Your data matches 2 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001498
Mapping
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00122: Dyck paths —Elizalde-Deutsch bijection⟶ Dyck paths
Mp00118: Dyck paths —swap returns and last descent⟶ Dyck paths
St001498: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,2] => [1,0,1,0]
 => [1,1,0,0]
 => [1,0,1,0]
 => 1
[1,2,3] => [1,0,1,0,1,0]
 => [1,1,0,0,1,0]
 => [1,1,0,1,0,0]
 => 0
[1,3,2] => [1,0,1,1,0,0]
 => [1,1,0,1,0,0]
 => [1,1,0,0,1,0]
 => 2
[2,1,3] => [1,1,0,0,1,0]
 => [1,1,1,0,0,0]
 => [1,0,1,0,1,0]
 => 1
[2,3,1] => [1,1,0,1,0,0]
 => [1,0,1,1,0,0]
 => [1,0,1,1,0,0]
 => 1
[1,2,3,4] => [1,0,1,0,1,0,1,0]
 => [1,1,0,0,1,1,0,0]
 => [1,1,0,0,1,1,0,0]
 => 2
[1,2,4,3] => [1,0,1,0,1,1,0,0]
 => [1,1,0,1,1,0,0,0]
 => [1,1,0,0,1,0,1,0]
 => 2
[1,3,2,4] => [1,0,1,1,0,0,1,0]
 => [1,1,0,0,1,0,1,0]
 => [1,1,0,1,1,0,0,0]
 => 0
[1,3,4,2] => [1,0,1,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0]
 => [1,1,0,1,0,1,0,0]
 => 0
[1,4,2,3] => [1,0,1,1,1,0,0,0]
 => [1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0]
 => 2
[1,4,3,2] => [1,0,1,1,1,0,0,0]
 => [1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0]
 => 2
[2,1,3,4] => [1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,1,0,0]
 => [1,1,1,0,0,0,1,0]
 => 3
[2,1,4,3] => [1,1,0,0,1,1,0,0]
 => [1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0]
 => 1
[2,3,1,4] => [1,1,0,1,0,0,1,0]
 => [1,1,1,0,0,0,1,0]
 => [1,1,1,0,0,1,0,0]
 => 0
[2,3,4,1] => [1,1,0,1,0,1,0,0]
 => [1,0,1,1,0,0,1,0]
 => [1,1,1,0,1,0,0,0]
 => 0
[2,4,1,3] => [1,1,0,1,1,0,0,0]
 => [1,0,1,1,0,1,0,0]
 => [1,0,1,1,0,1,0,0]
 => 1
[2,4,3,1] => [1,1,0,1,1,0,0,0]
 => [1,0,1,1,0,1,0,0]
 => [1,0,1,1,0,1,0,0]
 => 1
[3,1,2,4] => [1,1,1,0,0,0,1,0]
 => [1,1,1,0,1,0,0,0]
 => [1,0,1,1,0,0,1,0]
 => 2
[3,1,4,2] => [1,1,1,0,0,1,0,0]
 => [1,0,1,1,1,0,0,0]
 => [1,0,1,0,1,1,0,0]
 => 1
[3,2,1,4] => [1,1,1,0,0,0,1,0]
 => [1,1,1,0,1,0,0,0]
 => [1,0,1,1,0,0,1,0]
 => 2
[3,2,4,1] => [1,1,1,0,0,1,0,0]
 => [1,0,1,1,1,0,0,0]
 => [1,0,1,0,1,1,0,0]
 => 1
[3,4,1,2] => [1,1,1,0,1,0,0,0]
 => [1,0,1,0,1,1,0,0]
 => [1,0,1,1,1,0,0,0]
 => 1
[3,4,2,1] => [1,1,1,0,1,0,0,0]
 => [1,0,1,0,1,1,0,0]
 => [1,0,1,1,1,0,0,0]
 => 1
[1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,1,1,0,1,0,0,0]
 => 0
[1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,1,0,0,0,1,0]
 => [1,1,0,1,1,0,0,1,0,0]
 => 0
[1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,1,0,0]
 => [1,1,0,0,1,1,0,1,0,0]
 => 2
[1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0]
 => [1,1,0,1,1,0,0,1,0,0]
 => [1,1,0,1,1,0,0,0,1,0]
 => 3
[1,2,5,3,4] => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,0,1,1,1,0,0,0,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => 2
[1,2,5,4,3] => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,0,1,1,1,0,0,0,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => 2
[1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => [1,1,0,0,1,0,1,1,0,0]
 => 2
[1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0]
 => [1,1,0,1,1,0,1,0,0,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 2
