Your data matches 6 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000259
(load all 4 compositions to match this statistic)
Mapping
Mp00254: Permutations —Inverse fireworks map⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00157: Graphs —connected complement⟶ Graphs
St000259: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => [1] => ([],1)
 => ([],1)
 => 0
[2,1] => [2,1] => ([(0,1)],2)
 => ([(0,1)],2)
 => 1
[3,1,2] => [3,1,2] => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 2
[3,2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
[2,4,1,3] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
[3,4,1,2] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
[4,1,2,3] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => 2
[4,1,3,2] => [4,1,3,2] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 2
[4,2,1,3] => [4,2,1,3] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 2
[4,2,3,1] => [4,1,3,2] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 2
[4,3,1,2] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
[4,3,2,1] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
[2,5,1,3,4] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => 3
[2,5,1,4,3] => [2,5,1,4,3] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 3
[2,5,4,1,3] => [2,5,4,1,3] => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 3
[3,1,5,2,4] => [3,1,5,2,4] => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
[3,2,5,1,4] => [3,2,5,1,4] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 3
[3,5,1,2,4] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 3
[3,5,1,4,2] => [2,5,1,4,3] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 3
[3,5,2,1,4] => [3,5,2,1,4] => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 3
[3,5,2,4,1] => [2,5,1,4,3] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 3
[3,5,4,1,2] => [2,5,4,1,3] => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 3
[4,1,5,2,3] => [3,1,5,2,4] => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
[4,2,5,1,3] => [3,2,5,1,4] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 3
[4,3,5,1,2] => [3,2,5,1,4] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 3
[4,5,1,2,3] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 3
[4,5,1,3,2] => [2,5,1,4,3] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 3
[4,5,2,1,3] => [3,5,2,1,4] => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 3
[4,5,2,3,1] => [2,5,1,4,3] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 3
[4,5,3,1,2] => [2,5,4,1,3] => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 3
[5,1,2,3,4] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2
[5,1,2,4,3] => [5,1,2,4,3] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[5,1,3,2,4] => [5,1,3,2,4] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[5,1,3,4,2] => [5,1,2,4,3] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[5,1,4,2,3] => [5,1,4,2,3] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[5,1,4,3,2] => [5,1,4,3,2] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[5,2,1,3,4] => [5,2,1,3,4] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[5,2,1,4,3] => [5,2,1,4,3] => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => 2
[5,2,3,1,4] => [5,1,3,2,4] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[5,2,3,4,1] => [5,1,2,4,3] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[5,2,4,1,3] => [5,2,4,1,3] => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[5,2,4,3,1] => [5,1,4,3,2] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[5,3,1,2,4] => [5,3,1,2,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[5,3,1,4,2] => [5,2,1,4,3] => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => 2
[5,3,2,1,4] => [5,3,2,1,4] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[5,3,2,4,1] => [5,2,1,4,3] => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => 2
[5,3,4,1,2] => [5,2,4,1,3] => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[5,3,4,2,1] => [5,1,4,3,2] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[5,4,1,2,3] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[5,4,1,3,2] => [5,4,1,3,2] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
Description
The diameter of a connected graph. This is the greatest distance between any pair of vertices.
Matching statistic: St000455
(load all 5 compositions to match this statistic)
Mapping
Mp00061: Permutations —to increasing tree⟶ Binary trees
Mp00014: Binary trees —to 132-avoiding permutation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000455: Graphs ⟶ ℤResult quality: 24% ●values known / values provided: 24%●distinct values known / distinct values provided: 25%
Values
[1] => [.,.]
 => [1] => ([],1)
 => ? = 0 - 2
[2,1] => [[.,.],.]
 => [1,2] => ([],2)
 => ? = 1 - 2
[3,1,2] => [[.,.],[.,.]]
 => [3,1,2] => ([(0,2),(1,2)],3)
 => 0 = 2 - 2
[3,2,1] => [[[.,.],.],.]
 => [1,2,3] => ([],3)
 => ? = 1 - 2
[2,4,1,3] => [[.,[.,.]],[.,.]]
 => [4,2,1,3] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 3 - 2
[3,4,1,2] => [[.,[.,.]],[.,.]]
 => [4,2,1,3] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 3 - 2
[4,1,2,3] => [[.,.],[.,[.,.]]]
 => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 0 = 2 - 2
[4,1,3,2] => [[.,.],[[.,.],.]]
 => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 0 = 2 - 2
[4,2,1,3] => [[[.,.],.],[.,.]]
 => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4)
 => 0 = 2 - 2
[4,2,3,1] => [[[.,.],[.,.]],.]
 => [3,1,2,4] => ([(1,3),(2,3)],4)
 => 0 = 2 - 2
[4,3,1,2] => [[[.,.],.],[.,.]]
 => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4)
 => 0 = 2 - 2
[4,3,2,1] => [[[[.,.],.],.],.]
 => [1,2,3,4] => ([],4)
 => ? = 1 - 2
[2,5,1,3,4] => [[.,[.,.]],[.,[.,.]]]
 => [5,4,2,1,3] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 3 - 2
[2,5,1,4,3] => [[.,[.,.]],[[.,.],.]]
 => [4,5,2,1,3] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ? = 3 - 2
[2,5,4,1,3] => [[.,[[.,.],.]],[.,.]]
 => [5,2,3,1,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 3 - 2
[3,1,5,2,4] => [[.,.],[[.,.],[.,.]]]
 => [5,3,4,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 0 = 2 - 2
[3,2,5,1,4] => [[[.,.],[.,.]],[.,.]]
 => [5,3,1,2,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 3 - 2
[3,5,1,2,4] => [[.,[.,.]],[.,[.,.]]]
 => [5,4,2,1,3] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 3 - 2
[3,5,1,4,2] => [[.,[.,.]],[[.,.],.]]
 => [4,5,2,1,3] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ? = 3 - 2
[3,5,2,1,4] => [[[.,[.,.]],.],[.,.]]
 => [5,2,1,3,4] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 3 - 2
[3,5,2,4,1] => [[[.,[.,.]],[.,.]],.]
 => [4,2,1,3,5] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 3 - 2
[3,5,4,1,2] => [[.,[[.,.],.]],[.,.]]
 => [5,2,3,1,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 3 - 2
[4,1,5,2,3] => [[.,.],[[.,.],[.,.]]]
 => [5,3,4,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 0 = 2 - 2
[4,2,5,1,3] => [[[.,.],[.,.]],[.,.]]
 => [5,3,1,2,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 3 - 2
[4,3,5,1,2] => [[[.,.],[.,.]],[.,.]]
 => [5,3,1,2,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 3 - 2
[4,5,1,2,3] => [[.,[.,.]],[.,[.,.]]]
