2,3,5,4,1] => [1,1,0,1,0,1,1,0,0,0]
 => [3,4,2,1,5] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ? = 4 + 1
[5,1,2,3,4] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[5,1,3,2,4] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[5,1,4,2,3] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[5,2,3,1,4] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[5,2,4,1,3] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[5,3,4,1,2] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[6,1,2,3,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[6,1,3,2,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[6,1,4,2,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[6,1,5,2,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[6,2,3,1,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[6,2,4,1,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[6,2,5,1,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[6,3,4,1,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[6,3,5,1,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[6,4,5,1,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[7,1,2,3,4,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 6 + 1
[7,1,2,4,3,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 6 + 1
[7,1,2,5,3,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 6 + 1
[7,1,2,6,3,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 6 + 1
[7,1,3,2,4,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 6 + 1
[7,1,3,2,5,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 6 + 1
[7,1,3,2,6,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 6 + 1
[7,1,3,4,2,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 6 + 1
[7,1,3,5,2,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 6 + 1
[7,1,3,6,2,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 6 + 1
[7,1,4,2,3,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 6 + 1
[7,1,4,2,5,3,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 6 + 1
[7,1,4,2,6,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 6 + 1
[7,1,4,3,5,2,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 6 + 1
[7,1,4,3,6,2,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 6 + 1
[7,1,4,5,2,3,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 6 + 1
[7,1,4,6,2,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 6 + 1
[7,1,5,2,3,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 6 + 1
[7,1,5,2,4,3,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 6 + 1
[7,1,5,2,6,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 6 + 1
[7,1,5,3,4,2,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 6 + 1
[7,1,5,3,6,2,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 6 + 1
[7,1,5,4,6,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 6 + 1
[7,1,5,6,2,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 6 + 1
[7,1,6,2,3,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 6 + 1
[7,1,6,2,4,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 6 + 1
[7,1,6,2,5,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 6 + 1
[7,1,6,3,4,2,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 6 + 1
[7,1,6,3,5,2,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 6 + 1
[7,1,6,4,5,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 6 + 1
[7,2,3,1,4,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 6 + 1
