Your data matches 4 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001232
(load all 15 compositions to match this statistic)
Mapping
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00121: Dyck paths —Cori-Le Borgne involution⟶ Dyck paths
Mp00222: Dyck paths —peaks-to-valleys⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1]
 => [1,0,1,0]
 => [1,0,1,0]
 => [1,1,0,0]
 => 0
[2]
 => [1,1,0,0,1,0]
 => [1,1,0,0,1,0]
 => [1,0,1,1,0,0]
 => 2
[2,1]
 => [1,0,1,0,1,0]
 => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => 0
[3,1]
 => [1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0]
 => 2
[2,2]
 => [1,1,0,0,1,1,0,0]
 => [1,1,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,0]
 => 3
[3,2]
 => [1,1,0,0,1,0,1,0]
 => [1,1,0,0,1,0,1,0]
 => [1,0,1,1,1,0,0,0]
 => 3
[3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,1,0,0,0,1,0]
 => 5
[3,2,1]
 => [1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => 0
[4,2,1]
 => [1,1,0,1,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => 2
[3,3,1]
 => [1,1,0,1,0,0,1,1,0,0]
 => [1,1,0,0,1,0,1,1,0,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 4
[3,2,2]
 => [1,1,0,0,1,1,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3
[4,3,1]
 => [1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => 3
[4,2,2]
 => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 4
[4,4,1]
 => [1,1,1,0,1,0,0,0,1,1,0,0]
 => [1,0,1,1,1,0,0,0,1,1,0,0]
 => [1,1,1,0,0,1,1,0,0,0,1,0]
 => 5
[4,3,2]
 => [1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => 4
[3,3,3]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => [1,1,0,1,1,1,0,0,0,1,0,0]
 => 8
[4,4,2]
 => [1,1,1,0,0,1,0,0,1,1,0,0]
 => [1,1,1,0,0,0,1,1,0,0,1,0]
 => [1,1,0,1,1,0,0,0,1,1,0,0]
 => 6
[4,3,3]
 => [1,1,1,0,0,0,1,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,1,0,0]
 => [1,1,0,1,1,1,0,0,0,0,1,0]
 => 7
[4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => 0
[5,3,2,1]
 => [1,1,0,1,0,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => 2
[4,4,2,1]
 => [1,1,0,1,0,1,0,0,1,1,0,0]
 => [1,1,0,0,1,0,1,0,1,1,0,0]
 => [1,0,1,1,1,1,0,0,0,0,1,0]
 => 5
[4,3,3,1]
 => [1,1,0,1,0,0,1,1,0,1,0,0]
 => [1,0,1,1,0,0,1,0,1,1,0,0]
 => [1,1,0,0,1,1,1,0,0,0,1,0]
 => 4
[4,3,2,2]
 => [1,1,0,0,1,1,0,1,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0]
 => [1,1,1,0,0,0,1,1,0,0,1,0]
 => 3
[5,4,2,1]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 3
[5,3,3,1]
 => [1,1,0,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,1,0,0]
 => 5
[5,3,2,2]
 => [1,1,0,0,1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,1,0,0]
 => 4
[4,4,4]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => [1,1,1,0,1,1,1,0,0,0,0,1,0,0]
 => 11
[4,4,2,2]
 => [1,1,0,0,1,1,0,0,1,1,0,0]
 => [1,1,0,0,1,1,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 5
[5,5,2,1]
 => [1,1,1,0,1,0,1,0,0,0,1,1,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,1,0,0]
 => [1,1,1,1,0,0,0,1,1,0,0,0,1,0]
 => 5
[5,4,3,1]
 => [1,1,0,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => 4
[5,4,2,2]
 => [1,1,0,0,1,1,0,0,1,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0]
 => 5
[4,4,4,1]
 => [1,1,1,0,1,0,0,0,1,1,1,0,0,0]
 => [1,1,1,0,0,0,1,0,1,1,1,0,0,0]
 => [1,1,0,1,1,1,1,0,0,0,0,1,0,0]
 => 10
[4,3,3,3]
 => [1,1,1,0,0,0,1,1,1,0,1,0,0,0]
 => [1,0,1,1,1,0,0,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,1,1,0,0,0,1,0,0]
 => 8
[5,5,3,1]
 => [1,1,1,0,1,0,0,1,0,0,1,1,0,0]
 => [1,0,1,1,1,0,0,0,1,1,0,0,1,0]
 => [1,1,1,0,0,1,1,0,0,0,1,1,0,0]
 => 6
[5,5,2,2]
 => [1,1,1,0,0,1,1,0,0,0,1,1,0,0]
 => [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
 => [1,0,1,1,1,0,0,1,1,0,0,0,1,0]
 => 8
[5,4,4,1]
 => [1,1,1,0,1,0,0,0,1,1,0,1,0,0]
 => [1,0,1,1,1,0,0,0,1,0,1,1,0,0]
 => [1,1,1,0,0,1,1,1,0,0,0,0,1,0]
 => 7
[5,4,3,2]
 => [1,1,0,0,1,0,1,0,1,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => 5