[1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0]
 => [1,1,0,0,1,0,1,1,0,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => 2
[1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,1,0,0]
 => 2
[1,3,5,2,4] => [1,0,1,1,0,1,1,0,0,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => 2
[1,3,5,4,2] => [1,0,1,1,0,1,1,0,0,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => 2
[1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,1,1,1,0,0,0,0]
 => 0
[1,4,2,5,3] => [1,0,1,1,1,0,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => 0
[1,4,3,2,5] => [1,0,1,1,1,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,1,1,1,0,0,0,0]
 => 0
[1,4,3,5,2] => [1,0,1,1,1,0,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => 0
[1,4,5,2,3] => [1,0,1,1,1,0,1,0,0,0]
 => [1,1,0,1,0,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 0
[1,4,5,3,2] => [1,0,1,1,1,0,1,0,0,0]
 => [1,1,0,1,0,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 0
[1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0]
 => 2
[1,5,2,4,3] => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0]
 => 2
[1,5,3,2,4] => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0]
 => 2
[1,5,3,4,2] => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0]
 => 2
[1,5,4,2,3] => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0]
 => 2
[1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0]
 => 2
[2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,1,1,0,0,1,0,1,0,0]
 => 0
[2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => 0
[2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,0,0,1,0,0,1,0]
 => 3
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: St001645
(load all 2 compositions to match this statistic)
Mapping
Mp00254: Permutations —Inverse fireworks map⟶ Permutations
Mp00086: Permutations —first fundamental transformation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St001645: Graphs ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 14%
Values
[1,2] => [1,2] => [1,2] => ([],2)
 => ? = 1 + 6
[1,2,3] => [1,2,3] => [1,2,3] => ([],3)
 => ? = 0 + 6
[1,3,2] => [1,3,2] => [1,3,2] => ([(1,2)],3)
 => ? = 2 + 6
[2,1,3] => [2,1,3] => [2,1,3] => ([(1,2)],3)
 => ? = 1 + 6
[2,3,1] => [1,3,2] => [1,3,2] => ([(1,2)],3)
 => ? = 1 + 6
[1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([],4)
 => ? = 2 + 6
[1,2,4,3] => [1,2,4,3] => [1,2,4,3] => ([(2,3)],4)
 => ? = 2 + 6
[1,3,2,4] => [1,3,2,4] => [1,3,2,4] => ([(2,3)],4)
 => ? = 0 + 6
[1,3,4,2] => [1,2,4,3] => [1,2,4,3] => ([(2,3)],4)
 => ? = 0 + 6
[1,4,2,3] => [1,4,2,3] => [1,3,4,2] => ([(1,3),(2,3)],4)
 => ? = 2 + 6
[1,4,3,2] => [1,4,3,2] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ? = 2 + 6
[2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(2,3)],4)
 => ? = 3 + 6
[2,1,4,3] => [2,1,4,3] => [2,1,4,3] => ([(0,3),(1,2)],4)
 => ? = 1 + 6
[2,3,1,4] => [1,3,2,4] => [1,3,2,4] => ([(2,3)],4)
 => ? = 0 + 6
[2,3,4,1] => [1,2,4,3] => [1,2,4,3] => ([(2,3)],4)
 => ? = 0 + 6
[2,4,1,3] => [2,4,1,3] => [3,2,4,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 1 + 6
[2,4,3,1] => [1,4,3,2] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ? = 1 + 6
