Your data matches 3 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001232
(load all 2 compositions to match this statistic)
Mapping
Mp00061: Permutations —to increasing tree⟶ Binary trees
Mp00012: Binary trees —to Dyck path: up step, left tree, down step, right tree⟶ Dyck paths
Mp00099: Dyck paths —bounce path⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => [.,.]
 => [1,0]
 => [1,0]
 => 0
[1,2] => [.,[.,.]]
 => [1,0,1,0]
 => [1,0,1,0]
 => 1
[2,1] => [[.,.],.]
 => [1,1,0,0]
 => [1,1,0,0]
 => 0
[1,3,2] => [.,[[.,.],.]]
 => [1,0,1,1,0,0]
 => [1,0,1,1,0,0]
 => 2
[2,1,3] => [[.,.],[.,.]]
 => [1,1,0,0,1,0]
 => [1,1,0,0,1,0]
 => 1
[2,3,1] => [[.,[.,.]],.]
 => [1,1,0,1,0,0]
 => [1,0,1,1,0,0]
 => 2
[3,1,2] => [[.,.],[.,.]]
 => [1,1,0,0,1,0]
 => [1,1,0,0,1,0]
 => 1
[3,2,1] => [[[.,.],.],.]
 => [1,1,1,0,0,0]
 => [1,1,1,0,0,0]
 => 0
[1,3,2,4] => [.,[[.,.],[.,.]]]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
[1,4,2,3] => [.,[[.,.],[.,.]]]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
[1,4,3,2] => [.,[[[.,.],.],.]]
 => [1,0,1,1,1,0,0,0]
 => [1,0,1,1,1,0,0,0]
 => 3
[2,1,4,3] => [[.,.],[[.,.],.]]
 => [1,1,0,0,1,1,0,0]
 => [1,1,0,0,1,1,0,0]
 => 2
[2,3,1,4] => [[.,[.,.]],[.,.]]
 => [1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
[2,3,4,1] => [[.,[.,[.,.]]],.]
 => [1,1,0,1,0,1,0,0]
 => [1,1,0,0,1,1,0,0]
 => 2
[2,4,1,3] => [[.,[.,.]],[.,.]]
 => [1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
[2,4,3,1] => [[.,[[.,.],.]],.]
 => [1,1,0,1,1,0,0,0]
 => [1,0,1,1,1,0,0,0]
 => 3
[3,1,4,2] => [[.,.],[[.,.],.]]
 => [1,1,0,0,1,1,0,0]
 => [1,1,0,0,1,1,0,0]
 => 2
[3,2,1,4] => [[[.,.],.],[.,.]]
 => [1,1,1,0,0,0,1,0]
 => [1,1,1,0,0,0,1,0]
 => 1
[3,2,4,1] => [[[.,.],[.,.]],.]
 => [1,1,1,0,0,1,0,0]
 => [1,1,0,0,1,1,0,0]
 => 2
[3,4,1,2] => [[.,[.,.]],[.,.]]
 => [1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
[3,4,2,1] => [[[.,[.,.]],.],.]
 => [1,1,1,0,1,0,0,0]
 => [1,0,1,1,1,0,0,0]
 => 3
[4,1,3,2] => [[.,.],[[.,.],.]]
 => [1,1,0,0,1,1,0,0]
 => [1,1,0,0,1,1,0,0]
 => 2
[4,2,1,3] => [[[.,.],.],[.,.]]
 => [1,1,1,0,0,0,1,0]
 => [1,1,1,0,0,0,1,0]
 => 1
[4,2,3,1] => [[[.,.],[.,.]],.]
 => [1,1,1,0,0,1,0,0]
 => [1,1,0,0,1,1,0,0]
 => 2
[4,3,1,2] => [[[.,.],.],[.,.]]
 => [1,1,1,0,0,0,1,0]
 => [1,1,1,0,0,0,1,0]
 => 1
[4,3,2,1] => [[[[.,.],.],.],.]
 => [1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,0,0]
 => 0
[1,3,2,5,4] => [.,[[.,.],[[.,.],.]]]
 => [1,0,1,1,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 4
[1,3,4,5,2] => [.,[[.,[.,[.,.]]],.]]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 4
[1,4,2,5,3] => [.,[[.,.],[[.,.],.]]]
 => [1,0,1,1,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 4
[1,4,3,2,5] => [.,[[[.,.],.],[.,.]]]
 => [1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 4
[1,4,3,5,2] => [.,[[[.,.],[.,.]],.]]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 4
[1,5,2,4,3] => [.,[[.,.],[[.,.],.]]]