[5,3,3,3]
 => [1,1,1,0,0,0,1,1,1,0,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0,1,0]
 => [1,1,0,1,1,1,0,0,0,1,1,0,0,0]
 => 10
[5,5,3,2]
 => [1,1,1,0,0,1,0,1,0,0,1,1,0,0]
 => [1,1,1,0,0,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,1,0,0,0,1,1,1,0,0,0]
 => 7
[5,4,4,2]
 => [1,1,1,0,0,1,0,0,1,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,1,0,0,0,0,1,1,0,0]
 => 8
[5,4,3,3]
 => [1,1,1,0,0,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0,1,0]
 => 9
[5,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => 0
[6,4,3,2,1]
 => [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => 2
[5,5,3,3]
 => [1,1,1,0,0,0,1,1,0,0,1,1,0,0]
 => [1,1,1,0,0,0,1,1,0,0,1,1,0,0]
 => [1,1,0,1,1,0,0,0,1,1,0,0,1,0]
 => 7
[5,5,3,2,1]
 => [1,1,0,1,0,1,0,1,0,0,1,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0,1,1,0,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => 6
[5,4,4,2,1]
 => [1,1,0,1,0,1,0,0,1,1,0,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,1,0,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0,1,0]
 => 5
[5,4,3,3,1]
 => [1,1,0,1,0,0,1,1,0,1,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,1,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0,1,0]
 => 4
[5,4,3,2,2]
 => [1,1,0,0,1,1,0,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
 => 3
[6,5,3,2,1]
 => [1,1,0,1,0,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => 3
[6,4,4,2,1]
 => [1,1,0,1,0,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,1,1,0,0,0,0,1,1,0,0]
 => 6
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
Matching statistic: St001207
(load all 2 compositions to match this statistic)
Mapping
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00120: Dyck paths —Lalanne-Kreweras involution⟶ Dyck paths
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
St001207: Permutations ⟶ ℤResult quality: 11% ●values known / values provided: 11%●distinct values known / distinct values provided: 27%
Values
[1]
 => [1,0,1,0]
 => [1,1,0,0]
 => [1,2] => 0
[2]
 => [1,1,0,0,1,0]
 => [1,0,1,1,0,0]
 => [2,3,1] => 2
[2,1]
 => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => [1,2,3] => 0
[3,1]
 => [1,1,0,1,0,0,1,0]
 => [1,1,0,1,1,0,0,0]
 => [2,3,1,4] => 2
[2,2]
 => [1,1,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,0]
 => [4,2,3,1] => 3
[3,2]
 => [1,1,0,0,1,0,1,0]
 => [1,0,1,1,1,0,0,0]
 => [2,3,4,1] => 3
[3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [5,3,4,2,1] => ? = 5
[3,2,1]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => [1,2,3,4] => 0
[4,2,1]
 => [1,1,0,1,0,1,0,0,1,0]
 => [1,1,1,0,1,1,0,0,0,0]
 => [2,3,1,4,5] => ? = 2
[3,3,1]
 => [1,1,0,1,0,0,1,1,0,0]
 => [1,1,0,1,1,0,0,0,1,0]
 => [5,2,3,1,4] => ? = 4
[3,2,2]
 => [1,1,0,0,1,1,0,1,0,0]
 => [1,0,1,1,1,0,0,1,0,0]
 => [4,2,3,5,1] => ? = 3
[4,3,1]
 => [1,1,0,1,0,0,1,0,1,0]
 => [1,1,0,1,1,1,0,0,0,0]
 => [2,3,4,1,5] => ? = 3
[4,2,2]
 => [1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => [4,5,2,3,1] => ? = 4
[4,4,1]
 => [1,1,1,0,1,0,0,0,1,1,0,0]
 => [1,1,0,1,0,1,1,0,0,0,1,0]
 => [6,3,4,2,1,5] => ? = 5
[4,3,2]
 => [1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => [2,3,4,5,1] => ? = 4
[3,3,3]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [6,5,3,4,2,1] => ? = 8
[4,4,2]
 => [1,1,1,0,0,1,0,0,1,1,0,0]
 => [1,0,1,1,0,1,1,0,0,0,1,0]
 => [6,3,4,2,5,1] => ? = 6
[4,3,3]
 => [1,1,1,0,0,0,1,1,0,1,0,0]
 => [1,0,1,0,1,1,1,0,0,1,0,0]
 => [5,3,4,6,2,1] => ? = 7
[4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ? = 0
[5,3,2,1]
 => [1,1,0,1,0,1,0,1,0,0,1,0]
 => [1,1,1,1,0,1,1,0,0,0,0,0]
 => [2,3,1,4,5,6] => ? = 2
[4,4,2,1]
 => [1,1,0,1,0,1,0,0,1,1,0,0]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => [6,2,3,1,4,5] => ? = 5
[4,3,3,1]
 => [1,1,0,1,0,0,1,1,0,1,0,0]
 => [1,1,0,1,1,1,0,0,0,1,0,0]
 => [5,2,3,4,1,6] => ? = 4
[4,3,2,2]
 => [1,1,0,0,1,1,0,1,0,1,0,0]