[3,1,2,4] => [3,1,2,4] => [2,3,1,4] => ([(1,3),(2,3)],4)
 => ? = 2 + 6
[3,1,4,2] => [2,1,4,3] => [2,1,4,3] => ([(0,3),(1,2)],4)
 => ? = 1 + 6
[3,2,1,4] => [3,2,1,4] => [3,1,2,4] => ([(1,3),(2,3)],4)
 => ? = 2 + 6
[3,2,4,1] => [2,1,4,3] => [2,1,4,3] => ([(0,3),(1,2)],4)
 => ? = 1 + 6
[3,4,1,2] => [2,4,1,3] => [3,2,4,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 1 + 6
[3,4,2,1] => [1,4,3,2] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ? = 1 + 6
[1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([],5)
 => ? = 0 + 6
[1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ([(3,4)],5)
 => ? = 0 + 6
[1,2,4,3,5] => [1,2,4,3,5] => [1,2,4,3,5] => ([(3,4)],5)
 => ? = 2 + 6
[1,2,4,5,3] => [1,2,3,5,4] => [1,2,3,5,4] => ([(3,4)],5)
 => ? = 3 + 6
[1,2,5,3,4] => [1,2,5,3,4] => [1,2,4,5,3] => ([(2,4),(3,4)],5)
 => ? = 2 + 6
[1,2,5,4,3] => [1,2,5,4,3] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ? = 2 + 6
[1,3,2,4,5] => [1,3,2,4,5] => [1,3,2,4,5] => ([(3,4)],5)
 => ? = 2 + 6
[1,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => ([(1,4),(2,3)],5)
 => ? = 2 + 6
[1,3,4,2,5] => [1,2,4,3,5] => [1,2,4,3,5] => ([(3,4)],5)
 => ? = 2 + 6
[1,3,4,5,2] => [1,2,3,5,4] => [1,2,3,5,4] => ([(3,4)],5)
 => ? = 2 + 6
[1,3,5,2,4] => [1,3,5,2,4] => [1,4,3,5,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 2 + 6
[1,3,5,4,2] => [1,2,5,4,3] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ? = 2 + 6
[1,4,2,3,5] => [1,4,2,3,5] => [1,3,4,2,5] => ([(2,4),(3,4)],5)
 => ? = 0 + 6
[1,4,2,5,3] => [1,3,2,5,4] => [1,3,2,5,4] => ([(1,4),(2,3)],5)
 => ? = 0 + 6
[1,4,3,2,5] => [1,4,3,2,5] => [1,4,2,3,5] => ([(2,4),(3,4)],5)
 => ? = 0 + 6
[1,4,3,5,2] => [1,3,2,5,4] => [1,3,2,5,4] => ([(1,4),(2,3)],5)
 => ? = 0 + 6
[1,4,5,2,3] => [1,3,5,2,4] => [1,4,3,5,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0 + 6
[1,4,5,3,2] => [1,2,5,4,3] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ? = 0 + 6
[1,5,2,3,4] => [1,5,2,3,4] => [1,3,4,5,2] => ([(1,4),(2,4),(3,4)],5)
 => ? = 2 + 6
[1,5,2,4,3] => [1,5,2,4,3] => [1,4,5,3,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 2 + 6
[1,5,3,2,4] => [1,5,3,2,4] => [1,4,2,5,3] => ([(1,4),(2,3),(3,4)],5)
 => ? = 2 + 6
[1,5,3,4,2] => [1,5,2,4,3] => [1,4,5,3,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 2 + 6
[1,5,4,2,3] => [1,5,4,2,3] => [1,3,5,2,4] => ([(1,4),(2,3),(3,4)],5)
 => ? = 2 + 6
[1,5,4,3,2] => [1,5,4,3,2] => [1,5,2,3,4] => ([(1,4),(2,4),(3,4)],5)
 => ? = 2 + 6
[2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ([(3,4)],5)
 => ? = 0 + 6
[2,1,3,5,4] => [2,1,3,5,4] => [2,1,3,5,4] => ([(1,4),(2,3)],5)
 => ? = 0 + 6
[2,1,4,3,5] => [2,1,4,3,5] => [2,1,4,3,5] => ([(1,4),(2,3)],5)
 => ? = 3 + 6
[3,7,1,6,2,5,4] => [3,7,1,6,2,5,4] => [6,5,3,7,4,2,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 1 + 6
[3,7,1,6,5,2,4] => [3,7,1,6,5,2,4] => [6,4,3,7,2,5,1] => ([(0,1),(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 1 + 6
[3,7,2,6,1,5,4] => [3,7,2,6,1,5,4] => [5,6,3,7,4,1,2] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => 7 = 1 + 6