 => [1,0,1,1,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 4
[1,5,3,2,4] => [.,[[[.,.],.],[.,.]]]
 => [1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 4
[1,5,3,4,2] => [.,[[[.,.],[.,.]],.]]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 4
[1,5,4,2,3] => [.,[[[.,.],.],[.,.]]]
 => [1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 4
[1,5,4,3,2] => [.,[[[[.,.],.],.],.]]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => 4
[2,1,4,3,5] => [[.,.],[[.,.],[.,.]]]
 => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3
[2,1,5,3,4] => [[.,.],[[.,.],[.,.]]]
 => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3
[2,1,5,4,3] => [[.,.],[[[.,.],.],.]]
 => [1,1,0,0,1,1,1,0,0,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => 3
[2,3,1,5,4] => [[.,[.,.]],[[.,.],.]]
 => [1,1,0,1,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 4
[2,3,4,1,5] => [[.,[.,[.,.]]],[.,.]]
 => [1,1,0,1,0,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3
[2,3,4,5,1] => [[.,[.,[.,[.,.]]]],.]
 => [1,1,0,1,0,1,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 4
[2,3,5,1,4] => [[.,[.,[.,.]]],[.,.]]
 => [1,1,0,1,0,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3
[2,3,5,4,1] => [[.,[.,[[.,.],.]]],.]
 => [1,1,0,1,0,1,1,0,0,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => 3
[2,4,1,5,3] => [[.,[.,.]],[[.,.],.]]
 => [1,1,0,1,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 4
[2,4,3,1,5] => [[.,[[.,.],.]],[.,.]]
 => [1,1,0,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 4
[2,4,3,5,1] => [[.,[[.,.],[.,.]]],.]
 => [1,1,0,1,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 4
[2,4,5,1,3] => [[.,[.,[.,.]]],[.,.]]
 => [1,1,0,1,0,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3
[2,4,5,3,1] => [[.,[[.,[.,.]],.]],.]
 => [1,1,0,1,1,0,1,0,0,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => 3
[2,5,1,4,3] => [[.,[.,.]],[[.,.],.]]
 => [1,1,0,1,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 4
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
Matching statistic: St001227
Mapping
Mp00061: Permutations —to increasing tree⟶ Binary trees
Mp00012: Binary trees —to Dyck path: up step, left tree, down step, right tree⟶ Dyck paths
Mp00099: Dyck paths —bounce path⟶ Dyck paths
St001227: Dyck paths ⟶ ℤResult quality: 16% ●values known / values provided: 16%●distinct values known / distinct values provided: 86%
Values
[1] => [.,.]
 => [1,0]
 => [1,0]
 => 0
[1,2] => [.,[.,.]]
 => [1,0,1,0]
 => [1,0,1,0]
 => 1
[2,1] => [[.,.],.]
 => [1,1,0,0]
 => [1,1,0,0]
 => 0
[1,3,2] => [.,[[.,.],.]]
 => [1,0,1,1,0,0]
 => [1,0,1,1,0,0]
 => 2
[2,1,3] => [[.,.],[.,.]]
 => [1,1,0,0,1,0]
 => [1,1,0,0,1,0]
 => 1
[2,3,1] => [[.,[.,.]],.]
 => [1,1,0,1,0,0]
 => [1,0,1,1,0,0]
 => 2
[3,1,2] => [[.,.],[.,.]]
 => [1,1,0,0,1,0]
 => [1,1,0,0,1,0]
 => 1
[3,2,1] => [[[.,.],.],.]
 => [1,1,1,0,0,0]
 => [1,1,1,0,0,0]
 => 0
[1,3,2,4] => [.,[[.,.],[.,.]]]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
[1,4,2,3] => [.,[[.,.],[.,.]]]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
[1,4,3,2] => [.,[[[.,.],.],.]]
 => [1,0,1,1,1,0,0,0]
 => [1,0,1,1,1,0,0,0]
 => 3
[2,1,4,3] => [[.,.],[[.,.],.]]
 => [1,1,0,0,1,1,0,0]
 => [1,1,0,0,1,1,0,0]
 => 2
[2,3,1,4] => [[.,[.,.]],[.,.]]
 => [1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
[2,3,4,1] => [[.,[.,[.,.]]],.]
 => [1,1,0,1,0,1,0,0]
 => [1,1,0,0,1,1,0,0]
 => 2
[2,4,1,3] => [[.,[.,.]],[.,.]]