 => [1,0,1,1,1,1,0,0,1,0,0,0]
 => [4,2,3,5,6,1] => ? = 3
[5,4,2,1]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => [1,1,1,0,1,1,1,0,0,0,0,0]
 => [2,3,4,1,5,6] => ? = 3
[5,3,3,1]
 => [1,1,0,1,0,0,1,1,0,0,1,0]
 => [1,1,0,1,1,0,0,0,1,1,0,0]
 => [5,6,2,3,1,4] => ? = 5
[5,3,2,2]
 => [1,1,0,0,1,1,0,1,0,0,1,0]
 => [1,0,1,1,1,0,0,1,1,0,0,0]
 => [4,5,2,3,6,1] => ? = 4
[4,4,4]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [7,6,4,5,3,2,1] => ? = 11
[4,4,2,2]
 => [1,1,0,0,1,1,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => [6,4,5,2,3,1] => ? = 5
[5,5,2,1]
 => [1,1,1,0,1,0,1,0,0,0,1,1,0,0]
 => [1,1,1,0,1,0,1,1,0,0,0,0,1,0]
 => [7,3,4,2,1,5,6] => ? = 5
[5,4,3,1]
 => [1,1,0,1,0,0,1,0,1,0,1,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0]
 => [2,3,4,5,1,6] => ? = 4
[5,4,2,2]
 => [1,1,0,0,1,1,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0]
 => [4,5,6,2,3,1] => ? = 5
[4,4,4,1]
 => [1,1,1,0,1,0,0,0,1,1,1,0,0,0]
 => [1,1,0,1,0,1,1,0,0,0,1,0,1,0]
 => [7,6,3,4,2,1,5] => ? = 10
[4,3,3,3]
 => [1,1,1,0,0,0,1,1,1,0,1,0,0,0]
 => [1,0,1,0,1,1,1,0,0,1,0,1,0,0]
 => [6,5,3,4,7,2,1] => ? = 8
[5,5,3,1]
 => [1,1,1,0,1,0,0,1,0,0,1,1,0,0]
 => [1,1,0,1,1,0,1,1,0,0,0,0,1,0]
 => [7,3,4,2,5,1,6] => ? = 6
[5,5,2,2]
 => [1,1,1,0,0,1,1,0,0,0,1,1,0,0]
 => [1,0,1,1,0,1,0,0,1,1,0,0,1,0]
 => [7,5,6,3,2,4,1] => ? = 8
[5,4,4,1]
 => [1,1,1,0,1,0,0,0,1,1,0,1,0,0]
 => [1,1,0,1,0,1,1,1,0,0,0,1,0,0]
 => [6,3,4,5,2,1,7] => ? = 7
[5,4,3,2]
 => [1,1,0,0,1,0,1,0,1,0,1,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [2,3,4,5,6,1] => ? = 5
[5,3,3,3]
 => [1,1,1,0,0,0,1,1,1,0,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,1,0,1,0,0]
 => [6,5,7,3,4,2,1] => ? = 10
[5,5,3,2]
 => [1,1,1,0,0,1,0,1,0,0,1,1,0,0]
 => [1,0,1,1,1,0,1,1,0,0,0,0,1,0]
 => [7,3,4,2,5,6,1] => ? = 7
[5,4,4,2]
 => [1,1,1,0,0,1,0,0,1,1,0,1,0,0]
 => [1,0,1,1,0,1,1,1,0,0,0,1,0,0]
 => [6,3,4,5,2,7,1] => ? = 8
[5,4,3,3]
 => [1,1,1,0,0,0,1,1,0,1,0,1,0,0]
 => [1,0,1,0,1,1,1,1,0,0,1,0,0,0]
 => [5,3,4,6,7,2,1] => ? = 9
[5,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => ? = 0
[6,4,3,2,1]
 => [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
 => [1,1,1,1,1,0,1,1,0,0,0,0,0,0]
 => [2,3,1,4,5,6,7] => ? = 2
[5,5,3,3]
 => [1,1,1,0,0,0,1,1,0,0,1,1,0,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [7,5,6,3,4,2,1] => ? = 7
[5,5,3,2,1]
 => [1,1,0,1,0,1,0,1,0,0,1,1,0,0]
 => [1,1,1,1,0,1,1,0,0,0,0,0,1,0]
 => [7,2,3,1,4,5,6] => ? = 6
[5,4,4,2,1]
 => [1,1,0,1,0,1,0,0,1,1,0,1,0,0]
 => [1,1,1,0,1,1,1,0,0,0,0,1,0,0]
 => [6,2,3,4,1,5,7] => ? = 5
[5,4,3,3,1]
 => [1,1,0,1,0,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,1,1,1,0,0,0,1,0,0,0]
 => [5,2,3,4,6,1,7] => ? = 4
[5,4,3,2,2]
 => [1,1,0,0,1,1,0,1,0,1,0,1,0,0]
 => [1,0,1,1,1,1,1,0,0,1,0,0,0,0]
 => [4,2,3,5,6,7,1] => ? = 3
[6,5,3,2,1]
 => [1,1,0,1,0,1,0,1,0,0,1,0,1,0]
 => [1,1,1,1,0,1,1,1,0,0,0,0,0,0]
 => [2,3,4,1,5,6,7] => ? = 3
[6,4,4,2,1]
 => [1,1,0,1,0,1,0,0,1,1,0,0,1,0]
 => [1,1,1,0,1,1,0,0,0,0,1,1,0,0]
 => [6,7,2,3,1,4,5] => ? = 6
[6,4,3,3,1]
 => [1,1,0,1,0,0,1,1,0,1,0,0,1,0]
 => [1,1,0,1,1,1,0,0,0,1,1,0,0,0]
 => [5,6,2,3,4,1,7] => ? = 5
[6,4,3,2,2]
 => [1,1,0,0,1,1,0,1,0,1,0,0,1,0]
 => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
 => [4,5,2,3,6,7,1] => ? = 4
[5,5,3,3,1]
 => [1,1,0,1,0,0,1,1,0,0,1,1,0,0]
 => [1,1,0,1,1,0,0,0,1,1,0,0,1,0]
 => [7,5,6,2,3,1,4] => ? = 6
[5,5,3,2,2]
 => [1,1,0,0,1,1,0,1,0,0,1,1,0,0]
 => [1,0,1,1,1,0,0,1,1,0,0,0,1,0]
 => [7,4,5,2,3,6,1] => ? = 6
[5,4,4,2,2]
 => [1,1,0,0,1,1,0,0,1,1,0,1,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,1,0,0]
 => [6,4,5,7,2,3,1] => ? = 5
[6,5,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => ? = 0
[6,5,4,3,2]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => [2,3,4,5,6,7,1] => ? = 6
Description
The Lowey length of the algebra $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$.