[7,2,3,1,5,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 6 + 1
Description
The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice.
Matching statistic: St000136
(load all 2 compositions to match this statistic)
Mapping
Mp00064: Permutations —reverse⟶ Permutations
Mp00073: Permutations —major-index to inversion-number bijection⟶ Permutations
Mp00305: Permutations —parking function⟶ Parking functions
St000136: Parking functions ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 57%
Values
[1] => [1] => [1] => [1] => 0
[1,2] => [2,1] => [2,1] => [2,1] => 0
[2,1] => [1,2] => [1,2] => [1,2] => 1
[1,2,3] => [3,2,1] => [3,2,1] => [3,2,1] => 0
[1,3,2] => [2,3,1] => [3,1,2] => [3,1,2] => 1
[2,1,3] => [3,1,2] => [1,3,2] => [1,3,2] => 2
[2,3,1] => [1,3,2] => [2,3,1] => [2,3,1] => 1
[3,1,2] => [2,1,3] => [2,1,3] => [2,1,3] => 2
[1,2,3,4] => [4,3,2,1] => [4,3,2,1] => [4,3,2,1] => 0
[1,2,4,3] => [3,4,2,1] => [4,3,1,2] => [4,3,1,2] => 1
[1,3,2,4] => [4,2,3,1] => [4,1,3,2] => [4,1,3,2] => 2
[1,3,4,2] => [2,4,3,1] => [4,2,3,1] => [4,2,3,1] => 1
[1,4,2,3] => [3,2,4,1] => [4,2,1,3] => [4,2,1,3] => 2
[1,4,3,2] => [2,3,4,1] => [4,1,2,3] => [4,1,2,3] => 3
[2,1,3,4] => [4,3,1,2] => [1,4,3,2] => [1,4,3,2] => 3
[2,3,1,4] => [4,1,3,2] => [2,4,3,1] => [2,4,3,1] => 2
[2,3,4,1] => [1,4,3,2] => [3,4,2,1] => [3,4,2,1] => 1
[2,4,1,3] => [3,1,4,2] => [3,4,1,2] => [3,4,1,2] => 2
[2,4,3,1] => [1,3,4,2] => [2,4,1,3] => [2,4,1,3] => 3
[3,1,2,4] => [4,2,1,3] => [3,1,4,2] => [3,1,4,2] => 3
[3,4,1,2] => [2,1,4,3] => [3,2,4,1] => [3,2,4,1] => 2
[3,4,2,1] => [1,2,4,3] => [2,3,4,1] => [2,3,4,1] => 3
[4,1,2,3] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => 3
[1,2,3,4,5] => [5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => ? = 0
[1,2,3,5,4] => [4,5,3,2,1] => [5,4,3,1,2] => [5,4,3,1,2] => ? = 1
[1,2,4,3,5] => [5,3,4,2,1] => [5,4,1,3,2] => [5,4,1,3,2] => ? = 2
[1,2,4,5,3] => [3,5,4,2,1] => [5,4,2,3,1] => [5,4,2,3,1] => ? = 1
[1,2,5,3,4] => [4,3,5,2,1] => [5,4,2,1,3] => [5,4,2,1,3] => ? = 2
[1,2,5,4,3] => [3,4,5,2,1] => [5,4,1,2,3] => [5,4,1,2,3] => ? = 4
[1,3,2,4,5] => [5,4,2,3,1] => [5,1,4,3,2] => [5,1,4,3,2] => ? = 3
[1,3,2,5,4] => [4,5,2,3,1] => [5,1,4,2,3] => [5,1,4,2,3] => ? = 3
[1,3,4,2,5] => [5,2,4,3,1] => [5,2,4,3,1] => [5,2,4,3,1] => ? = 2
[1,3,4,5,2] => [2,5,4,3,1] => [5,3,4,2,1] => [5,3,4,2,1] => ? = 1
[1,3,5,2,4] => [4,2,5,3,1] => [5,3,4,1,2] => [5,3,4,1,2] => ? = 2
[1,3,5,4,2] => [2,4,5,3,1] => [5,2,4,1,3] => [5,2,4,1,3] => ? = 4
[1,4,2,3,5] => [5,3,2,4,1] => [5,3,1,4,2] => [5,3,1,4,2] => ? = 3
[1,4,2,5,3] => [3,5,2,4,1] => [5,1,3,4,2] => [5,1,3,4,2] => ? = 3
[1,4,3,5,2] => [2,5,3,4,1] => [5,2,1,4,3] => [5,2,1,4,3] => ? = 3
[1,4,5,2,3] => [3,2,5,4,1] => [5,3,2,4,1] => [5,3,2,4,1] => ? = 2
[1,4,5,3,2] => [2,3,5,4,1] => [5,2,3,4,1] => [5,2,3,4,1] => ? = 4
[1,5,2,3,4] => [4,3,2,5,1] => [5,3,2,1,4] => [5,3,2,1,4] => ? = 3
[1,5,2,4,3] => [3,4,2,5,1] => [5,3,1,2,4] => [5,3,1,2,4] => ? = 3
[1,5,3,4,2] => [2,4,3,5,1] => [5,2,3,1,4] => [5,2,3,1,4] => ? = 3
[2,1,3,4,5] => [5,4,3,1,2] => [1,5,4,3,2] => [1,5,4,3,2] => ? = 4
[2,1,4,3,5] => [5,3,4,1,2] => [1,5,2,4,3] => [1,5,2,4,3] => ? = 4
[2,1,5,3,4] => [4,3,5,1,2] => [1,5,3,2,4] => [1,5,3,2,4] => ? = 4
[2,3,1,4,5] => [5,4,1,3,2] => [2,5,4,3,1] => [2,5,4,3,1] => ? = 3
[2,3,1,5,4] => [4,5,1,3,2] => [2,5,4,1,3] => [2,5,4,1,3] => ? = 3