 => [1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
[2,4,3,1] => [[.,[[.,.],.]],.]
 => [1,1,0,1,1,0,0,0]
 => [1,0,1,1,1,0,0,0]
 => 3
[3,1,4,2] => [[.,.],[[.,.],.]]
 => [1,1,0,0,1,1,0,0]
 => [1,1,0,0,1,1,0,0]
 => 2
[3,2,1,4] => [[[.,.],.],[.,.]]
 => [1,1,1,0,0,0,1,0]
 => [1,1,1,0,0,0,1,0]
 => 1
[3,2,4,1] => [[[.,.],[.,.]],.]
 => [1,1,1,0,0,1,0,0]
 => [1,1,0,0,1,1,0,0]
 => 2
[3,4,1,2] => [[.,[.,.]],[.,.]]
 => [1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
[3,4,2,1] => [[[.,[.,.]],.],.]
 => [1,1,1,0,1,0,0,0]
 => [1,0,1,1,1,0,0,0]
 => 3
[4,1,3,2] => [[.,.],[[.,.],.]]
 => [1,1,0,0,1,1,0,0]
 => [1,1,0,0,1,1,0,0]
 => 2
[4,2,1,3] => [[[.,.],.],[.,.]]
 => [1,1,1,0,0,0,1,0]
 => [1,1,1,0,0,0,1,0]
 => 1
[4,2,3,1] => [[[.,.],[.,.]],.]
 => [1,1,1,0,0,1,0,0]
 => [1,1,0,0,1,1,0,0]
 => 2
[4,3,1,2] => [[[.,.],.],[.,.]]
 => [1,1,1,0,0,0,1,0]
 => [1,1,1,0,0,0,1,0]
 => 1
[4,3,2,1] => [[[[.,.],.],.],.]
 => [1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,0,0]
 => 0
[1,3,2,5,4] => [.,[[.,.],[[.,.],.]]]
 => [1,0,1,1,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 4
[1,3,4,5,2] => [.,[[.,[.,[.,.]]],.]]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 4
[1,4,2,5,3] => [.,[[.,.],[[.,.],.]]]
 => [1,0,1,1,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 4
[1,4,3,2,5] => [.,[[[.,.],.],[.,.]]]
 => [1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 4
[1,4,3,5,2] => [.,[[[.,.],[.,.]],.]]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 4
[1,5,2,4,3] => [.,[[.,.],[[.,.],.]]]
 => [1,0,1,1,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 4
[1,5,3,2,4] => [.,[[[.,.],.],[.,.]]]
 => [1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 4
[1,5,3,4,2] => [.,[[[.,.],[.,.]],.]]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 4
[1,5,4,2,3] => [.,[[[.,.],.],[.,.]]]
 => [1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 4
[1,5,4,3,2] => [.,[[[[.,.],.],.],.]]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => 4
[2,1,4,3,5] => [[.,.],[[.,.],[.,.]]]
 => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3
[2,1,5,3,4] => [[.,.],[[.,.],[.,.]]]
 => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3
[2,1,5,4,3] => [[.,.],[[[.,.],.],.]]
 => [1,1,0,0,1,1,1,0,0,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => 3
[2,3,1,5,4] => [[.,[.,.]],[[.,.],.]]
 => [1,1,0,1,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 4
[2,3,4,1,5] => [[.,[.,[.,.]]],[.,.]]
 => [1,1,0,1,0,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3
[2,3,4,5,1] => [[.,[.,[.,[.,.]]]],.]
 => [1,1,0,1,0,1,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 4
[2,3,5,1,4] => [[.,[.,[.,.]]],[.,.]]
 => [1,1,0,1,0,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3
[2,3,5,4,1] => [[.,[.,[[.,.],.]]],.]
 => [1,1,0,1,0,1,1,0,0,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => 3
[2,4,1,5,3] => [[.,[.,.]],[[.,.],.]]
 => [1,1,0,1,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 4
[2,4,3,1,5] => [[.,[[.,.],.]],[.,.]]
 => [1,1,0,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 4
[2,4,3,5,1] => [[.,[[.,.],[.,.]]],.]
 => [1,1,0,1,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 4
[2,4,5,1,3] => [[.,[.,[.,.]]],[.,.]]
 => [1,1,0,1,0,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3
[2,4,5,3,1] => [[.,[[.,[.,.]],.]],.]
 => [1,1,0,1,1,0,1,0,0,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => 3
[2,5,1,4,3] => [[.,[.,.]],[[.,.],.]]