Matching statistic: St001557
Mapping
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
Mp00068: Permutations —Simion-Schmidt map⟶ Permutations
St001557: Permutations ⟶ ℤResult quality: 11% ●values known / values provided: 11%●distinct values known / distinct values provided: 27%
Values
[1]
 => [1,0,1,0]
 => [3,1,2] => [3,1,2] => 0
[2]
 => [1,1,0,0,1,0]
 => [2,4,1,3] => [2,4,1,3] => 2
[2,1]
 => [1,0,1,0,1,0]
 => [4,1,2,3] => [4,1,3,2] => 0
[3,1]
 => [1,1,0,1,0,0,1,0]
 => [5,3,1,2,4] => [5,3,1,4,2] => 2
[2,2]
 => [1,1,0,0,1,1,0,0]
 => [2,4,1,5,3] => [2,5,1,4,3] => 3
[3,2]
 => [1,1,0,0,1,0,1,0]
 => [2,5,1,3,4] => [2,5,1,4,3] => 3
[3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [2,3,5,1,6,4] => [2,6,5,1,4,3] => ? = 5
[3,2,1]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => [5,1,4,3,2] => 0
[4,2,1]
 => [1,1,0,1,0,1,0,0,1,0]
 => [6,4,1,2,3,5] => [6,4,1,5,3,2] => ? = 2
[3,3,1]
 => [1,1,0,1,0,0,1,1,0,0]
 => [5,3,1,2,6,4] => [5,3,1,6,4,2] => ? = 4
[3,2,2]
 => [1,1,0,0,1,1,0,1,0,0]
 => [2,6,1,5,3,4] => [2,6,1,5,4,3] => ? = 3
[4,3,1]
 => [1,1,0,1,0,0,1,0,1,0]
 => [6,3,1,2,4,5] => [6,3,1,5,4,2] => ? = 3
[4,2,2]
 => [1,1,0,0,1,1,0,0,1,0]
 => [2,4,1,6,3,5] => [2,6,1,5,4,3] => ? = 4
[4,4,1]
 => [1,1,1,0,1,0,0,0,1,1,0,0]
 => [6,3,4,1,2,7,5] => [6,3,7,1,5,4,2] => ? = 5
[4,3,2]
 => [1,1,0,0,1,0,1,0,1,0]
 => [2,6,1,3,4,5] => [2,6,1,5,4,3] => ? = 4
[3,3,3]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => [2,3,5,1,6,7,4] => [2,7,6,1,5,4,3] => ? = 8
[4,4,2]
 => [1,1,1,0,0,1,0,0,1,1,0,0]
 => [2,6,4,1,3,7,5] => [2,7,6,1,5,4,3] => ? = 6
[4,3,3]
 => [1,1,1,0,0,0,1,1,0,1,0,0]
 => [2,3,7,1,6,4,5] => [2,7,6,1,5,4,3] => ? = 7
[4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => [6,1,2,3,4,5] => [6,1,5,4,3,2] => ? = 0
[5,3,2,1]
 => [1,1,0,1,0,1,0,1,0,0,1,0]
 => [5,7,1,2,3,4,6] => [5,7,1,6,4,3,2] => ? = 2
[4,4,2,1]
 => [1,1,0,1,0,1,0,0,1,1,0,0]
 => [6,4,1,2,3,7,5] => [6,4,1,7,5,3,2] => ? = 5
[4,3,3,1]
 => [1,1,0,1,0,0,1,1,0,1,0,0]
 => [7,3,1,2,6,4,5] => [7,3,1,6,5,4,2] => ? = 4
[4,3,2,2]
 => [1,1,0,0,1,1,0,1,0,1,0,0]
 => [2,7,1,6,3,4,5] => [2,7,1,6,5,4,3] => ? = 3
[5,4,2,1]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => [7,4,1,2,3,5,6] => [7,4,1,6,5,3,2] => ? = 3
[5,3,3,1]
 => [1,1,0,1,0,0,1,1,0,0,1,0]
 => [5,3,1,2,7,4,6] => [5,3,1,7,6,4,2] => ? = 5
[5,3,2,2]
 => [1,1,0,0,1,1,0,1,0,0,1,0]
 => [2,7,1,5,3,4,6] => [2,7,1,6,5,4,3] => ? = 4
[4,4,4]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => [2,3,4,6,1,7,8,5] => [2,8,7,6,1,5,4,3] => ? = 11
[4,4,2,2]
 => [1,1,0,0,1,1,0,0,1,1,0,0]
 => [2,4,1,6,3,7,5] => [2,7,1,6,5,4,3] => ? = 5
[5,5,2,1]
 => [1,1,1,0,1,0,1,0,0,0,1,1,0,0]
 => [7,5,4,1,2,3,8,6] => [7,5,4,1,8,6,3,2] => ? = 5
[5,4,3,1]
 => [1,1,0,1,0,0,1,0,1,0,1,0]
 => [7,3,1,2,4,5,6] => [7,3,1,6,5,4,2] => ? = 4
[5,4,2,2]
 => [1,1,0,0,1,1,0,0,1,0,1,0]
 => [2,4,1,7,3,5,6] => [2,7,1,6,5,4,3] => ? = 5
[4,4,4,1]
 => [1,1,1,0,1,0,0,0,1,1,1,0,0,0]
 => [6,3,4,1,2,7,8,5] => [6,3,8,1,7,5,4,2] => ? = 10