 => [5,4,2,1,3] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 3 - 2
[4,5,1,3,2] => [[.,[.,.]],[[.,.],.]]
 => [4,5,2,1,3] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ? = 3 - 2
[4,5,2,1,3] => [[[.,[.,.]],.],[.,.]]
 => [5,2,1,3,4] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 3 - 2
[4,5,2,3,1] => [[[.,[.,.]],[.,.]],.]
 => [4,2,1,3,5] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 3 - 2
[4,5,3,1,2] => [[[.,[.,.]],.],[.,.]]
 => [5,2,1,3,4] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 3 - 2
[5,1,2,3,4] => [[.,.],[.,[.,[.,.]]]]
 => [5,4,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 0 = 2 - 2
[5,1,2,4,3] => [[.,.],[.,[[.,.],.]]]
 => [4,5,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 0 = 2 - 2
[5,1,3,2,4] => [[.,.],[[.,.],[.,.]]]
 => [5,3,4,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 0 = 2 - 2
[5,1,3,4,2] => [[.,.],[[.,[.,.]],.]]
 => [4,3,5,1,2] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ? = 2 - 2
[5,1,4,2,3] => [[.,.],[[.,.],[.,.]]]
 => [5,3,4,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 0 = 2 - 2
[5,1,4,3,2] => [[.,.],[[[.,.],.],.]]
 => [3,4,5,1,2] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 0 = 2 - 2
[5,2,1,3,4] => [[[.,.],.],[.,[.,.]]]
 => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 0 = 2 - 2
[5,2,1,4,3] => [[[.,.],.],[[.,.],.]]
 => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 0 = 2 - 2
[5,2,3,1,4] => [[[.,.],[.,.]],[.,.]]
 => [5,3,1,2,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 2 - 2
[5,2,3,4,1] => [[[.,.],[.,[.,.]]],.]
 => [4,3,1,2,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 0 = 2 - 2
[5,2,4,1,3] => [[[.,.],[.,.]],[.,.]]
 => [5,3,1,2,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 2 - 2
[5,2,4,3,1] => [[[.,.],[[.,.],.]],.]
 => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5)
 => 0 = 2 - 2
[5,3,1,2,4] => [[[.,.],.],[.,[.,.]]]
 => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 0 = 2 - 2
[5,3,1,4,2] => [[[.,.],.],[[.,.],.]]
 => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 0 = 2 - 2
[5,3,2,1,4] => [[[[.,.],.],.],[.,.]]
 => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 0 = 2 - 2
[5,3,2,4,1] => [[[[.,.],.],[.,.]],.]
 => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5)
 => 0 = 2 - 2
[5,3,4,1,2] => [[[.,.],[.,.]],[.,.]]
 => [5,3,1,2,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 2 - 2
[5,3,4,2,1] => [[[[.,.],[.,.]],.],.]
 => [3,1,2,4,5] => ([(2,4),(3,4)],5)
 => 0 = 2 - 2
[5,4,1,2,3] => [[[.,.],.],[.,[.,.]]]
 => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 0 = 2 - 2
[5,4,1,3,2] => [[[.,.],.],[[.,.],.]]
 => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 0 = 2 - 2
[5,4,2,1,3] => [[[[.,.],.],.],[.,.]]
 => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 0 = 2 - 2
[5,4,2,3,1] => [[[[.,.],.],[.,.]],.]
 => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5)
 => 0 = 2 - 2
[5,4,3,1,2] => [[[[.,.],.],.],[.,.]]
 => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 0 = 2 - 2
[5,4,3,2,1] => [[[[[.,.],.],.],.],.]
 => [1,2,3,4,5] => ([],5)
 => ? = 1 - 2
[2,4,1,6,3,5] => [[.,[.,.]],[[.,.],[.,.]]]
 => [6,4,5,2,1,3] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 2 - 2
[2,4,6,1,3,5] => [[.,[.,[.,.]]],[.,[.,.]]]
 => [6,5,3,2,1,4] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 - 2
[2,5,1,6,3,4] => [[.,[.,.]],[[.,.],[.,.]]]
 => [6,4,5,2,1,3] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 2 - 2
[2,5,6,1,3,4] => [[.,[.,[.,.]]],[.,[.,.]]]
 => [6,5,3,2,1,4] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 - 2
[2,6,1,3,4,5] => [[.,[.,.]],[.,[.,[.,.]]]]
 => [6,5,4,2,1,3] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 - 2
[2,6,1,3,5,4] => [[.,[.,.]],[.,[[.,.],.]]]
 => [5,6,4,2,1,3] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 3 - 2
[2,6,1,4,3,5] => [[.,[.,.]],[[.,.],[.,.]]]
 => [6,4,5,2,1,3] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 3 - 2
[2,6,1,4,5,3] => [[.,[.,.]],[[.,[.,.]],.]]
 => [5,4,6,2,1,3] => ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 - 2
[2,6,1,5,3,4] => [[.,[.,.]],[[.,.],[.,.]]]
 => [6,4,5,2,1,3] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 3 - 2
[2,6,1,5,4,3] => [[.,[.,.]],[[[.,.],.],.]]
 => [4,5,6,2,1,3] => ([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 - 2
[2,6,4,1,3,5] => [[.,[[.,.],.]],[.,[.,.]]]
 => [6,5,2,3,1,4] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 - 2
[2,6,5,1,3,4] => [[.,[[.,.],.]],[.,[.,.]]]
 => [6,5,2,3,1,4] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 - 2
[2,6,5,1,4,3] => [[.,[[.,.],.]],[[.,.],.]]
 => [5,6,2,3,1,4] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ? = 3 - 2
[2,6,5,4,1,3] => [[.,[[[.,.],.],.]],[.,.]]
 => [6,2,3,4,1,5] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 - 2
[3,1,6,2,4,5] => [[.,.],[[.,.],[.,[.,.]]]]
 => [6,5,3,4,1,2] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 0 = 2 - 2
[3,1,6,2,5,4] => [[.,.],[[.,.],[[.,.],.]]]
 => [5,6,3,4,1,2] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 0 = 2 - 2
[3,1,6,5,2,4] => [[.,.],[[[.,.],.],[.,.]]]
 => [6,3,4,5,1,2] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 0 = 2 - 2
[3,2,6,1,4,5] => [[[.,.],[.,.]],[.,[.,.]]]
 => [6,5,3,1,2,4] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 - 2
[3,2,6,1,5,4] => [[[.,.],[.,.]],[[.,.],.]]
 => [5,6,3,1,2,4] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ? = 3 - 2
[3,2,6,5,1,4] => [[[.,.],[[.,.],.]],[.,.]]
 => [6,3,4,1,2,5] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 3 - 2
[3,4,1,6,2,5] => [[.,[.,.]],[[.,.],[.,.]]]