 => [1,1,0,1,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 4
[1,3,2,5,4,7,6] => [.,[[.,.],[[.,.],[[.,.],.]]]]
 => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
 => ? = 6
[1,3,2,5,6,7,4] => [.,[[.,.],[[.,[.,[.,.]]],.]]]
 => [1,0,1,1,0,0,1,1,0,1,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
 => ? = 6
[1,3,2,6,4,7,5] => [.,[[.,.],[[.,.],[[.,.],.]]]]
 => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
 => ? = 6
[1,3,2,6,5,4,7] => [.,[[.,.],[[[.,.],.],[.,.]]]]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => ? = 6
[1,3,2,6,5,7,4] => [.,[[.,.],[[[.,.],[.,.]],.]]]
 => [1,0,1,1,0,0,1,1,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
 => ? = 6
[1,3,2,7,4,6,5] => [.,[[.,.],[[.,.],[[.,.],.]]]]
 => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
 => ? = 6
[1,3,2,7,5,4,6] => [.,[[.,.],[[[.,.],.],[.,.]]]]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => ? = 6
[1,3,2,7,5,6,4] => [.,[[.,.],[[[.,.],[.,.]],.]]]
 => [1,0,1,1,0,0,1,1,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
 => ? = 6
[1,3,2,7,6,4,5] => [.,[[.,.],[[[.,.],.],[.,.]]]]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => ? = 6
[1,3,2,7,6,5,4] => [.,[[.,.],[[[[.,.],.],.],.]]]
 => [1,0,1,1,0,0,1,1,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,1,1,0,0,0,0]
 => ? = 6
[1,3,4,5,2,7,6] => [.,[[.,[.,[.,.]]],[[.,.],.]]]
 => [1,0,1,1,0,1,0,1,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
 => ? = 6
[1,3,4,5,6,7,2] => [.,[[.,[.,[.,[.,[.,.]]]]],.]]
 => [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
 => ? = 6
[1,3,4,6,2,7,5] => [.,[[.,[.,[.,.]]],[[.,.],.]]]
 => [1,0,1,1,0,1,0,1,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
 => ? = 6
[1,3,4,6,5,2,7] => [.,[[.,[.,[[.,.],.]]],[.,.]]]
 => [1,0,1,1,0,1,0,1,1,0,0,0,1,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => ? = 6
[1,3,4,6,5,7,2] => [.,[[.,[.,[[.,.],[.,.]]]],.]]
 => [1,0,1,1,0,1,0,1,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
 => ? = 6
[1,3,4,7,2,6,5] => [.,[[.,[.,[.,.]]],[[.,.],.]]]
 => [1,0,1,1,0,1,0,1,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
 => ? = 6
[1,3,4,7,5,2,6] => [.,[[.,[.,[[.,.],.]]],[.,.]]]
 => [1,0,1,1,0,1,0,1,1,0,0,0,1,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => ? = 6
[1,3,4,7,5,6,2] => [.,[[.,[.,[[.,.],[.,.]]]],.]]
 => [1,0,1,1,0,1,0,1,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
 => ? = 6
[1,3,4,7,6,2,5] => [.,[[.,[.,[[.,.],.]]],[.,.]]]
 => [1,0,1,1,0,1,0,1,1,0,0,0,1,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => ? = 6
[1,3,4,7,6,5,2] => [.,[[.,[.,[[[.,.],.],.]]],.]]
 => [1,0,1,1,0,1,0,1,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,1,1,0,0,0,0]
 => ? = 6
[1,3,5,6,2,7,4] => [.,[[.,[.,[.,.]]],[[.,.],.]]]
 => [1,0,1,1,0,1,0,1,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
 => ? = 6
[1,3,5,6,4,2,7] => [.,[[.,[[.,[.,.]],.]],[.,.]]]
 => [1,0,1,1,0,1,1,0,1,0,0,0,1,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => ? = 6
[1,3,5,7,2,6,4] => [.,[[.,[.,[.,.]]],[[.,.],.]]]
 => [1,0,1,1,0,1,0,1,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
 => ? = 6
[1,3,5,7,4,2,6] => [.,[[.,[[.,[.,.]],.]],[.,.]]]
 => [1,0,1,1,0,1,1,0,1,0,0,0,1,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => ? = 6
[1,3,5,7,6,2,4] => [.,[[.,[.,[[.,.],.]]],[.,.]]]