[4,3,3,3]
 => [1,1,1,0,0,0,1,1,1,0,1,0,0,0]
 => [2,3,8,1,6,7,4,5] => [2,8,7,1,6,5,4,3] => ? = 8
[5,5,3,1]
 => [1,1,1,0,1,0,0,1,0,0,1,1,0,0]
 => [7,3,5,1,2,4,8,6] => [7,3,8,1,6,5,4,2] => ? = 6
[5,5,2,2]
 => [1,1,1,0,0,1,1,0,0,0,1,1,0,0]
 => [2,5,4,1,7,3,8,6] => [2,8,7,1,6,5,4,3] => ? = 8
[5,4,4,1]
 => [1,1,1,0,1,0,0,0,1,1,0,1,0,0]
 => [8,3,4,1,2,7,5,6] => [8,3,7,1,6,5,4,2] => ? = 7
[5,4,3,2]
 => [1,1,0,0,1,0,1,0,1,0,1,0]
 => [2,7,1,3,4,5,6] => [2,7,1,6,5,4,3] => ? = 5
[5,3,3,3]
 => [1,1,1,0,0,0,1,1,1,0,0,1,0,0]
 => [2,3,5,1,8,7,4,6] => [2,8,7,1,6,5,4,3] => ? = 10
[5,5,3,2]
 => [1,1,1,0,0,1,0,1,0,0,1,1,0,0]
 => [2,7,5,1,3,4,8,6] => [2,8,7,1,6,5,4,3] => ? = 7
[5,4,4,2]
 => [1,1,1,0,0,1,0,0,1,1,0,1,0,0]
 => [2,8,4,1,3,7,5,6] => [2,8,7,1,6,5,4,3] => ? = 8
[5,4,3,3]
 => [1,1,1,0,0,0,1,1,0,1,0,1,0,0]
 => [2,3,8,1,7,4,5,6] => [2,8,7,1,6,5,4,3] => ? = 9
[5,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [7,1,2,3,4,5,6] => [7,1,6,5,4,3,2] => ? = 0
[6,4,3,2,1]
 => [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
 => [8,6,1,2,3,4,5,7] => [8,6,1,7,5,4,3,2] => ? = 2
[5,5,3,3]
 => [1,1,1,0,0,0,1,1,0,0,1,1,0,0]
 => [2,3,5,1,7,4,8,6] => [2,8,7,1,6,5,4,3] => ? = 7
[5,5,3,2,1]
 => [1,1,0,1,0,1,0,1,0,0,1,1,0,0]
 => [5,7,1,2,3,4,8,6] => [5,8,1,7,6,4,3,2] => ? = 6
[5,4,4,2,1]
 => [1,1,0,1,0,1,0,0,1,1,0,1,0,0]
 => [8,4,1,2,3,7,5,6] => [8,4,1,7,6,5,3,2] => ? = 5
[5,4,3,3,1]
 => [1,1,0,1,0,0,1,1,0,1,0,1,0,0]
 => [8,3,1,2,7,4,5,6] => [8,3,1,7,6,5,4,2] => ? = 4
[5,4,3,2,2]
 => [1,1,0,0,1,1,0,1,0,1,0,1,0,0]
 => [2,7,1,8,3,4,5,6] => [2,8,1,7,6,5,4,3] => ? = 3
[6,5,3,2,1]
 => [1,1,0,1,0,1,0,1,0,0,1,0,1,0]
 => [5,8,1,2,3,4,6,7] => [5,8,1,7,6,4,3,2] => ? = 3
[6,4,4,2,1]
 => [1,1,0,1,0,1,0,0,1,1,0,0,1,0]
 => [6,4,1,2,3,8,5,7] => [6,4,1,8,7,5,3,2] => ? = 6
[6,4,3,3,1]
 => [1,1,0,1,0,0,1,1,0,1,0,0,1,0]
 => [8,3,1,2,6,4,5,7] => [8,3,1,7,6,5,4,2] => ? = 5
[6,4,3,2,2]
 => [1,1,0,0,1,1,0,1,0,1,0,0,1,0]
 => [2,8,1,6,3,4,5,7] => [2,8,1,7,6,5,4,3] => ? = 4
[5,5,3,3,1]
 => [1,1,0,1,0,0,1,1,0,0,1,1,0,0]
 => [5,3,1,2,7,4,8,6] => [5,3,1,8,7,6,4,2] => ? = 6
[5,5,3,2,2]
 => [1,1,0,0,1,1,0,1,0,0,1,1,0,0]
 => [2,7,1,5,3,4,8,6] => [2,8,1,7,6,5,4,3] => ? = 6
[5,4,4,2,2]
 => [1,1,0,0,1,1,0,0,1,1,0,1,0,0]
 => [2,4,1,8,3,7,5,6] => [2,8,1,7,6,5,4,3] => ? = 5
[6,5,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [8,1,2,3,4,5,6,7] => [8,1,7,6,5,4,3,2] => ? = 0
[6,5,4,3,2]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0]
 => [2,8,1,3,4,5,6,7] => [2,8,1,7,6,5,4,3] => ? = 6
Description
The number of inversions of the second entry of a permutation. This is, for a permutation $\pi$ of length $n$, $$\# \{2 < k \leq n \mid \pi(2) > \pi(k)\}.$$ The number of inversions of the first entry is [[St000054]] and the number of inversions of the third entry is [[St001556]]. The sequence of inversions of all the entries define the [[http://www.findstat.org/Permutations#The_Lehmer_code_and_the_major_code_of_a_permutation|Lehmer code]] of a permutation.