[2,3,4,1,5] => [5,1,4,3,2] => [3,5,4,2,1] => [3,5,4,2,1] => ? = 2
[2,3,4,5,1] => [1,5,4,3,2] => [4,5,3,2,1] => [4,5,3,2,1] => ? = 1
[2,3,5,1,4] => [4,1,5,3,2] => [4,5,3,1,2] => [4,5,3,1,2] => ? = 2
[2,3,5,4,1] => [1,4,5,3,2] => [3,5,4,1,2] => [3,5,4,1,2] => ? = 4
[2,4,1,3,5] => [5,3,1,4,2] => [4,5,1,3,2] => [4,5,1,3,2] => ? = 3
[2,4,1,5,3] => [3,5,1,4,2] => [2,5,3,4,1] => [2,5,3,4,1] => ? = 3
[2,4,3,5,1] => [1,5,3,4,2] => [3,5,1,4,2] => [3,5,1,4,2] => ? = 3
[2,4,5,1,3] => [3,1,5,4,2] => [4,5,2,3,1] => [4,5,2,3,1] => ? = 2
[2,4,5,3,1] => [1,3,5,4,2] => [3,5,2,4,1] => [3,5,2,4,1] => ? = 4
[2,5,1,3,4] => [4,3,1,5,2] => [4,5,2,1,3] => [4,5,2,1,3] => ? = 3
[2,5,1,4,3] => [3,4,1,5,2] => [4,5,1,2,3] => [4,5,1,2,3] => ? = 3
[2,5,3,4,1] => [1,4,3,5,2] => [3,5,2,1,4] => [3,5,2,1,4] => ? = 3
[3,1,2,4,5] => [5,4,2,1,3] => [4,1,5,3,2] => [4,1,5,3,2] => ? = 4
[3,1,4,2,5] => [5,2,4,1,3] => [1,3,5,4,2] => [1,3,5,4,2] => ? = 4
[3,1,5,2,4] => [4,2,5,1,3] => [1,4,5,2,3] => [1,4,5,2,3] => ? = 4
[3,2,4,1,5] => [5,1,4,2,3] => [2,1,5,4,3] => [2,1,5,4,3] => ? = 4
[3,2,5,1,4] => [4,1,5,2,3] => [3,1,5,2,4] => [3,1,5,2,4] => ? = 4
[3,4,1,2,5] => [5,2,1,4,3] => [4,2,5,3,1] => [4,2,5,3,1] => ? = 3
[3,4,1,5,2] => [2,5,1,4,3] => [2,4,5,3,1] => [2,4,5,3,1] => ? = 3
[3,4,2,5,1] => [1,5,2,4,3] => [3,2,5,4,1] => [3,2,5,4,1] => ? = 3
[3,4,5,1,2] => [2,1,5,4,3] => [4,3,5,2,1] => [4,3,5,2,1] => ? = 2
[3,4,5,2,1] => [1,2,5,4,3] => [3,4,5,2,1] => [3,4,5,2,1] => ? = 4
[3,5,1,2,4] => [4,2,1,5,3] => [4,3,5,1,2] => [4,3,5,1,2] => ? = 3
[3,5,1,4,2] => [2,4,1,5,3] => [4,2,5,1,3] => [4,2,5,1,3] => ? = 3
[3,5,2,4,1] => [1,4,2,5,3] => [3,4,5,1,2] => [3,4,5,1,2] => ? = 3
Description
The dinv of a parking function.
Matching statistic: St000194
(load all 2 compositions to match this statistic)
Mapping
Mp00064: Permutations —reverse⟶ Permutations
Mp00073: Permutations —major-index to inversion-number bijection⟶ Permutations
Mp00305: Permutations —parking function⟶ Parking functions
St000194: Parking functions ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 57%
Values
[1] => [1] => [1] => [1] => 0
[1,2] => [2,1] => [2,1] => [2,1] => 0
[2,1] => [1,2] => [1,2] => [1,2] => 1
[1,2,3] => [3,2,1] => [3,2,1] => [3,2,1] => 0
[1,3,2] => [2,3,1] => [3,1,2] => [3,1,2] => 1
[2,1,3] => [3,1,2] => [1,3,2] => [1,3,2] => 2
[2,3,1] => [1,3,2] => [2,3,1] => [2,3,1] => 1
[3,1,2] => [2,1,3] => [2,1,3] => [2,1,3] => 2
[1,2,3,4] => [4,3,2,1] => [4,3,2,1] => [4,3,2,1] => 0
[1,2,4,3] => [3,4,2,1] => [4,3,1,2] => [4,3,1,2] => 1
[1,3,2,4] => [4,2,3,1] => [4,1,3,2] => [4,1,3,2] => 2
[1,3,4,2] => [2,4,3,1] => [4,2,3,1] => [4,2,3,1] => 1
[1,4,2,3] => [3,2,4,1] => [4,2,1,3] => [4,2,1,3] => 2
[1,4,3,2] => [2,3,4,1] => [4,1,2,3] => [4,1,2,3] => 3
[2,1,3,4] => [4,3,1,2] => [1,4,3,2] => [1,4,3,2] => 3
[2,3,1,4] => [4,1,3,2] => [2,4,3,1] => [2,4,3,1] => 2
[2,3,4,1] => [1,4,3,2] => [3,4,2,1] => [3,4,2,1] => 1
[2,4,1,3] => [3,1,4,2] => [3,4,1,2] => [3,4,1,2] => 2
[2,4,3,1] => [1,3,4,2] => [2,4,1,3] => [2,4,1,3] => 3
[3,1,2,4] => [4,2,1,3] => [3,1,4,2] => [3,1,4,2] => 3
[3,4,1,2] => [2,1,4,3] => [3,2,4,1] => [3,2,4,1] => 2
[3,4,2,1] => [1,2,4,3] => [2,3,4,1] => [2,3,4,1] => 3
[4,1,2,3] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => 3
[1,2,3,4,5] => [5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => ? = 0