 => [1,0,1,1,0,1,0,1,1,0,0,0,1,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => ? = 6
[1,3,5,7,6,4,2] => [.,[[.,[[.,[[.,.],.]],.]],.]]
 => [1,0,1,1,0,1,1,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,1,1,0,0,0,0]
 => ? = 6
[1,3,6,7,2,5,4] => [.,[[.,[.,[.,.]]],[[.,.],.]]]
 => [1,0,1,1,0,1,0,1,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
 => ? = 6
[1,3,6,7,4,2,5] => [.,[[.,[[.,[.,.]],.]],[.,.]]]
 => [1,0,1,1,0,1,1,0,1,0,0,0,1,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => ? = 6
[1,3,6,7,5,2,4] => [.,[[.,[[.,[.,.]],.]],[.,.]]]
 => [1,0,1,1,0,1,1,0,1,0,0,0,1,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => ? = 6
[1,3,6,7,5,4,2] => [.,[[.,[[[.,[.,.]],.],.]],.]]
 => [1,0,1,1,0,1,1,1,0,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,1,1,0,0,0,0]
 => ? = 6
[1,4,2,5,3,7,6] => [.,[[.,.],[[.,.],[[.,.],.]]]]
 => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
 => ? = 6
[1,4,2,5,6,7,3] => [.,[[.,.],[[.,[.,[.,.]]],.]]]
 => [1,0,1,1,0,0,1,1,0,1,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
 => ? = 6
[1,4,2,6,3,7,5] => [.,[[.,.],[[.,.],[[.,.],.]]]]
 => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
 => ? = 6
[1,4,2,6,5,3,7] => [.,[[.,.],[[[.,.],.],[.,.]]]]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => ? = 6
[1,4,2,6,5,7,3] => [.,[[.,.],[[[.,.],[.,.]],.]]]
 => [1,0,1,1,0,0,1,1,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
 => ? = 6
[1,4,2,7,3,6,5] => [.,[[.,.],[[.,.],[[.,.],.]]]]
 => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
 => ? = 6
[1,4,2,7,5,3,6] => [.,[[.,.],[[[.,.],.],[.,.]]]]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => ? = 6
[1,4,2,7,5,6,3] => [.,[[.,.],[[[.,.],[.,.]],.]]]
 => [1,0,1,1,0,0,1,1,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
 => ? = 6
[1,4,2,7,6,3,5] => [.,[[.,.],[[[.,.],.],[.,.]]]]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => ? = 6
[1,4,2,7,6,5,3] => [.,[[.,.],[[[[.,.],.],.],.]]]
 => [1,0,1,1,0,0,1,1,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,1,1,0,0,0,0]
 => ? = 6
[1,4,3,2,6,5,7] => [.,[[[.,.],.],[[.,.],[.,.]]]]
 => [1,0,1,1,1,0,0,0,1,1,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,1,0,0,1,0]
 => ? = 6
[1,4,3,2,7,5,6] => [.,[[[.,.],.],[[.,.],[.,.]]]]
 => [1,0,1,1,1,0,0,0,1,1,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,1,0,0,1,0]
 => ? = 6
[1,4,3,2,7,6,5] => [.,[[[.,.],.],[[[.,.],.],.]]]
 => [1,0,1,1,1,0,0,0,1,1,1,0,0,0]
 => [1,0,1,1,1,0,0,0,1,1,1,0,0,0]
 => ? = 6
[1,4,3,5,2,7,6] => [.,[[[.,.],[.,.]],[[.,.],.]]]
 => [1,0,1,1,1,0,0,1,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
 => ? = 6
[1,4,3,5,6,2,7] => [.,[[[.,.],[.,[.,.]]],[.,.]]]
 => [1,0,1,1,1,0,0,1,0,1,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,1,0,0,1,0]
 => ? = 6
[1,4,3,5,6,7,2] => [.,[[[.,.],[.,[.,[.,.]]]],.]]
 => [1,0,1,1,1,0,0,1,0,1,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
 => ? = 6
[1,4,3,5,7,2,6] => [.,[[[.,.],[.,[.,.]]],[.,.]]]
 => [1,0,1,1,1,0,0,1,0,1,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,1,0,0,1,0]
 => ? = 6
[1,4,3,5,7,6,2] => [.,[[[.,.],[.,[[.,.],.]]],.]]