 => [6,4,5,2,1,3] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 2 - 2
[3,4,6,1,2,5] => [[.,[.,[.,.]]],[.,[.,.]]]
 => [6,5,3,2,1,4] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 - 2
[3,5,1,6,2,4] => [[.,[.,.]],[[.,.],[.,.]]]
 => [6,4,5,2,1,3] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 2 - 2
[3,5,6,1,2,4] => [[.,[.,[.,.]]],[.,[.,.]]]
 => [6,5,3,2,1,4] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 - 2
[3,6,1,2,4,5] => [[.,[.,.]],[.,[.,[.,.]]]]
 => [6,5,4,2,1,3] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 - 2
[3,6,1,2,5,4] => [[.,[.,.]],[.,[[.,.],.]]]
 => [5,6,4,2,1,3] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 3 - 2
[4,1,2,6,3,5] => [[.,.],[.,[[.,.],[.,.]]]]
 => [6,4,5,3,1,2] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 0 = 2 - 2
[4,1,6,2,3,5] => [[.,.],[[.,.],[.,[.,.]]]]
 => [6,5,3,4,1,2] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 0 = 2 - 2
[4,1,6,2,5,3] => [[.,.],[[.,.],[[.,.],.]]]
 => [5,6,3,4,1,2] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 0 = 2 - 2
[4,1,6,3,2,5] => [[.,.],[[[.,.],.],[.,.]]]
 => [6,3,4,5,1,2] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 0 = 2 - 2
[4,1,6,5,2,3] => [[.,.],[[[.,.],.],[.,.]]]
 => [6,3,4,5,1,2] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 0 = 2 - 2
[4,2,1,6,3,5] => [[[.,.],.],[[.,.],[.,.]]]
 => [6,4,5,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 0 = 2 - 2
[4,2,6,3,5,1] => [[[.,.],[[.,.],[.,.]]],.]
 => [5,3,4,1,2,6] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 0 = 2 - 2
[4,3,1,6,2,5] => [[[.,.],.],[[.,.],[.,.]]]
 => [6,4,5,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 0 = 2 - 2
[5,1,2,6,3,4] => [[.,.],[.,[[.,.],[.,.]]]]
 => [6,4,5,3,1,2] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 0 = 2 - 2
[5,1,6,2,3,4] => [[.,.],[[.,.],[.,[.,.]]]]
 => [6,5,3,4,1,2] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 0 = 2 - 2
[5,1,6,2,4,3] => [[.,.],[[.,.],[[.,.],.]]]
 => [5,6,3,4,1,2] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 0 = 2 - 2
[5,1,6,3,2,4] => [[.,.],[[[.,.],.],[.,.]]]
 => [6,3,4,5,1,2] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 0 = 2 - 2
[5,1,6,4,2,3] => [[.,.],[[[.,.],.],[.,.]]]
 => [6,3,4,5,1,2] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 0 = 2 - 2
[5,2,1,6,3,4] => [[[.,.],.],[[.,.],[.,.]]]
 => [6,4,5,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 0 = 2 - 2
[5,2,6,3,4,1] => [[[.,.],[[.,.],[.,.]]],.]
 => [5,3,4,1,2,6] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 0 = 2 - 2
[5,3,1,6,2,4] => [[[.,.],.],[[.,.],[.,.]]]
 => [6,4,5,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 0 = 2 - 2
[5,4,1,6,2,3] => [[[.,.],.],[[.,.],[.,.]]]
 => [6,4,5,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 0 = 2 - 2
[6,1,2,3,4,5] => [[.,.],[.,[.,[.,[.,.]]]]]
 => [6,5,4,3,1,2] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 0 = 2 - 2
[6,1,2,3,5,4] => [[.,.],[.,[.,[[.,.],.]]]]
 => [5,6,4,3,1,2] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 0 = 2 - 2
[6,1,2,4,3,5] => [[.,.],[.,[[.,.],[.,.]]]]
 => [6,4,5,3,1,2] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 0 = 2 - 2
Description
The second largest eigenvalue of a graph if it is integral. This statistic is undefined if the second largest eigenvalue of the graph is not integral. Chapter 4 of [1] provides lots of context.
Matching statistic: St001199
Mapping
Mp00066: Permutations —inverse⟶ Permutations
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
St001199: Dyck paths ⟶ ℤResult quality: 15% ●values known / values provided: 15%●distinct values known / distinct values provided: 25%
Values
[1] => [1] => [1] => [1,0]
 => ? = 0 - 1
[2,1] => [2,1] => [2,1] => [1,1,0,0]
 => ? = 1 - 1
[3,1,2] => [2,3,1] => [3,2,1] => [1,1,1,0,0,0]
 => ? = 2 - 1
[3,2,1] => [3,2,1] => [3,2,1] => [1,1,1,0,0,0]
 => ? = 1 - 1
[2,4,1,3] => [3,1,4,2] => [4,2,3,1] => [1,1,1,1,0,0,0,0]
 => ? = 3 - 1
[3,4,1,2] => [3,4,1,2] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
 => ? = 3 - 1
[4,1,2,3] => [2,3,4,1] => [4,2,3,1] => [1,1,1,1,0,0,0,0]
 => ? = 2 - 1
[4,1,3,2] => [2,4,3,1] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
 => ? = 2 - 1
[4,2,1,3] => [3,2,4,1] => [4,2,3,1] => [1,1,1,1,0,0,0,0]
 => ? = 2 - 1
[4,2,3,1] => [4,2,3,1] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
 => ? = 2 - 1
[4,3,1,2] => [3,4,2,1] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
 => ? = 2 - 1
[4,3,2,1] => [4,3,2,1] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
 => ? = 1 - 1
[2,5,1,3,4] => [3,1,4,5,2] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3 - 1
[2,5,1,4,3] => [3,1,5,4,2] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3 - 1
[2,5,4,1,3] => [4,1,5,3,2] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3 - 1
[3,1,5,2,4] => [2,4,1,5,3] => [3,5,1,4,2] => [1,1,1,0,1,1,0,0,0,0]
 => 1 = 2 - 1
[3,2,5,1,4] => [4,2,1,5,3] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3 - 1
[3,5,1,2,4] => [3,4,1,5,2] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3 - 1
[3,5,1,4,2] => [3,5,1,4,2] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3 - 1
[3,5,2,1,4] => [4,3,1,5,2] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3 - 1
[3,5,2,4,1] => [5,3,1,4,2] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3 - 1
[3,5,4,1,2] => [4,5,1,3,2] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3 - 1
[4,1,5,2,3] => [2,4,5,1,3] => [4,5,3,1,2] => [1,1,1,1,0,1,0,0,0,0]
 => 1 = 2 - 1
[4,2,5,1,3] => [4,2,5,1,3] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3 - 1
[4,3,5,1,2] => [4,5,2,1,3] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3 - 1
[4,5,1,2,3] => [3,4,5,1,2] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3 - 1
[4,5,1,3,2] => [3,5,4,1,2] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3 - 1
[4,5,2,1,3] => [4,3,5,1,2] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3 - 1
[4,5,2,3,1] => [5,3,4,1,2] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3 - 1
[4,5,3,1,2] => [4,5,3,1,2] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3 - 1
[5,1,2,3,4] => [2,3,4,5,1] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2 - 1
[5,1,2,4,3] => [2,3,5,4,1] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2 - 1
[5,1,3,2,4] => [2,4,3,5,1] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2 - 1
[5,1,3,4,2] => [2,5,3,4,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2 - 1
[5,1,4,2,3] => [2,4,5,3,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2 - 1
[5,1,4,3,2] => [2,5,4,3,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2 - 1