Matching statistic: St000651
Mapping
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00146: Dyck paths —to tunnel matching⟶ Perfect matchings
Mp00283: Perfect matchings —non-nesting-exceedence permutation⟶ Permutations
St000651: Permutations ⟶ ℤResult quality: 11% ●values known / values provided: 11%●distinct values known / distinct values provided: 27%
Values
[1]
 => [1,0,1,0]
 => [(1,2),(3,4)]
 => [2,1,4,3] => 3 = 0 + 3
[2]
 => [1,1,0,0,1,0]
 => [(1,4),(2,3),(5,6)]
 => [3,4,2,1,6,5] => 5 = 2 + 3
[2,1]
 => [1,0,1,0,1,0]
 => [(1,2),(3,4),(5,6)]
 => [2,1,4,3,6,5] => 3 = 0 + 3
[3,1]
 => [1,1,0,1,0,0,1,0]
 => [(1,6),(2,3),(4,5),(7,8)]
 => [3,5,2,6,4,1,8,7] => ? = 2 + 3
[2,2]
 => [1,1,0,0,1,1,0,0]
 => [(1,4),(2,3),(5,8),(6,7)]
 => [3,4,2,1,7,8,6,5] => 6 = 3 + 3
[3,2]
 => [1,1,0,0,1,0,1,0]
 => [(1,4),(2,3),(5,6),(7,8)]
 => [3,4,2,1,6,5,8,7] => ? = 3 + 3
[3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [(1,6),(2,5),(3,4),(7,10),(8,9)]
 => [4,5,6,3,2,1,9,10,8,7] => ? = 5 + 3
[3,2,1]
 => [1,0,1,0,1,0,1,0]
 => [(1,2),(3,4),(5,6),(7,8)]
 => [2,1,4,3,6,5,8,7] => 3 = 0 + 3
[4,2,1]
 => [1,1,0,1,0,1,0,0,1,0]
 => [(1,8),(2,3),(4,5),(6,7),(9,10)]
 => [3,5,2,7,4,8,6,1,10,9] => ? = 2 + 3
[3,3,1]
 => [1,1,0,1,0,0,1,1,0,0]
 => [(1,6),(2,3),(4,5),(7,10),(8,9)]
 => [3,5,2,6,4,1,9,10,8,7] => ? = 4 + 3
[3,2,2]
 => [1,1,0,0,1,1,0,1,0,0]
 => [(1,4),(2,3),(5,10),(6,7),(8,9)]
 => [3,4,2,1,7,9,6,10,8,5] => ? = 3 + 3
[4,3,1]
 => [1,1,0,1,0,0,1,0,1,0]
 => [(1,6),(2,3),(4,5),(7,8),(9,10)]
 => [3,5,2,6,4,1,8,7,10,9] => ? = 3 + 3
[4,2,2]
 => [1,1,0,0,1,1,0,0,1,0]
 => [(1,4),(2,3),(5,8),(6,7),(9,10)]
 => [3,4,2,1,7,8,6,5,10,9] => ? = 4 + 3
[4,4,1]
 => [1,1,1,0,1,0,0,0,1,1,0,0]
 => [(1,8),(2,7),(3,4),(5,6),(9,12),(10,11)]
 => [4,6,7,3,8,5,2,1,11,12,10,9] => ? = 5 + 3
[4,3,2]
 => [1,1,0,0,1,0,1,0,1,0]
 => [(1,4),(2,3),(5,6),(7,8),(9,10)]
 => [3,4,2,1,6,5,8,7,10,9] => ? = 4 + 3
[3,3,3]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => [(1,6),(2,5),(3,4),(7,12),(8,11),(9,10)]
 => [4,5,6,3,2,1,10,11,12,9,8,7] => ? = 8 + 3
[4,4,2]
 => [1,1,1,0,0,1,0,0,1,1,0,0]
 => [(1,8),(2,5),(3,4),(6,7),(9,12),(10,11)]
 => [4,5,7,3,2,8,6,1,11,12,10,9] => ? = 6 + 3
[4,3,3]
 => [1,1,1,0,0,0,1,1,0,1,0,0]
 => [(1,6),(2,5),(3,4),(7,12),(8,9),(10,11)]
 => [4,5,6,3,2,1,9,11,8,12,10,7] => ? = 7 + 3
[4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => [(1,2),(3,4),(5,6),(7,8),(9,10)]
 => [2,1,4,3,6,5,8,7,10,9] => 3 = 0 + 3
[5,3,2,1]
 => [1,1,0,1,0,1,0,1,0,0,1,0]
 => [(1,10),(2,3),(4,5),(6,7),(8,9),(11,12)]
 => [3,5,2,7,4,9,6,10,8,1,12,11] => ? = 2 + 3
[4,4,2,1]
 => [1,1,0,1,0,1,0,0,1,1,0,0]
 => [(1,8),(2,3),(4,5),(6,7),(9,12),(10,11)]
 => [3,5,2,7,4,8,6,1,11,12,10,9] => ? = 5 + 3
[4,3,3,1]