 => [1,0,1,1,1,0,0,1,0,1,1,0,0,0]
 => [1,0,1,1,1,0,0,0,1,1,1,0,0,0]
 => ? = 6
[1,4,3,6,2,7,5] => [.,[[[.,.],[.,.]],[[.,.],.]]]
 => [1,0,1,1,1,0,0,1,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
 => ? = 6
[1,4,3,6,5,2,7] => [.,[[[.,.],[[.,.],.]],[.,.]]]
 => [1,0,1,1,1,0,0,1,1,0,0,0,1,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => ? = 6
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: St001645
Mapping
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
Mp00089: Permutations —Inverse Kreweras complement⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St001645: Graphs ⟶ ℤResult quality: 8% ●values known / values provided: 8%●distinct values known / distinct values provided: 100%
Values
[1] => [1] => [1] => ([],1)
 => 1 = 0 + 1
[1,2] => [1,2] => [2,1] => ([(0,1)],2)
 => 2 = 1 + 1
[2,1] => [2,1] => [1,2] => ([],2)
 => ? = 0 + 1
[1,3,2] => [1,3,2] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
 => 3 = 2 + 1
[2,1,3] => [2,1,3] => [1,3,2] => ([(1,2)],3)
 => ? = 1 + 1
[2,3,1] => [3,2,1] => [2,1,3] => ([(1,2)],3)
 => ? = 2 + 1
[3,1,2] => [3,2,1] => [2,1,3] => ([(1,2)],3)
 => ? = 1 + 1
[3,2,1] => [3,2,1] => [2,1,3] => ([(1,2)],3)
 => ? = 0 + 1
[1,3,2,4] => [1,3,2,4] => [3,2,4,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 3 + 1
[1,4,2,3] => [1,4,3,2] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 3 + 1
[1,4,3,2] => [1,4,3,2] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 3 + 1
[2,1,4,3] => [2,1,4,3] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? = 2 + 1
[2,3,1,4] => [3,2,1,4] => [2,1,4,3] => ([(0,3),(1,2)],4)
 => ? = 3 + 1
[2,3,4,1] => [4,2,3,1] => [2,3,1,4] => ([(1,3),(2,3)],4)
 => ? = 2 + 1
[2,4,1,3] => [3,4,1,2] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4)
 => ? = 3 + 1
[2,4,3,1] => [4,3,2,1] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
 => ? = 3 + 1
[3,1,4,2] => [4,2,3,1] => [2,3,1,4] => ([(1,3),(2,3)],4)
 => ? = 2 + 1
[3,2,1,4] => [3,2,1,4] => [2,1,4,3] => ([(0,3),(1,2)],4)
 => ? = 1 + 1
[3,2,4,1] => [4,2,3,1] => [2,3,1,4] => ([(1,3),(2,3)],4)
 => ? = 2 + 1
[3,4,1,2] => [4,3,2,1] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
 => ? = 3 + 1
[3,4,2,1] => [4,3,2,1] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
 => ? = 3 + 1
[4,1,3,2] => [4,2,3,1] => [2,3,1,4] => ([(1,3),(2,3)],4)
 => ? = 2 + 1
[4,2,1,3] => [4,3,2,1] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
 => ? = 1 + 1
[4,2,3,1] => [4,3,2,1] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
 => ? = 2 + 1
[4,3,1,2] => [4,3,2,1] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
 => ? = 1 + 1
[4,3,2,1] => [4,3,2,1] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
 => ? = 0 + 1
[1,3,2,5,4] => [1,3,2,5,4] => [3,2,5,4,1] => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ? = 4 + 1
[1,3,4,5,2] => [1,5,3,4,2] => [5,3,4,2,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 5 = 4 + 1
[1,4,2,5,3] => [1,5,3,4,2] => [5,3,4,2,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 5 = 4 + 1
[1,4,3,2,5] => [1,4,3,2,5] => [4,3,2,5,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 4 + 1
[1,4,3,5,2] => [1,5,3,4,2] => [5,3,4,2,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 5 = 4 + 1
[1,5,2,4,3] => [1,5,3,4,2] => [5,3,4,2,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 5 = 4 + 1
[1,5,3,2,4] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 5 = 4 + 1
[1,5,3,4,2] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 5 = 4 + 1
[1,5,4,2,3] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 5 = 4 + 1
[1,5,4,3,2] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 5 = 4 + 1