[5,2,1,3,4] => [3,2,4,5,1] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2 - 1
[5,2,1,4,3] => [3,2,5,4,1] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2 - 1
[5,2,3,1,4] => [4,2,3,5,1] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2 - 1
[5,2,3,4,1] => [5,2,3,4,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2 - 1
[5,2,4,1,3] => [4,2,5,3,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2 - 1
[5,2,4,3,1] => [5,2,4,3,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2 - 1
[5,3,1,2,4] => [3,4,2,5,1] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2 - 1
[5,3,1,4,2] => [3,5,2,4,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2 - 1
[5,3,2,1,4] => [4,3,2,5,1] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2 - 1
[5,3,2,4,1] => [5,3,2,4,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2 - 1
[5,3,4,1,2] => [4,5,2,3,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2 - 1
[5,3,4,2,1] => [5,4,2,3,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2 - 1
[5,4,1,2,3] => [3,4,5,2,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2 - 1
[5,4,1,3,2] => [3,5,4,2,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2 - 1
[5,4,2,1,3] => [4,3,5,2,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2 - 1
[5,4,2,3,1] => [5,3,4,2,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2 - 1
[2,4,1,6,3,5] => [3,1,5,2,6,4] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0]
 => 1 = 2 - 1
[2,5,1,6,3,4] => [3,1,5,6,2,4] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 1 = 2 - 1
[3,1,6,2,4,5] => [2,4,1,5,6,3] => [3,6,1,4,5,2] => [1,1,1,0,1,1,1,0,0,0,0,0]
 => 1 = 2 - 1
[3,1,6,2,5,4] => [2,4,1,6,5,3] => [3,6,1,5,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0]
 => 1 = 2 - 1
[3,1,6,5,2,4] => [2,5,1,6,4,3] => [3,6,1,5,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0]
 => 1 = 2 - 1
[3,4,1,6,2,5] => [3,5,1,2,6,4] => [4,6,3,1,5,2] => [1,1,1,1,0,1,1,0,0,0,0,0]
 => 1 = 2 - 1
[3,5,1,6,2,4] => [3,5,1,6,2,4] => [5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 1 = 2 - 1
[4,1,2,6,3,5] => [2,3,5,1,6,4] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0]
 => 1 = 2 - 1
[4,1,3,6,2,5] => [2,5,3,1,6,4] => [4,6,3,1,5,2] => [1,1,1,1,0,1,1,0,0,0,0,0]
 => 1 = 2 - 1
[4,1,6,2,3,5] => [2,4,5,1,6,3] => [4,6,3,1,5,2] => [1,1,1,1,0,1,1,0,0,0,0,0]
 => 1 = 2 - 1
[4,1,6,2,5,3] => [2,4,6,1,5,3] => [4,6,5,1,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0]
 => 1 = 2 - 1
[4,1,6,3,2,5] => [2,5,4,1,6,3] => [4,6,3,1,5,2] => [1,1,1,1,0,1,1,0,0,0,0,0]
 => 1 = 2 - 1
[4,1,6,3,5,2] => [2,6,4,1,5,3] => [4,6,5,1,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0]
 => 1 = 2 - 1
[4,1,6,5,2,3] => [2,5,6,1,4,3] => [4,6,5,1,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0]
 => 1 = 2 - 1
[4,2,1,6,3,5] => [3,2,5,1,6,4] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0]
 => 1 = 2 - 1
[4,3,1,6,2,5] => [3,5,2,1,6,4] => [4,6,3,1,5,2] => [1,1,1,1,0,1,1,0,0,0,0,0]
 => 1 = 2 - 1
[4,5,1,6,2,3] => [3,5,6,1,2,4] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 1 = 2 - 1
[5,1,2,6,3,4] => [2,3,5,6,1,4] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 1 = 2 - 1
[5,1,3,6,2,4] => [2,5,3,6,1,4] => [5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 1 = 2 - 1
[5,1,4,6,2,3] => [2,5,6,3,1,4] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 1 = 2 - 1
[5,1,6,2,3,4] => [2,4,5,6,1,3] => [5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 1 = 2 - 1
[5,1,6,2,4,3] => [2,4,6,5,1,3] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 1 = 2 - 1
[5,1,6,3,2,4] => [2,5,4,6,1,3] => [5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 1 = 2 - 1
[5,1,6,3,4,2] => [2,6,4,5,1,3] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 1 = 2 - 1
[5,1,6,4,2,3] => [2,5,6,4,1,3] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 1 = 2 - 1
[5,2,1,6,3,4] => [3,2,5,6,1,4] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 1 = 2 - 1
[5,3,1,6,2,4] => [3,5,2,6,1,4] => [5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 1 = 2 - 1
[5,4,1,6,2,3] => [3,5,6,2,1,4] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 1 = 2 - 1
[2,4,1,7,3,5,6] => [3,1,5,2,6,7,4] => [4,2,7,1,5,6,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => 1 = 2 - 1
[2,4,1,7,3,6,5] => [3,1,5,2,7,6,4] => [4,2,7,1,6,5,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => 1 = 2 - 1
[2,4,1,7,6,3,5] => [3,1,6,2,7,5,4] => [4,2,7,1,6,5,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => 1 = 2 - 1
[2,5,1,3,7,4,6] => [3,1,4,6,2,7,5] => [5,2,3,7,1,6,4] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0]
 => 1 = 2 - 1
[2,5,1,4,7,3,6] => [3,1,6,4,2,7,5] => [5,2,7,4,1,6,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0]
 => 1 = 2 - 1
[2,5,1,7,3,4,6] => [3,1,5,6,2,7,4] => [5,2,7,4,1,6,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0]
 => 1 = 2 - 1
[2,5,1,7,3,6,4] => [3,1,5,7,2,6,4] => [5,2,7,6,1,4,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0]
 => 1 = 2 - 1
[2,5,1,7,4,3,6] => [3,1,6,5,2,7,4] => [5,2,7,4,1,6,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0]
 => 1 = 2 - 1
[2,5,1,7,4,6,3] => [3,1,7,5,2,6,4] => [5,2,7,6,1,4,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0]
 => 1 = 2 - 1
[2,5,1,7,6,3,4] => [3,1,6,7,2,5,4] => [5,2,7,6,1,4,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0]
 => 1 = 2 - 1
[2,5,4,1,7,3,6] => [4,1,6,3,2,7,5] => [5,2,7,4,1,6,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0]
 => 1 = 2 - 1
[2,6,1,3,7,4,5] => [3,1,4,6,7,2,5] => [6,2,3,7,5,1,4] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => 1 = 2 - 1
[2,6,1,4,7,3,5] => [3,1,6,4,7,2,5] => [6,2,7,4,5,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => 1 = 2 - 1
[2,6,1,5,7,3,4] => [3,1,6,7,4,2,5] => [6,2,7,5,4,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => 1 = 2 - 1
[2,6,1,7,3,4,5] => [3,1,5,6,7,2,4] => [6,2,7,4,5,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => 1 = 2 - 1
[2,6,1,7,3,5,4] => [3,1,5,7,6,2,4] => [6,2,7,5,4,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => 1 = 2 - 1
[2,6,1,7,4,3,5] => [3,1,6,5,7,2,4] => [6,2,7,4,5,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => 1 = 2 - 1
[2,6,1,7,4,5,3] => [3,1,7,5,6,2,4] => [6,2,7,5,4,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => 1 = 2 - 1
[2,6,1,7,5,3,4] => [3,1,6,7,5,2,4] => [6,2,7,5,4,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => 1 = 2 - 1
[2,6,4,1,7,3,5] => [4,1,6,3,7,2,5] => [6,2,7,4,5,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => 1 = 2 - 1
Description
The dominant dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$.