[1,2,3,5,4] => [4,5,3,2,1] => [5,4,3,1,2] => [5,4,3,1,2] => ? = 1
[1,2,4,3,5] => [5,3,4,2,1] => [5,4,1,3,2] => [5,4,1,3,2] => ? = 2
[1,2,4,5,3] => [3,5,4,2,1] => [5,4,2,3,1] => [5,4,2,3,1] => ? = 1
[1,2,5,3,4] => [4,3,5,2,1] => [5,4,2,1,3] => [5,4,2,1,3] => ? = 2
[1,2,5,4,3] => [3,4,5,2,1] => [5,4,1,2,3] => [5,4,1,2,3] => ? = 4
[1,3,2,4,5] => [5,4,2,3,1] => [5,1,4,3,2] => [5,1,4,3,2] => ? = 3
[1,3,2,5,4] => [4,5,2,3,1] => [5,1,4,2,3] => [5,1,4,2,3] => ? = 3
[1,3,4,2,5] => [5,2,4,3,1] => [5,2,4,3,1] => [5,2,4,3,1] => ? = 2
[1,3,4,5,2] => [2,5,4,3,1] => [5,3,4,2,1] => [5,3,4,2,1] => ? = 1
[1,3,5,2,4] => [4,2,5,3,1] => [5,3,4,1,2] => [5,3,4,1,2] => ? = 2
[1,3,5,4,2] => [2,4,5,3,1] => [5,2,4,1,3] => [5,2,4,1,3] => ? = 4
[1,4,2,3,5] => [5,3,2,4,1] => [5,3,1,4,2] => [5,3,1,4,2] => ? = 3
[1,4,2,5,3] => [3,5,2,4,1] => [5,1,3,4,2] => [5,1,3,4,2] => ? = 3
[1,4,3,5,2] => [2,5,3,4,1] => [5,2,1,4,3] => [5,2,1,4,3] => ? = 3
[1,4,5,2,3] => [3,2,5,4,1] => [5,3,2,4,1] => [5,3,2,4,1] => ? = 2
[1,4,5,3,2] => [2,3,5,4,1] => [5,2,3,4,1] => [5,2,3,4,1] => ? = 4
[1,5,2,3,4] => [4,3,2,5,1] => [5,3,2,1,4] => [5,3,2,1,4] => ? = 3
[1,5,2,4,3] => [3,4,2,5,1] => [5,3,1,2,4] => [5,3,1,2,4] => ? = 3
[1,5,3,4,2] => [2,4,3,5,1] => [5,2,3,1,4] => [5,2,3,1,4] => ? = 3
[2,1,3,4,5] => [5,4,3,1,2] => [1,5,4,3,2] => [1,5,4,3,2] => ? = 4
[2,1,4,3,5] => [5,3,4,1,2] => [1,5,2,4,3] => [1,5,2,4,3] => ? = 4
[2,1,5,3,4] => [4,3,5,1,2] => [1,5,3,2,4] => [1,5,3,2,4] => ? = 4
[2,3,1,4,5] => [5,4,1,3,2] => [2,5,4,3,1] => [2,5,4,3,1] => ? = 3
[2,3,1,5,4] => [4,5,1,3,2] => [2,5,4,1,3] => [2,5,4,1,3] => ? = 3
[2,3,4,1,5] => [5,1,4,3,2] => [3,5,4,2,1] => [3,5,4,2,1] => ? = 2
[2,3,4,5,1] => [1,5,4,3,2] => [4,5,3,2,1] => [4,5,3,2,1] => ? = 1
[2,3,5,1,4] => [4,1,5,3,2] => [4,5,3,1,2] => [4,5,3,1,2] => ? = 2
[2,3,5,4,1] => [1,4,5,3,2] => [3,5,4,1,2] => [3,5,4,1,2] => ? = 4
[2,4,1,3,5] => [5,3,1,4,2] => [4,5,1,3,2] => [4,5,1,3,2] => ? = 3
[2,4,1,5,3] => [3,5,1,4,2] => [2,5,3,4,1] => [2,5,3,4,1] => ? = 3
[2,4,3,5,1] => [1,5,3,4,2] => [3,5,1,4,2] => [3,5,1,4,2] => ? = 3
[2,4,5,1,3] => [3,1,5,4,2] => [4,5,2,3,1] => [4,5,2,3,1] => ? = 2
[2,4,5,3,1] => [1,3,5,4,2] => [3,5,2,4,1] => [3,5,2,4,1] => ? = 4
[2,5,1,3,4] => [4,3,1,5,2] => [4,5,2,1,3] => [4,5,2,1,3] => ? = 3
[2,5,1,4,3] => [3,4,1,5,2] => [4,5,1,2,3] => [4,5,1,2,3] => ? = 3
[2,5,3,4,1] => [1,4,3,5,2] => [3,5,2,1,4] => [3,5,2,1,4] => ? = 3
[3,1,2,4,5] => [5,4,2,1,3] => [4,1,5,3,2] => [4,1,5,3,2] => ? = 4
[3,1,4,2,5] => [5,2,4,1,3] => [1,3,5,4,2] => [1,3,5,4,2] => ? = 4
[3,1,5,2,4] => [4,2,5,1,3] => [1,4,5,2,3] => [1,4,5,2,3] => ? = 4
[3,2,4,1,5] => [5,1,4,2,3] => [2,1,5,4,3] => [2,1,5,4,3] => ? = 4
[3,2,5,1,4] => [4,1,5,2,3] => [3,1,5,2,4] => [3,1,5,2,4] => ? = 4
[3,4,1,2,5] => [5,2,1,4,3] => [4,2,5,3,1] => [4,2,5,3,1] => ? = 3
[3,4,1,5,2] => [2,5,1,4,3] => [2,4,5,3,1] => [2,4,5,3,1] => ? = 3
[3,4,2,5,1] => [1,5,2,4,3] => [3,2,5,4,1] => [3,2,5,4,1] => ? = 3
[3,4,5,1,2] => [2,1,5,4,3] => [4,3,5,2,1] => [4,3,5,2,1] => ? = 2
[3,4,5,2,1] => [1,2,5,4,3] => [3,4,5,2,1] => [3,4,5,2,1] => ? = 4
[3,5,1,2,4] => [4,2,1,5,3] => [4,3,5,1,2] => [4,3,5,1,2] => ? = 3
[3,5,1,4,2] => [2,4,1,5,3] => [4,2,5,1,3] => [4,2,5,1,3] => ? = 3
[3,5,2,4,1] => [1,4,2,5,3] => [3,4,5,1,2] => [3,4,5,1,2] => ? = 3
Description
The number of primary dinversion pairs of a labelled dyck path corresponding to a parking function.