[2,1,4,3,5] => [2,1,4,3,5] => [1,4,3,5,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 3 + 1
[2,1,5,3,4] => [2,1,5,4,3] => [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 3 + 1
[2,1,5,4,3] => [2,1,5,4,3] => [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 3 + 1
[2,3,1,5,4] => [3,2,1,5,4] => [2,1,5,4,3] => ([(0,1),(2,3),(2,4),(3,4)],5)
 => ? = 4 + 1
[2,3,4,1,5] => [4,2,3,1,5] => [2,3,1,5,4] => ([(0,1),(2,4),(3,4)],5)
 => ? = 3 + 1
[2,3,4,5,1] => [5,2,3,4,1] => [2,3,4,1,5] => ([(1,4),(2,4),(3,4)],5)
 => ? = 4 + 1
[2,3,5,1,4] => [4,2,5,1,3] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ? = 3 + 1
[2,3,5,4,1] => [5,2,4,3,1] => [2,4,3,1,5] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 3 + 1
[2,4,1,5,3] => [3,5,1,4,2] => [5,1,4,2,3] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 4 + 1
[2,4,3,1,5] => [4,3,2,1,5] => [3,2,1,5,4] => ([(0,1),(2,3),(2,4),(3,4)],5)
 => ? = 4 + 1
[2,4,3,5,1] => [5,3,2,4,1] => [3,2,4,1,5] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 4 + 1
[2,4,5,1,3] => [4,5,3,1,2] => [5,3,1,2,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 3 + 1
[2,4,5,3,1] => [5,4,3,2,1] => [4,3,2,1,5] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 3 + 1
[2,5,1,4,3] => [3,5,1,4,2] => [5,1,4,2,3] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 4 + 1
[2,5,3,1,4] => [4,5,3,1,2] => [5,3,1,2,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 4 + 1
[2,5,3,4,1] => [5,4,3,2,1] => [4,3,2,1,5] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 4 + 1
[2,5,4,1,3] => [4,5,3,1,2] => [5,3,1,2,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 4 + 1
[2,5,4,3,1] => [5,4,3,2,1] => [4,3,2,1,5] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 4 + 1
[3,1,4,2,5] => [4,2,3,1,5] => [2,3,1,5,4] => ([(0,1),(2,4),(3,4)],5)
 => ? = 3 + 1
[3,1,5,2,4] => [4,2,5,1,3] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ? = 3 + 1
[3,1,5,4,2] => [5,2,4,3,1] => [2,4,3,1,5] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 3 + 1
[3,2,1,5,4] => [3,2,1,5,4] => [2,1,5,4,3] => ([(0,1),(2,3),(2,4),(3,4)],5)
 => ? = 2 + 1
[3,2,4,1,5] => [4,2,3,1,5] => [2,3,1,5,4] => ([(0,1),(2,4),(3,4)],5)
 => ? = 3 + 1
[3,2,4,5,1] => [5,2,3,4,1] => [2,3,4,1,5] => ([(1,4),(2,4),(3,4)],5)
 => ? = 2 + 1
[3,2,5,1,4] => [4,2,5,1,3] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ? = 3 + 1
[3,2,5,4,1] => [5,2,4,3,1] => [2,4,3,1,5] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 3 + 1
[3,4,1,5,2] => [5,3,2,4,1] => [3,2,4,1,5] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 4 + 1
[1,3,4,6,2,5] => [1,5,3,6,2,4] => [5,3,6,2,4,1] => ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 6 = 5 + 1
[1,3,4,6,5,2] => [1,6,3,5,4,2] => [6,3,5,4,2,1] => ([(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)
 => 6 = 5 + 1
[1,3,5,6,2,4] => [1,5,6,4,2,3] => [5,6,4,2,3,1] => ([(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)
 => 6 = 5 + 1
[1,3,5,6,4,2] => [1,6,5,4,3,2] => [6,5,4,3,2,1] => ([(0,1),(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)
 => 6 = 5 + 1
[1,4,2,6,3,5] => [1,5,3,6,2,4] => [5,3,6,2,4,1] => ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 6 = 5 + 1
[1,4,2,6,5,3] => [1,6,3,5,4,2] => [6,3,5,4,2,1] => ([(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)
 => 6 = 5 + 1
[1,4,3,5,6,2] => [1,6,3,4,5,2] => [6,3,4,5,2,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 6 = 5 + 1
[1,4,3,6,2,5] => [1,5,3,6,2,4] => [5,3,6,2,4,1] => ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 6 = 5 + 1
[1,4,3,6,5,2] => [1,6,3,5,4,2] => [6,3,5,4,2,1] => ([(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)
 => 6 = 5 + 1