Matching statistic: St001498
Mapping
Mp00066: Permutations —inverse⟶ Permutations
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
St001498: Dyck paths ⟶ ℤResult quality: 15% ●values known / values provided: 15%●distinct values known / distinct values provided: 25%
Values
[1] => [1] => [1] => [1,0]
 => ? = 0 - 2
[2,1] => [2,1] => [2,1] => [1,1,0,0]
 => ? = 1 - 2
[3,1,2] => [2,3,1] => [3,2,1] => [1,1,1,0,0,0]
 => ? = 2 - 2
[3,2,1] => [3,2,1] => [3,2,1] => [1,1,1,0,0,0]
 => ? = 1 - 2
[2,4,1,3] => [3,1,4,2] => [4,2,3,1] => [1,1,1,1,0,0,0,0]
 => ? = 3 - 2
[3,4,1,2] => [3,4,1,2] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
 => ? = 3 - 2
[4,1,2,3] => [2,3,4,1] => [4,2,3,1] => [1,1,1,1,0,0,0,0]
 => ? = 2 - 2
[4,1,3,2] => [2,4,3,1] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
 => ? = 2 - 2
[4,2,1,3] => [3,2,4,1] => [4,2,3,1] => [1,1,1,1,0,0,0,0]
 => ? = 2 - 2
[4,2,3,1] => [4,2,3,1] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
 => ? = 2 - 2
[4,3,1,2] => [3,4,2,1] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
 => ? = 2 - 2
[4,3,2,1] => [4,3,2,1] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
 => ? = 1 - 2
[2,5,1,3,4] => [3,1,4,5,2] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3 - 2
[2,5,1,4,3] => [3,1,5,4,2] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3 - 2
[2,5,4,1,3] => [4,1,5,3,2] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3 - 2
[3,1,5,2,4] => [2,4,1,5,3] => [3,5,1,4,2] => [1,1,1,0,1,1,0,0,0,0]
 => 0 = 2 - 2
[3,2,5,1,4] => [4,2,1,5,3] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3 - 2
[3,5,1,2,4] => [3,4,1,5,2] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3 - 2
[3,5,1,4,2] => [3,5,1,4,2] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3 - 2
[3,5,2,1,4] => [4,3,1,5,2] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3 - 2
[3,5,2,4,1] => [5,3,1,4,2] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3 - 2
[3,5,4,1,2] => [4,5,1,3,2] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3 - 2
[4,1,5,2,3] => [2,4,5,1,3] => [4,5,3,1,2] => [1,1,1,1,0,1,0,0,0,0]
 => 0 = 2 - 2
[4,2,5,1,3] => [4,2,5,1,3] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3 - 2
[4,3,5,1,2] => [4,5,2,1,3] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3 - 2
[4,5,1,2,3] => [3,4,5,1,2] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3 - 2
[4,5,1,3,2] => [3,5,4,1,2] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3 - 2
[4,5,2,1,3] => [4,3,5,1,2] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3 - 2
[4,5,2,3,1] => [5,3,4,1,2] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3 - 2
[4,5,3,1,2] => [4,5,3,1,2] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3 - 2
[5,1,2,3,4] => [2,3,4,5,1] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2 - 2
[5,1,2,4,3] => [2,3,5,4,1] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2 - 2
[5,1,3,2,4] => [2,4,3,5,1] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2 - 2
[5,1,3,4,2] => [2,5,3,4,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2 - 2
[5,1,4,2,3] => [2,4,5,3,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2 - 2
[5,1,4,3,2] => [2,5,4,3,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2 - 2
[5,2,1,3,4] => [3,2,4,5,1] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2 - 2
[5,2,1,4,3] => [3,2,5,4,1] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2 - 2
[5,2,3,1,4] => [4,2,3,5,1] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2 - 2
[5,2,3,4,1] => [5,2,3,4,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2 - 2
[5,2,4,1,3] => [4,2,5,3,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2 - 2
[5,2,4,3,1] => [5,2,4,3,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2 - 2
[5,3,1,2,4] => [3,4,2,5,1] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2 - 2
[5,3,1,4,2] => [3,5,2,4,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2 - 2
[5,3,2,1,4] => [4,3,2,5,1] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2 - 2
[5,3,2,4,1] => [5,3,2,4,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2 - 2
[5,3,4,1,2] => [4,5,2,3,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2 - 2
[5,3,4,2,1] => [5,4,2,3,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2 - 2
[5,4,1,2,3] => [3,4,5,2,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2 - 2
[5,4,1,3,2] => [3,5,4,2,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2 - 2
[5,4,2,1,3] => [4,3,5,2,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2 - 2
[5,4,2,3,1] => [5,3,4,2,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2 - 2
[2,4,1,6,3,5] => [3,1,5,2,6,4] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0]
 => 0 = 2 - 2
[2,5,1,6,3,4] => [3,1,5,6,2,4] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 0 = 2 - 2
[3,1,6,2,4,5] => [2,4,1,5,6,3] => [3,6,1,4,5,2] => [1,1,1,0,1,1,1,0,0,0,0,0]
 => 0 = 2 - 2
[3,1,6,2,5,4] => [2,4,1,6,5,3] => [3,6,1,5,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0]
 => 0 = 2 - 2
[3,1,6,5,2,4] => [2,5,1,6,4,3] => [3,6,1,5,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0]
 => 0 = 2 - 2
[3,4,1,6,2,5] => [3,5,1,2,6,4] => [4,6,3,1,5,2] => [1,1,1,1,0,1,1,0,0,0,0,0]
 => 0 = 2 - 2
[3,5,1,6,2,4] => [3,5,1,6,2,4] => [5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 0 = 2 - 2
[4,1,2,6,3,5] => [2,3,5,1,6,4] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0]
 => 0 = 2 - 2
[4,1,3,6,2,5] => [2,5,3,1,6,4] => [4,6,3,1,5,2] => [1,1,1,1,0,1,1,0,0,0,0,0]
 => 0 = 2 - 2
[4,1,6,2,3,5] => [2,4,5,1,6,3] => [4,6,3,1,5,2] => [1,1,1,1,0,1,1,0,0,0,0,0]
 => 0 = 2 - 2
[4,1,6,2,5,3] => [2,4,6,1,5,3] => [4,6,5,1,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0]
 => 0 = 2 - 2
[4,1,6,3,2,5] => [2,5,4,1,6,3] => [4,6,3,1,5,2] => [1,1,1,1,0,1,1,0,0,0,0,0]
 => 0 = 2 - 2
[4,1,6,3,5,2] => [2,6,4,1,5,3] => [4,6,5,1,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0]
 => 0 = 2 - 2