Matching statistic: St001209
(load all 3 compositions to match this statistic)
Mapping
Mp00061: Permutations —to increasing tree⟶ Binary trees
Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
Mp00305: Permutations —parking function⟶ Parking functions
St001209: Parking functions ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 57%
Values
[1] => [.,.]
 => [1] => [1] => 0
[1,2] => [.,[.,.]]
 => [2,1] => [2,1] => 0
[2,1] => [[.,.],.]
 => [1,2] => [1,2] => 1
[1,2,3] => [.,[.,[.,.]]]
 => [3,2,1] => [3,2,1] => 0
[1,3,2] => [.,[[.,.],.]]
 => [2,3,1] => [2,3,1] => 1
[2,1,3] => [[.,.],[.,.]]
 => [1,3,2] => [1,3,2] => 2
[2,3,1] => [[.,[.,.]],.]
 => [2,1,3] => [2,1,3] => 1
[3,1,2] => [[.,.],[.,.]]
 => [1,3,2] => [1,3,2] => 2
[1,2,3,4] => [.,[.,[.,[.,.]]]]
 => [4,3,2,1] => [4,3,2,1] => 0
[1,2,4,3] => [.,[.,[[.,.],.]]]
 => [3,4,2,1] => [3,4,2,1] => 1
[1,3,2,4] => [.,[[.,.],[.,.]]]
 => [2,4,3,1] => [2,4,3,1] => 2
[1,3,4,2] => [.,[[.,[.,.]],.]]
 => [3,2,4,1] => [3,2,4,1] => 1
[1,4,2,3] => [.,[[.,.],[.,.]]]
 => [2,4,3,1] => [2,4,3,1] => 2
[1,4,3,2] => [.,[[[.,.],.],.]]
 => [2,3,4,1] => [2,3,4,1] => 3
[2,1,3,4] => [[.,.],[.,[.,.]]]
 => [1,4,3,2] => [1,4,3,2] => 3
[2,3,1,4] => [[.,[.,.]],[.,.]]
 => [2,1,4,3] => [2,1,4,3] => 2
[2,3,4,1] => [[.,[.,[.,.]]],.]
 => [3,2,1,4] => [3,2,1,4] => 1
[2,4,1,3] => [[.,[.,.]],[.,.]]
 => [2,1,4,3] => [2,1,4,3] => 2
[2,4,3,1] => [[.,[[.,.],.]],.]
 => [2,3,1,4] => [2,3,1,4] => 3
[3,1,2,4] => [[.,.],[.,[.,.]]]
 => [1,4,3,2] => [1,4,3,2] => 3
[3,4,1,2] => [[.,[.,.]],[.,.]]
 => [2,1,4,3] => [2,1,4,3] => 2
[3,4,2,1] => [[[.,[.,.]],.],.]
 => [2,1,3,4] => [2,1,3,4] => 3
[4,1,2,3] => [[.,.],[.,[.,.]]]
 => [1,4,3,2] => [1,4,3,2] => 3
[1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
 => [5,4,3,2,1] => [5,4,3,2,1] => ? = 0
[1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]]
 => [4,5,3,2,1] => [4,5,3,2,1] => ? = 1
[1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]]
 => [3,5,4,2,1] => [3,5,4,2,1] => ? = 2
[1,2,4,5,3] => [.,[.,[[.,[.,.]],.]]]
 => [4,3,5,2,1] => [4,3,5,2,1] => ? = 1
[1,2,5,3,4] => [.,[.,[[.,.],[.,.]]]]
 => [3,5,4,2,1] => [3,5,4,2,1] => ? = 2
[1,2,5,4,3] => [.,[.,[[[.,.],.],.]]]
 => [3,4,5,2,1] => [3,4,5,2,1] => ? = 4
[1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]]
 => [2,5,4,3,1] => [2,5,4,3,1] => ? = 3
[1,3,2,5,4] => [.,[[.,.],[[.,.],.]]]
 => [2,4,5,3,1] => [2,4,5,3,1] => ? = 3
[1,3,4,2,5] => [.,[[.,[.,.]],[.,.]]]