 => [1,1,0,1,0,0,1,1,0,1,0,0]
 => [(1,6),(2,3),(4,5),(7,12),(8,9),(10,11)]
 => [3,5,2,6,4,1,9,11,8,12,10,7] => ? = 4 + 3
[4,3,2,2]
 => [1,1,0,0,1,1,0,1,0,1,0,0]
 => [(1,4),(2,3),(5,12),(6,7),(8,9),(10,11)]
 => [3,4,2,1,7,9,6,11,8,12,10,5] => ? = 3 + 3
[5,4,2,1]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => [(1,8),(2,3),(4,5),(6,7),(9,10),(11,12)]
 => [3,5,2,7,4,8,6,1,10,9,12,11] => ? = 3 + 3
[5,3,3,1]
 => [1,1,0,1,0,0,1,1,0,0,1,0]
 => [(1,6),(2,3),(4,5),(7,10),(8,9),(11,12)]
 => [3,5,2,6,4,1,9,10,8,7,12,11] => ? = 5 + 3
[5,3,2,2]
 => [1,1,0,0,1,1,0,1,0,0,1,0]
 => [(1,4),(2,3),(5,10),(6,7),(8,9),(11,12)]
 => [3,4,2,1,7,9,6,10,8,5,12,11] => ? = 4 + 3
[4,4,4]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => [(1,8),(2,7),(3,6),(4,5),(9,14),(10,13),(11,12)]
 => [5,6,7,8,4,3,2,1,12,13,14,11,10,9] => ? = 11 + 3
[4,4,2,2]
 => [1,1,0,0,1,1,0,0,1,1,0,0]
 => [(1,4),(2,3),(5,8),(6,7),(9,12),(10,11)]
 => [3,4,2,1,7,8,6,5,11,12,10,9] => ? = 5 + 3
[5,5,2,1]
 => [1,1,1,0,1,0,1,0,0,0,1,1,0,0]
 => [(1,10),(2,9),(3,4),(5,6),(7,8),(11,14),(12,13)]
 => [4,6,8,3,9,5,10,7,2,1,13,14,12,11] => ? = 5 + 3
[5,4,3,1]
 => [1,1,0,1,0,0,1,0,1,0,1,0]
 => [(1,6),(2,3),(4,5),(7,8),(9,10),(11,12)]
 => [3,5,2,6,4,1,8,7,10,9,12,11] => ? = 4 + 3
[5,4,2,2]
 => [1,1,0,0,1,1,0,0,1,0,1,0]
 => [(1,4),(2,3),(5,8),(6,7),(9,10),(11,12)]
 => [3,4,2,1,7,8,6,5,10,9,12,11] => ? = 5 + 3
[4,4,4,1]
 => [1,1,1,0,1,0,0,0,1,1,1,0,0,0]
 => [(1,8),(2,7),(3,4),(5,6),(9,14),(10,13),(11,12)]
 => [4,6,7,3,8,5,2,1,12,13,14,11,10,9] => ? = 10 + 3
[4,3,3,3]
 => [1,1,1,0,0,0,1,1,1,0,1,0,0,0]
 => [(1,6),(2,5),(3,4),(7,14),(8,13),(9,10),(11,12)]
 => [4,5,6,3,2,1,10,12,13,9,14,11,8,7] => ? = 8 + 3
[5,5,3,1]
 => [1,1,1,0,1,0,0,1,0,0,1,1,0,0]
 => [(1,10),(2,7),(3,4),(5,6),(8,9),(11,14),(12,13)]
 => [4,6,7,3,9,5,2,10,8,1,13,14,12,11] => ? = 6 + 3
[5,5,2,2]
 => [1,1,1,0,0,1,1,0,0,0,1,1,0,0]
 => [(1,10),(2,5),(3,4),(6,9),(7,8),(11,14),(12,13)]
 => [4,5,8,3,2,9,10,7,6,1,13,14,12,11] => ? = 8 + 3
[5,4,4,1]
 => [1,1,1,0,1,0,0,0,1,1,0,1,0,0]
 => [(1,8),(2,7),(3,4),(5,6),(9,14),(10,11),(12,13)]
 => [4,6,7,3,8,5,2,1,11,13,10,14,12,9] => ? = 7 + 3
[5,4,3,2]
 => [1,1,0,0,1,0,1,0,1,0,1,0]
 => [(1,4),(2,3),(5,6),(7,8),(9,10),(11,12)]
 => [3,4,2,1,6,5,8,7,10,9,12,11] => ? = 5 + 3
[5,3,3,3]
 => [1,1,1,0,0,0,1,1,1,0,0,1,0,0]
 => [(1,6),(2,5),(3,4),(7,14),(8,11),(9,10),(12,13)]
 => [4,5,6,3,2,1,10,11,13,9,8,14,12,7] => ? = 10 + 3
[5,5,3,2]
 => [1,1,1,0,0,1,0,1,0,0,1,1,0,0]
 => [(1,10),(2,5),(3,4),(6,7),(8,9),(11,14),(12,13)]
 => [4,5,7,3,2,9,6,10,8,1,13,14,12,11] => ? = 7 + 3
[5,4,4,2]
 => [1,1,1,0,0,1,0,0,1,1,0,1,0,0]
 => [(1,8),(2,5),(3,4),(6,7),(9,14),(10,11),(12,13)]
 => [4,5,7,3,2,8,6,1,11,13,10,14,12,9] => ? = 8 + 3