[4,1,6,5,2,3] => [2,5,6,1,4,3] => [4,6,5,1,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0]
 => 0 = 2 - 2
[4,2,1,6,3,5] => [3,2,5,1,6,4] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0]
 => 0 = 2 - 2
[4,3,1,6,2,5] => [3,5,2,1,6,4] => [4,6,3,1,5,2] => [1,1,1,1,0,1,1,0,0,0,0,0]
 => 0 = 2 - 2
[4,5,1,6,2,3] => [3,5,6,1,2,4] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 0 = 2 - 2
[5,1,2,6,3,4] => [2,3,5,6,1,4] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 0 = 2 - 2
[5,1,3,6,2,4] => [2,5,3,6,1,4] => [5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 0 = 2 - 2
[5,1,4,6,2,3] => [2,5,6,3,1,4] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 0 = 2 - 2
[5,1,6,2,3,4] => [2,4,5,6,1,3] => [5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 0 = 2 - 2
[5,1,6,2,4,3] => [2,4,6,5,1,3] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 0 = 2 - 2
[5,1,6,3,2,4] => [2,5,4,6,1,3] => [5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 0 = 2 - 2
[5,1,6,3,4,2] => [2,6,4,5,1,3] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 0 = 2 - 2
[5,1,6,4,2,3] => [2,5,6,4,1,3] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 0 = 2 - 2
[5,2,1,6,3,4] => [3,2,5,6,1,4] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 0 = 2 - 2
[5,3,1,6,2,4] => [3,5,2,6,1,4] => [5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 0 = 2 - 2
[5,4,1,6,2,3] => [3,5,6,2,1,4] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 0 = 2 - 2
[2,4,1,7,3,5,6] => [3,1,5,2,6,7,4] => [4,2,7,1,5,6,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => 0 = 2 - 2
[2,4,1,7,3,6,5] => [3,1,5,2,7,6,4] => [4,2,7,1,6,5,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => 0 = 2 - 2
[2,4,1,7,6,3,5] => [3,1,6,2,7,5,4] => [4,2,7,1,6,5,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => 0 = 2 - 2
[2,5,1,3,7,4,6] => [3,1,4,6,2,7,5] => [5,2,3,7,1,6,4] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0]
 => 0 = 2 - 2
[2,5,1,4,7,3,6] => [3,1,6,4,2,7,5] => [5,2,7,4,1,6,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0]
 => 0 = 2 - 2
[2,5,1,7,3,4,6] => [3,1,5,6,2,7,4] => [5,2,7,4,1,6,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0]
 => 0 = 2 - 2
[2,5,1,7,3,6,4] => [3,1,5,7,2,6,4] => [5,2,7,6,1,4,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0]
 => 0 = 2 - 2
[2,5,1,7,4,3,6] => [3,1,6,5,2,7,4] => [5,2,7,4,1,6,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0]
 => 0 = 2 - 2
[2,5,1,7,4,6,3] => [3,1,7,5,2,6,4] => [5,2,7,6,1,4,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0]
 => 0 = 2 - 2
[2,5,1,7,6,3,4] => [3,1,6,7,2,5,4] => [5,2,7,6,1,4,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0]
 => 0 = 2 - 2
[2,5,4,1,7,3,6] => [4,1,6,3,2,7,5] => [5,2,7,4,1,6,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0]
 => 0 = 2 - 2
[2,6,1,3,7,4,5] => [3,1,4,6,7,2,5] => [6,2,3,7,5,1,4] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => 0 = 2 - 2
[2,6,1,4,7,3,5] => [3,1,6,4,7,2,5] => [6,2,7,4,5,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => 0 = 2 - 2
[2,6,1,5,7,3,4] => [3,1,6,7,4,2,5] => [6,2,7,5,4,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => 0 = 2 - 2
[2,6,1,7,3,4,5] => [3,1,5,6,7,2,4] => [6,2,7,4,5,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => 0 = 2 - 2
[2,6,1,7,3,5,4] => [3,1,5,7,6,2,4] => [6,2,7,5,4,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => 0 = 2 - 2
[2,6,1,7,4,3,5] => [3,1,6,5,7,2,4] => [6,2,7,4,5,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => 0 = 2 - 2
[2,6,1,7,4,5,3] => [3,1,7,5,6,2,4] => [6,2,7,5,4,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => 0 = 2 - 2
[2,6,1,7,5,3,4] => [3,1,6,7,5,2,4] => [6,2,7,5,4,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => 0 = 2 - 2
[2,6,4,1,7,3,5] => [4,1,6,3,7,2,5] => [6,2,7,4,5,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => 0 = 2 - 2
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: St001198
Mapping
Mp00066: Permutations —inverse⟶ Permutations
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
St001198: Dyck paths ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 25%
Values
[1] => [1] => [1] => [1,0]
 => ? = 0
[2,1] => [2,1] => [2,1] => [1,1,0,0]
 => ? = 1
[3,1,2] => [2,3,1] => [3,2,1] => [1,1,1,0,0,0]
 => ? = 2
[3,2,1] => [3,2,1] => [3,2,1] => [1,1,1,0,0,0]
 => ? = 1
[2,4,1,3] => [3,1,4,2] => [4,2,3,1] => [1,1,1,1,0,0,0,0]
 => ? = 3
[3,4,1,2] => [3,4,1,2] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
 => ? = 3
[4,1,2,3] => [2,3,4,1] => [4,2,3,1] => [1,1,1,1,0,0,0,0]
 => ? = 2
[4,1,3,2] => [2,4,3,1] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
 => ? = 2
[4,2,1,3] => [3,2,4,1] => [4,2,3,1] => [1,1,1,1,0,0,0,0]
 => ? = 2
[4,2,3,1] => [4,2,3,1] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
 => ? = 2
[4,3,1,2] => [3,4,2,1] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
 => ? = 2
[4,3,2,1] => [4,3,2,1] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
 => ? = 1
[2,5,1,3,4] => [3,1,4,5,2] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3
[2,5,1,4,3] => [3,1,5,4,2] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3
[2,5,4,1,3] => [4,1,5,3,2] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3
[3,1,5,2,4] => [2,4,1,5,3] => [3,5,1,4,2] => [1,1,1,0,1,1,0,0,0,0]
 => 2
[3,2,5,1,4] => [4,2,1,5,3] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3
[3,5,1,2,4] => [3,4,1,5,2] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3
[3,5,1,4,2] => [3,5,1,4,2] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3
[3,5,2,1,4] => [4,3,1,5,2] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3
[3,5,2,4,1] => [5,3,1,4,2] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3
[3,5,4,1,2] => [4,5,1,3,2] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3
[4,1,5,2,3] => [2,4,5,1,3] => [4,5,3,1,2] => [1,1,1,1,0,1,0,0,0,0]
 => 2
[4,2,5,1,3] => [4,2,5,1,3] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3