 => [3,2,5,4,1] => [3,2,5,4,1] => ? = 2
[1,3,4,5,2] => [.,[[.,[.,[.,.]]],.]]
 => [4,3,2,5,1] => [4,3,2,5,1] => ? = 1
[1,3,5,2,4] => [.,[[.,[.,.]],[.,.]]]
 => [3,2,5,4,1] => [3,2,5,4,1] => ? = 2
[1,3,5,4,2] => [.,[[.,[[.,.],.]],.]]
 => [3,4,2,5,1] => [3,4,2,5,1] => ? = 4
[1,4,2,3,5] => [.,[[.,.],[.,[.,.]]]]
 => [2,5,4,3,1] => [2,5,4,3,1] => ? = 3
[1,4,2,5,3] => [.,[[.,.],[[.,.],.]]]
 => [2,4,5,3,1] => [2,4,5,3,1] => ? = 3
[1,4,3,5,2] => [.,[[[.,.],[.,.]],.]]
 => [2,4,3,5,1] => [2,4,3,5,1] => ? = 3
[1,4,5,2,3] => [.,[[.,[.,.]],[.,.]]]
 => [3,2,5,4,1] => [3,2,5,4,1] => ? = 2
[1,4,5,3,2] => [.,[[[.,[.,.]],.],.]]
 => [3,2,4,5,1] => [3,2,4,5,1] => ? = 4
[1,5,2,3,4] => [.,[[.,.],[.,[.,.]]]]
 => [2,5,4,3,1] => [2,5,4,3,1] => ? = 3
[1,5,2,4,3] => [.,[[.,.],[[.,.],.]]]
 => [2,4,5,3,1] => [2,4,5,3,1] => ? = 3
[1,5,3,4,2] => [.,[[[.,.],[.,.]],.]]
 => [2,4,3,5,1] => [2,4,3,5,1] => ? = 3
[2,1,3,4,5] => [[.,.],[.,[.,[.,.]]]]
 => [1,5,4,3,2] => [1,5,4,3,2] => ? = 4
[2,1,4,3,5] => [[.,.],[[.,.],[.,.]]]
 => [1,3,5,4,2] => [1,3,5,4,2] => ? = 4
[2,1,5,3,4] => [[.,.],[[.,.],[.,.]]]
 => [1,3,5,4,2] => [1,3,5,4,2] => ? = 4
[2,3,1,4,5] => [[.,[.,.]],[.,[.,.]]]
 => [2,1,5,4,3] => [2,1,5,4,3] => ? = 3
[2,3,1,5,4] => [[.,[.,.]],[[.,.],.]]
 => [2,1,4,5,3] => [2,1,4,5,3] => ? = 3
[2,3,4,1,5] => [[.,[.,[.,.]]],[.,.]]
 => [3,2,1,5,4] => [3,2,1,5,4] => ? = 2
[2,3,4,5,1] => [[.,[.,[.,[.,.]]]],.]
 => [4,3,2,1,5] => [4,3,2,1,5] => ? = 1
[2,3,5,1,4] => [[.,[.,[.,.]]],[.,.]]
 => [3,2,1,5,4] => [3,2,1,5,4] => ? = 2
[2,3,5,4,1] => [[.,[.,[[.,.],.]]],.]
 => [3,4,2,1,5] => [3,4,2,1,5] => ? = 4
[2,4,1,3,5] => [[.,[.,.]],[.,[.,.]]]
 => [2,1,5,4,3] => [2,1,5,4,3] => ? = 3
[2,4,1,5,3] => [[.,[.,.]],[[.,.],.]]
 => [2,1,4,5,3] => [2,1,4,5,3] => ? = 3
[2,4,3,5,1] => [[.,[[.,.],[.,.]]],.]
 => [2,4,3,1,5] => [2,4,3,1,5] => ? = 3
[2,4,5,1,3] => [[.,[.,[.,.]]],[.,.]]
 => [3,2,1,5,4] => [3,2,1,5,4] => ? = 2
[2,4,5,3,1] => [[.,[[.,[.,.]],.]],.]
 => [3,2,4,1,5] => [3,2,4,1,5] => ? = 4
[2,5,1,3,4] => [[.,[.,.]],[.,[.,.]]]
 => [2,1,5,4,3] => [2,1,5,4,3] => ? = 3
[2,5,1,4,3] => [[.,[.,.]],[[.,.],.]]
 => [2,1,4,5,3] => [2,1,4,5,3] => ? = 3
[2,5,3,4,1] => [[.,[[.,.],[.,.]]],.]
 => [2,4,3,1,5] => [2,4,3,1,5] => ? = 3
[3,1,2,4,5] => [[.,.],[.,[.,[.,.]]]]
 => [1,5,4,3,2] => [1,5,4,3,2] => ? = 4
[3,1,4,2,5] => [[.,.],[[.,.],[.,.]]]