[1,4,5,3,6,2] => [1,6,4,3,5,2] => [6,4,3,5,2,1] => ([(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)
 => 6 = 5 + 1
[1,4,5,6,2,3] => [1,6,5,4,3,2] => [6,5,4,3,2,1] => ([(0,1),(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)
 => 6 = 5 + 1
[1,4,5,6,3,2] => [1,6,5,4,3,2] => [6,5,4,3,2,1] => ([(0,1),(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)
 => 6 = 5 + 1
[1,4,6,3,5,2] => [1,6,5,4,3,2] => [6,5,4,3,2,1] => ([(0,1),(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)
 => 6 = 5 + 1
[1,5,2,6,3,4] => [1,6,3,5,4,2] => [6,3,5,4,2,1] => ([(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)
 => 6 = 5 + 1
[1,5,2,6,4,3] => [1,6,3,5,4,2] => [6,3,5,4,2,1] => ([(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)
 => 6 = 5 + 1
[1,5,3,2,6,4] => [1,6,4,3,5,2] => [6,4,3,5,2,1] => ([(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)
 => 6 = 5 + 1
[1,5,3,4,6,2] => [1,6,4,3,5,2] => [6,4,3,5,2,1] => ([(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)
 => 6 = 5 + 1
[1,5,3,6,2,4] => [1,6,5,4,3,2] => [6,5,4,3,2,1] => ([(0,1),(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)
 => 6 = 5 + 1
[1,5,3,6,4,2] => [1,6,5,4,3,2] => [6,5,4,3,2,1] => ([(0,1),(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)
 => 6 = 5 + 1
[1,5,4,2,6,3] => [1,6,4,3,5,2] => [6,4,3,5,2,1] => ([(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)
 => 6 = 5 + 1
[1,5,4,3,6,2] => [1,6,4,3,5,2] => [6,4,3,5,2,1] => ([(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)
 => 6 = 5 + 1
[1,5,4,6,2,3] => [1,6,5,4,3,2] => [6,5,4,3,2,1] => ([(0,1),(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)
 => 6 = 5 + 1
[1,5,4,6,3,2] => [1,6,5,4,3,2] => [6,5,4,3,2,1] => ([(0,1),(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)
 => 6 = 5 + 1
[1,5,6,3,4,2] => [1,6,5,4,3,2] => [6,5,4,3,2,1] => ([(0,1),(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)
 => 6 = 5 + 1
[1,6,2,4,3,5] => [1,6,3,5,4,2] => [6,3,5,4,2,1] => ([(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)
 => 6 = 5 + 1
[1,6,2,5,3,4] => [1,6,3,5,4,2] => [6,3,5,4,2,1] => ([(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)
 => 6 = 5 + 1
[1,6,2,5,4,3] => [1,6,3,5,4,2] => [6,3,5,4,2,1] => ([(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)
 => 6 = 5 + 1
[1,6,3,2,5,4] => [1,6,4,3,5,2] => [6,4,3,5,2,1] => ([(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)
 => 6 = 5 + 1
[1,6,3,4,2,5] => [1,6,5,4,3,2] => [6,5,4,3,2,1] => ([(0,1),(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)
 => 6 = 5 + 1
[1,6,3,4,5,2] => [1,6,5,4,3,2] => [6,5,4,3,2,1] => ([(0,1),(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)
 => 6 = 5 + 1
[1,6,3,5,2,4] => [1,6,5,4,3,2] => [6,5,4,3,2,1] => ([(0,1),(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)
 => 6 = 5 + 1
[1,6,3,5,4,2] => [1,6,5,4,3,2] => [6,5,4,3,2,1] => ([(0,1),(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)
 => 6 = 5 + 1
[1,6,4,2,5,3] => [1,6,5,4,3,2] => [6,5,4,3,2,1] => ([(0,1),(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)
 => 6 = 5 + 1
[1,6,4,3,2,5] => [1,6,5,4,3,2] => [6,5,4,3,2,1] => ([(0,1),(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)
 => 6 = 5 + 1
[1,6,4,3,5,2] => [1,6,5,4,3,2] => [6,5,4,3,2,1] => ([(0,1),(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)
 => 6 = 5 + 1
[1,6,4,5,2,3] => [1,6,5,4,3,2] => [6,5,4,3,2,1] => ([(0,1),(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)
 => 6 = 5 + 1
[1,6,4,5,3,2] => [1,6,5,4,3,2] => [6,5,4,3,2,1] => ([(0,1),(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)
 => 6 = 5 + 1
Description
The pebbling number of a connected graph.