[4,3,5,1,2] => [4,5,2,1,3] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3
[4,5,1,2,3] => [3,4,5,1,2] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3
[4,5,1,3,2] => [3,5,4,1,2] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3
[4,5,2,1,3] => [4,3,5,1,2] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3
[4,5,2,3,1] => [5,3,4,1,2] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3
[4,5,3,1,2] => [4,5,3,1,2] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3
[5,1,2,3,4] => [2,3,4,5,1] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2
[5,1,2,4,3] => [2,3,5,4,1] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2
[5,1,3,2,4] => [2,4,3,5,1] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2
[5,1,3,4,2] => [2,5,3,4,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2
[5,1,4,2,3] => [2,4,5,3,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2
[5,1,4,3,2] => [2,5,4,3,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2
[5,2,1,3,4] => [3,2,4,5,1] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2
[5,2,1,4,3] => [3,2,5,4,1] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2
[5,2,3,1,4] => [4,2,3,5,1] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2
[5,2,3,4,1] => [5,2,3,4,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2
[5,2,4,1,3] => [4,2,5,3,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2
[5,2,4,3,1] => [5,2,4,3,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2
[5,3,1,2,4] => [3,4,2,5,1] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2
[5,3,1,4,2] => [3,5,2,4,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2
[5,3,2,1,4] => [4,3,2,5,1] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2
[5,3,2,4,1] => [5,3,2,4,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2
[5,3,4,1,2] => [4,5,2,3,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2
[5,3,4,2,1] => [5,4,2,3,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2
[5,4,1,2,3] => [3,4,5,2,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2
[5,4,1,3,2] => [3,5,4,2,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2
[5,4,2,1,3] => [4,3,5,2,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2
[5,4,2,3,1] => [5,3,4,2,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2
[2,4,1,6,3,5] => [3,1,5,2,6,4] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0]
 => 2
[2,5,1,6,3,4] => [3,1,5,6,2,4] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 2
[3,1,6,2,4,5] => [2,4,1,5,6,3] => [3,6,1,4,5,2] => [1,1,1,0,1,1,1,0,0,0,0,0]
 => 2
[3,1,6,2,5,4] => [2,4,1,6,5,3] => [3,6,1,5,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0]
 => 2
[3,1,6,5,2,4] => [2,5,1,6,4,3] => [3,6,1,5,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0]
 => 2
[3,4,1,6,2,5] => [3,5,1,2,6,4] => [4,6,3,1,5,2] => [1,1,1,1,0,1,1,0,0,0,0,0]
 => 2
[3,5,1,6,2,4] => [3,5,1,6,2,4] => [5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 2
[4,1,2,6,3,5] => [2,3,5,1,6,4] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0]
 => 2
[4,1,3,6,2,5] => [2,5,3,1,6,4] => [4,6,3,1,5,2] => [1,1,1,1,0,1,1,0,0,0,0,0]
 => 2
[4,1,6,2,3,5] => [2,4,5,1,6,3] => [4,6,3,1,5,2] => [1,1,1,1,0,1,1,0,0,0,0,0]
 => 2
[4,1,6,2,5,3] => [2,4,6,1,5,3] => [4,6,5,1,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0]
 => 2
[4,1,6,3,2,5] => [2,5,4,1,6,3] => [4,6,3,1,5,2] => [1,1,1,1,0,1,1,0,0,0,0,0]
 => 2
[4,1,6,3,5,2] => [2,6,4,1,5,3] => [4,6,5,1,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0]
 => 2
[4,1,6,5,2,3] => [2,5,6,1,4,3] => [4,6,5,1,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0]
 => 2
[4,2,1,6,3,5] => [3,2,5,1,6,4] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0]
 => 2
[4,3,1,6,2,5] => [3,5,2,1,6,4] => [4,6,3,1,5,2] => [1,1,1,1,0,1,1,0,0,0,0,0]
 => 2
[4,5,1,6,2,3] => [3,5,6,1,2,4] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 2
[5,1,2,6,3,4] => [2,3,5,6,1,4] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 2
[5,1,3,6,2,4] => [2,5,3,6,1,4] => [5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 2
[5,1,4,6,2,3] => [2,5,6,3,1,4] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 2
[5,1,6,2,3,4] => [2,4,5,6,1,3] => [5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 2
[5,1,6,2,4,3] => [2,4,6,5,1,3] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 2
[5,1,6,3,2,4] => [2,5,4,6,1,3] => [5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 2
[5,1,6,3,4,2] => [2,6,4,5,1,3] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 2
[5,1,6,4,2,3] => [2,5,6,4,1,3] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 2
[5,2,1,6,3,4] => [3,2,5,6,1,4] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 2
[5,3,1,6,2,4] => [3,5,2,6,1,4] => [5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 2
[5,4,1,6,2,3] => [3,5,6,2,1,4] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 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
Mapping
Mp00066: Permutations —inverse⟶ Permutations
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
St001206: Dyck paths ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 25%
Values
[1] => [1] => [1] => [1,0]
 => ? = 0
[2,1] => [2,1] => [2,1] => [1,1,0,0]
 => ? = 1
[3,1,2] => [2,3,1] => [3,2,1] => [1,1,1,0,0,0]
 => ? = 2
[3,2,1] => [3,2,1] => [3,2,1] => [1,1,1,0,0,0]
 => ? = 1
[2,4,1,3] => [3,1,4,2] => [4,2,3,1] => [1,1,1,1,0,0,0,0]
 => ? = 3
[3,4,1,2] => [3,4,1,2] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
 => ? = 3
[4,1,2,3] => [2,3,4,1] => [4,2,3,1] => [1,1,1,1,0,0,0,0]
 => ? = 2
[4,1,3,2] => [2,4,3,1] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
 => ? = 2
[4,2,1,3] => [3,2,4,1] => [4,2,3,1] => [1,1,1,1,0,0,0,0]
 => ? = 2
[4,2,3,1] => [4,2,3,1] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
 => ? = 2
[4,3,1,2] => [3,4,2,1] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
 => ? = 2
[4,3,2,1] => [4,3,2,1] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