 => [1,3,5,4,2] => [1,3,5,4,2] => ? = 4
[3,1,5,2,4] => [[.,.],[[.,.],[.,.]]]
 => [1,3,5,4,2] => [1,3,5,4,2] => ? = 4
[3,2,4,1,5] => [[[.,.],[.,.]],[.,.]]
 => [1,3,2,5,4] => [1,3,2,5,4] => ? = 4
[3,2,5,1,4] => [[[.,.],[.,.]],[.,.]]
 => [1,3,2,5,4] => [1,3,2,5,4] => ? = 4
[3,4,1,2,5] => [[.,[.,.]],[.,[.,.]]]
 => [2,1,5,4,3] => [2,1,5,4,3] => ? = 3
[3,4,1,5,2] => [[.,[.,.]],[[.,.],.]]
 => [2,1,4,5,3] => [2,1,4,5,3] => ? = 3
[3,4,2,5,1] => [[[.,[.,.]],[.,.]],.]
 => [2,1,4,3,5] => [2,1,4,3,5] => ? = 3
[3,4,5,1,2] => [[.,[.,[.,.]]],[.,.]]
 => [3,2,1,5,4] => [3,2,1,5,4] => ? = 2
[3,4,5,2,1] => [[[.,[.,[.,.]]],.],.]
 => [3,2,1,4,5] => [3,2,1,4,5] => ? = 4
[3,5,1,2,4] => [[.,[.,.]],[.,[.,.]]]
 => [2,1,5,4,3] => [2,1,5,4,3] => ? = 3
[3,5,1,4,2] => [[.,[.,.]],[[.,.],.]]
 => [2,1,4,5,3] => [2,1,4,5,3] => ? = 3
[3,5,2,4,1] => [[[.,[.,.]],[.,.]],.]
 => [2,1,4,3,5] => [2,1,4,3,5] => ? = 3
Description
The pmaj statistic of a parking function. This is the parking function analogue of the bounce statistic, see [1, Section 1.3]. The definition given there is equivalent to the following: One again and again scans the parking function from right to left, keeping track of how often one has started over again. At step $i$, one marks the next position whose value is at most $i$ with the number of restarts from the end of the parking function. The pmaj statistic is then the sum of the markings. For example, consider the parking function $[6,2,4,1,4,1,7,3]$. In the first round, we mark positions $6,4,2$ with $0$'s. In the second round, we mark positions $8,5,3,1$ with $1$'s. In the third round, we mark position $7$ with a $2$. In total, we obtain that $$\operatorname{pmaj}([6,2,4,1,4,1,7,3]) = 6.$$ This statistic is equidistributed with the area statistic [[St000188]] and the dinv statistic [[St000136]].
Matching statistic: St001583
(load all 13 compositions to match this statistic)
Mapping
Mp00064: Permutations —reverse⟶ Permutations
Mp00073: Permutations —major-index to inversion-number bijection⟶ Permutations
St001583: Permutations ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 57%
Values
[1] => [1] => [1] => ? = 0
[1,2] => [2,1] => [2,1] => 0
[2,1] => [1,2] => [1,2] => 1
[1,2,3] => [3,2,1] => [3,2,1] => 0
[1,3,2] => [2,3,1] => [3,1,2] => 1
[2,1,3] => [3,1,2] => [1,3,2] => 2
[2,3,1] => [1,3,2] => [2,3,1] => 1
[3,1,2] => [2,1,3] => [2,1,3] => 2
[1,2,3,4] => [4,3,2,1] => [4,3,2,1] => 0
[1,2,4,3] => [3,4,2,1] => [4,3,1,2] => 1
[1,3,2,4] => [4,2,3,1] => [4,1,3,2] => 2
[1,3,4,2] => [2,4,3,1] => [4,2,3,1] => 1
[1,4,2,3] => [3,2,4,1] => [4,2,1,3] => 2
[1,4,3,2] => [2,3,4,1] => [4,1,2,3] => 3
[2,1,3,4] => [4,3,1,2] => [1,4,3,2] => 3
[2,3,1,4] => [4,1,3,2] => [2,4,3,1] => 2
[2,3,4,1] => [1,4,3,2] => [3,4,2,1] => 1
[2,4,1,3] => [3,1,4,2] => [3,4,1,2] => 2
[2,4,3,1] => [1,3,4,2] => [2,4,1,3] => 3