[5,4,3,3]
 => [1,1,1,0,0,0,1,1,0,1,0,1,0,0]
 => [(1,6),(2,5),(3,4),(7,14),(8,9),(10,11),(12,13)]
 => [4,5,6,3,2,1,9,11,8,13,10,14,12,7] => ? = 9 + 3
[5,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]
 => [2,1,4,3,6,5,8,7,10,9,12,11] => 3 = 0 + 3
[6,4,3,2,1]
 => [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
 => [(1,12),(2,3),(4,5),(6,7),(8,9),(10,11),(13,14)]
 => [3,5,2,7,4,9,6,11,8,12,10,1,14,13] => ? = 2 + 3
[5,5,3,3]
 => [1,1,1,0,0,0,1,1,0,0,1,1,0,0]
 => [(1,6),(2,5),(3,4),(7,10),(8,9),(11,14),(12,13)]
 => [4,5,6,3,2,1,9,10,8,7,13,14,12,11] => ? = 7 + 3
[5,5,3,2,1]
 => [1,1,0,1,0,1,0,1,0,0,1,1,0,0]
 => [(1,10),(2,3),(4,5),(6,7),(8,9),(11,14),(12,13)]
 => [3,5,2,7,4,9,6,10,8,1,13,14,12,11] => ? = 6 + 3
[5,4,4,2,1]
 => [1,1,0,1,0,1,0,0,1,1,0,1,0,0]
 => [(1,8),(2,3),(4,5),(6,7),(9,14),(10,11),(12,13)]
 => [3,5,2,7,4,8,6,1,11,13,10,14,12,9] => ? = 5 + 3
[5,4,3,3,1]
 => [1,1,0,1,0,0,1,1,0,1,0,1,0,0]
 => [(1,6),(2,3),(4,5),(7,14),(8,9),(10,11),(12,13)]
 => [3,5,2,6,4,1,9,11,8,13,10,14,12,7] => ? = 4 + 3
[5,4,3,2,2]
 => [1,1,0,0,1,1,0,1,0,1,0,1,0,0]
 => [(1,4),(2,3),(5,14),(6,7),(8,9),(10,11),(12,13)]
 => [3,4,2,1,7,9,6,11,8,13,10,14,12,5] => ? = 3 + 3
[6,5,3,2,1]
 => [1,1,0,1,0,1,0,1,0,0,1,0,1,0]
 => [(1,10),(2,3),(4,5),(6,7),(8,9),(11,12),(13,14)]
 => [3,5,2,7,4,9,6,10,8,1,12,11,14,13] => ? = 3 + 3
[6,4,4,2,1]
 => [1,1,0,1,0,1,0,0,1,1,0,0,1,0]
 => [(1,8),(2,3),(4,5),(6,7),(9,12),(10,11),(13,14)]
 => [3,5,2,7,4,8,6,1,11,12,10,9,14,13] => ? = 6 + 3
[6,4,3,3,1]
 => [1,1,0,1,0,0,1,1,0,1,0,0,1,0]
 => [(1,6),(2,3),(4,5),(7,12),(8,9),(10,11),(13,14)]
 => [3,5,2,6,4,1,9,11,8,12,10,7,14,13] => ? = 5 + 3
[6,4,3,2,2]
 => [1,1,0,0,1,1,0,1,0,1,0,0,1,0]
 => [(1,4),(2,3),(5,12),(6,7),(8,9),(10,11),(13,14)]
 => [3,4,2,1,7,9,6,11,8,12,10,5,14,13] => ? = 4 + 3
[5,5,3,3,1]
 => [1,1,0,1,0,0,1,1,0,0,1,1,0,0]
 => [(1,6),(2,3),(4,5),(7,10),(8,9),(11,14),(12,13)]
 => [3,5,2,6,4,1,9,10,8,7,13,14,12,11] => ? = 6 + 3
[5,5,3,2,2]
 => [1,1,0,0,1,1,0,1,0,0,1,1,0,0]
 => [(1,4),(2,3),(5,10),(6,7),(8,9),(11,14),(12,13)]
 => [3,4,2,1,7,9,6,10,8,5,13,14,12,11] => ? = 6 + 3
[5,4,4,2,2]
 => [1,1,0,0,1,1,0,0,1,1,0,1,0,0]
 => [(1,4),(2,3),(5,8),(6,7),(9,14),(10,11),(12,13)]
 => [3,4,2,1,7,8,6,5,11,13,10,14,12,9] => ? = 5 + 3
[6,5,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,14)]
 => [2,1,4,3,6,5,8,7,10,9,12,11,14,13] => ? = 0 + 3
[6,5,4,3,2]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0]
 => [(1,4),(2,3),(5,6),(7,8),(9,10),(11,12),(13,14)]
 => [3,4,2,1,6,5,8,7,10,9,12,11,14,13] => ? = 6 + 3
Description
The maximal size of a rise in a permutation. This is $\max_i \sigma_{i+1}-\sigma_i$, except for the permutations without rises, where it is $0$.