 => ? = 1
[2,5,1,3,4] => [3,1,4,5,2] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3
[2,5,1,4,3] => [3,1,5,4,2] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3
[2,5,4,1,3] => [4,1,5,3,2] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3
[3,1,5,2,4] => [2,4,1,5,3] => [3,5,1,4,2] => [1,1,1,0,1,1,0,0,0,0]
 => 2
[3,2,5,1,4] => [4,2,1,5,3] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3
[3,5,1,2,4] => [3,4,1,5,2] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3
[3,5,1,4,2] => [3,5,1,4,2] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3
[3,5,2,1,4] => [4,3,1,5,2] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3
[3,5,2,4,1] => [5,3,1,4,2] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3
[3,5,4,1,2] => [4,5,1,3,2] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3
[4,1,5,2,3] => [2,4,5,1,3] => [4,5,3,1,2] => [1,1,1,1,0,1,0,0,0,0]
 => 2
[4,2,5,1,3] => [4,2,5,1,3] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3
[4,3,5,1,2] => [4,5,2,1,3] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3
[4,5,1,2,3] => [3,4,5,1,2] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3
[4,5,1,3,2] => [3,5,4,1,2] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3
[4,5,2,1,3] => [4,3,5,1,2] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3
[4,5,2,3,1] => [5,3,4,1,2] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3
[4,5,3,1,2] => [4,5,3,1,2] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 3
[5,1,2,3,4] => [2,3,4,5,1] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2
[5,1,2,4,3] => [2,3,5,4,1] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2
[5,1,3,2,4] => [2,4,3,5,1] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2
[5,1,3,4,2] => [2,5,3,4,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2
[5,1,4,2,3] => [2,4,5,3,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2
[5,1,4,3,2] => [2,5,4,3,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2
[5,2,1,3,4] => [3,2,4,5,1] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2
[5,2,1,4,3] => [3,2,5,4,1] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2
[5,2,3,1,4] => [4,2,3,5,1] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2
[5,2,3,4,1] => [5,2,3,4,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2
[5,2,4,1,3] => [4,2,5,3,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2
[5,2,4,3,1] => [5,2,4,3,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2
[5,3,1,2,4] => [3,4,2,5,1] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2
[5,3,1,4,2] => [3,5,2,4,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2
[5,3,2,1,4] => [4,3,2,5,1] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2
[5,3,2,4,1] => [5,3,2,4,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2
[5,3,4,1,2] => [4,5,2,3,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2
[5,3,4,2,1] => [5,4,2,3,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2
[5,4,1,2,3] => [3,4,5,2,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2
[5,4,1,3,2] => [3,5,4,2,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2
[5,4,2,1,3] => [4,3,5,2,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2
[5,4,2,3,1] => [5,3,4,2,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2
[2,4,1,6,3,5] => [3,1,5,2,6,4] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0]
 => 2
[2,5,1,6,3,4] => [3,1,5,6,2,4] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 2
[3,1,6,2,4,5] => [2,4,1,5,6,3] => [3,6,1,4,5,2] => [1,1,1,0,1,1,1,0,0,0,0,0]
 => 2
[3,1,6,2,5,4] => [2,4,1,6,5,3] => [3,6,1,5,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0]
 => 2
[3,1,6,5,2,4] => [2,5,1,6,4,3] => [3,6,1,5,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0]
 => 2
[3,4,1,6,2,5] => [3,5,1,2,6,4] => [4,6,3,1,5,2] => [1,1,1,1,0,1,1,0,0,0,0,0]
 => 2
[3,5,1,6,2,4] => [3,5,1,6,2,4] => [5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 2
[4,1,2,6,3,5] => [2,3,5,1,6,4] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0]
 => 2
[4,1,3,6,2,5] => [2,5,3,1,6,4] => [4,6,3,1,5,2] => [1,1,1,1,0,1,1,0,0,0,0,0]
 => 2
[4,1,6,2,3,5] => [2,4,5,1,6,3] => [4,6,3,1,5,2] => [1,1,1,1,0,1,1,0,0,0,0,0]
 => 2
[4,1,6,2,5,3] => [2,4,6,1,5,3] => [4,6,5,1,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0]
 => 2
[4,1,6,3,2,5] => [2,5,4,1,6,3] => [4,6,3,1,5,2] => [1,1,1,1,0,1,1,0,0,0,0,0]
 => 2
[4,1,6,3,5,2] => [2,6,4,1,5,3] => [4,6,5,1,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0]
 => 2
[4,1,6,5,2,3] => [2,5,6,1,4,3] => [4,6,5,1,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0]
 => 2
[4,2,1,6,3,5] => [3,2,5,1,6,4] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0]
 => 2
[4,3,1,6,2,5] => [3,5,2,1,6,4] => [4,6,3,1,5,2] => [1,1,1,1,0,1,1,0,0,0,0,0]
 => 2
[4,5,1,6,2,3] => [3,5,6,1,2,4] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 2
[5,1,2,6,3,4] => [2,3,5,6,1,4] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 2
[5,1,3,6,2,4] => [2,5,3,6,1,4] => [5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 2
[5,1,4,6,2,3] => [2,5,6,3,1,4] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 2
[5,1,6,2,3,4] => [2,4,5,6,1,3] => [5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 2
[5,1,6,2,4,3] => [2,4,6,5,1,3] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 2
[5,1,6,3,2,4] => [2,5,4,6,1,3] => [5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 2
[5,1,6,3,4,2] => [2,6,4,5,1,3] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 2
[5,1,6,4,2,3] => [2,5,6,4,1,3] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 2
[5,2,1,6,3,4] => [3,2,5,6,1,4] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 2
[5,3,1,6,2,4] => [3,5,2,6,1,4] => [5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 2
[5,4,1,6,2,3] => [3,5,6,2,1,4] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 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 $eA$.