[3,1,2,4] => [4,2,1,3] => [3,1,4,2] => 3
[3,4,1,2] => [2,1,4,3] => [3,2,4,1] => 2
[3,4,2,1] => [1,2,4,3] => [2,3,4,1] => 3
[4,1,2,3] => [3,2,1,4] => [3,2,1,4] => 3
[1,2,3,4,5] => [5,4,3,2,1] => [5,4,3,2,1] => ? = 0
[1,2,3,5,4] => [4,5,3,2,1] => [5,4,3,1,2] => ? = 1
[1,2,4,3,5] => [5,3,4,2,1] => [5,4,1,3,2] => ? = 2
[1,2,4,5,3] => [3,5,4,2,1] => [5,4,2,3,1] => ? = 1
[1,2,5,3,4] => [4,3,5,2,1] => [5,4,2,1,3] => ? = 2
[1,2,5,4,3] => [3,4,5,2,1] => [5,4,1,2,3] => ? = 4
[1,3,2,4,5] => [5,4,2,3,1] => [5,1,4,3,2] => ? = 3
[1,3,2,5,4] => [4,5,2,3,1] => [5,1,4,2,3] => ? = 3
[1,3,4,2,5] => [5,2,4,3,1] => [5,2,4,3,1] => ? = 2
[1,3,4,5,2] => [2,5,4,3,1] => [5,3,4,2,1] => ? = 1
[1,3,5,2,4] => [4,2,5,3,1] => [5,3,4,1,2] => ? = 2
[1,3,5,4,2] => [2,4,5,3,1] => [5,2,4,1,3] => ? = 4
[1,4,2,3,5] => [5,3,2,4,1] => [5,3,1,4,2] => ? = 3
[1,4,2,5,3] => [3,5,2,4,1] => [5,1,3,4,2] => ? = 3
[1,4,3,5,2] => [2,5,3,4,1] => [5,2,1,4,3] => ? = 3
[1,4,5,2,3] => [3,2,5,4,1] => [5,3,2,4,1] => ? = 2
[1,4,5,3,2] => [2,3,5,4,1] => [5,2,3,4,1] => ? = 4
[1,5,2,3,4] => [4,3,2,5,1] => [5,3,2,1,4] => ? = 3
[1,5,2,4,3] => [3,4,2,5,1] => [5,3,1,2,4] => ? = 3
[1,5,3,4,2] => [2,4,3,5,1] => [5,2,3,1,4] => ? = 3
[2,1,3,4,5] => [5,4,3,1,2] => [1,5,4,3,2] => ? = 4
[2,1,4,3,5] => [5,3,4,1,2] => [1,5,2,4,3] => ? = 4
[2,1,5,3,4] => [4,3,5,1,2] => [1,5,3,2,4] => ? = 4
[2,3,1,4,5] => [5,4,1,3,2] => [2,5,4,3,1] => ? = 3
[2,3,1,5,4] => [4,5,1,3,2] => [2,5,4,1,3] => ? = 3
[2,3,4,1,5] => [5,1,4,3,2] => [3,5,4,2,1] => ? = 2
[2,3,4,5,1] => [1,5,4,3,2] => [4,5,3,2,1] => ? = 1
[2,3,5,1,4] => [4,1,5,3,2] => [4,5,3,1,2] => ? = 2
[2,3,5,4,1] => [1,4,5,3,2] => [3,5,4,1,2] => ? = 4
[2,4,1,3,5] => [5,3,1,4,2] => [4,5,1,3,2] => ? = 3
[2,4,1,5,3] => [3,5,1,4,2] => [2,5,3,4,1] => ? = 3
[2,4,3,5,1] => [1,5,3,4,2] => [3,5,1,4,2] => ? = 3
[2,4,5,1,3] => [3,1,5,4,2] => [4,5,2,3,1] => ? = 2
[2,4,5,3,1] => [1,3,5,4,2] => [3,5,2,4,1] => ? = 4
[2,5,1,3,4] => [4,3,1,5,2] => [4,5,2,1,3] => ? = 3
[2,5,1,4,3] => [3,4,1,5,2] => [4,5,1,2,3] => ? = 3
[2,5,3,4,1] => [1,4,3,5,2] => [3,5,2,1,4] => ? = 3
[3,1,2,4,5] => [5,4,2,1,3] => [4,1,5,3,2] => ? = 4
[3,1,4,2,5] => [5,2,4,1,3] => [1,3,5,4,2] => ? = 4
[3,1,5,2,4] => [4,2,5,1,3] => [1,4,5,2,3] => ? = 4
[3,2,4,1,5] => [5,1,4,2,3] => [2,1,5,4,3] => ? = 4
[3,2,5,1,4] => [4,1,5,2,3] => [3,1,5,2,4] => ? = 4
[3,4,1,2,5] => [5,2,1,4,3] => [4,2,5,3,1] => ? = 3
[3,4,1,5,2] => [2,5,1,4,3] => [2,4,5,3,1] => ? = 3
[3,4,2,5,1] => [1,5,2,4,3] => [3,2,5,4,1] => ? = 3
[3,4,5,1,2] => [2,1,5,4,3] => [4,3,5,2,1] => ? = 2
[3,4,5,2,1] => [1,2,5,4,3] => [3,4,5,2,1] => ? = 4
[3,5,1,2,4] => [4,2,1,5,3] => [4,3,5,1,2] => ? = 3
[3,5,1,4,2] => [2,4,1,5,3] => [4,2,5,1,3] => ? = 3
Description
The projective dimension of the simple module corresponding to the point in the poset of the symmetric group under bruhat order.