[3,7,2,6,5,1,4] => [3,7,2,6,5,1,4] => [4,6,3,7,1,5,2] => ([(0,1),(0,4),(0,6),(1,3),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => 7 = 1 + 6
[4,7,1,6,2,5,3] => [3,7,1,6,2,5,4] => [6,5,3,7,4,2,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 1 + 6
[4,7,1,6,3,5,2] => [3,7,1,6,2,5,4] => [6,5,3,7,4,2,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 1 + 6
[4,7,1,6,5,2,3] => [3,7,1,6,5,2,4] => [6,4,3,7,2,5,1] => ([(0,1),(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 1 + 6
[4,7,2,6,1,5,3] => [3,7,2,6,1,5,4] => [5,6,3,7,4,1,2] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => 7 = 1 + 6
[4,7,2,6,3,5,1] => [3,7,1,6,2,5,4] => [6,5,3,7,4,2,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 1 + 6
[4,7,2,6,5,1,3] => [3,7,2,6,5,1,4] => [4,6,3,7,1,5,2] => ([(0,1),(0,4),(0,6),(1,3),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => 7 = 1 + 6
[4,7,3,6,1,5,2] => [3,7,2,6,1,5,4] => [5,6,3,7,4,1,2] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => 7 = 1 + 6
[4,7,3,6,2,5,1] => [3,7,2,6,1,5,4] => [5,6,3,7,4,1,2] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => 7 = 1 + 6
[4,7,3,6,5,1,2] => [3,7,2,6,5,1,4] => [4,6,3,7,1,5,2] => ([(0,1),(0,4),(0,6),(1,3),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => 7 = 1 + 6
[5,7,1,6,2,4,3] => [3,7,1,6,2,5,4] => [6,5,3,7,4,2,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 1 + 6
[5,7,1,6,3,4,2] => [3,7,1,6,2,5,4] => [6,5,3,7,4,2,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 1 + 6
[5,7,1,6,4,2,3] => [3,7,1,6,5,2,4] => [6,4,3,7,2,5,1] => ([(0,1),(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 1 + 6
[5,7,2,6,1,4,3] => [3,7,2,6,1,5,4] => [5,6,3,7,4,1,2] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => 7 = 1 + 6
[5,7,2,6,3,4,1] => [3,7,1,6,2,5,4] => [6,5,3,7,4,2,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 1 + 6
[5,7,2,6,4,1,3] => [3,7,2,6,5,1,4] => [4,6,3,7,1,5,2] => ([(0,1),(0,4),(0,6),(1,3),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => 7 = 1 + 6
[5,7,3,6,1,4,2] => [3,7,2,6,1,5,4] => [5,6,3,7,4,1,2] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => 7 = 1 + 6
[5,7,3,6,2,4,1] => [3,7,2,6,1,5,4] => [5,6,3,7,4,1,2] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => 7 = 1 + 6
[5,7,3,6,4,1,2] => [3,7,2,6,5,1,4] => [4,6,3,7,1,5,2] => ([(0,1),(0,4),(0,6),(1,3),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => 7 = 1 + 6
[5,7,4,6,1,3,2] => [3,7,2,6,1,5,4] => [5,6,3,7,4,1,2] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => 7 = 1 + 6
[5,7,4,6,2,3,1] => [3,7,2,6,1,5,4] => [5,6,3,7,4,1,2] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => 7 = 1 + 6
[5,7,4,6,3,1,2] => [3,7,2,6,5,1,4] => [4,6,3,7,1,5,2] => ([(0,1),(0,4),(0,6),(1,3),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => 7 = 1 + 6
[6,7,1,5,2,4,3] => [3,7,1,6,2,5,4] => [6,5,3,7,4,2,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 1 + 6
[6,7,1,5,3,4,2] => [3,7,1,6,2,5,4] => [6,5,3,7,4,2,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 1 + 6
[6,7,1,5,4,2,3] => [3,7,1,6,5,2,4] => [6,4,3,7,2,5,1] => ([(0,1),(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 1 + 6
[6,7,2,5,1,4,3] => [3,7,2,6,1,5,4] => [5,6,3,7,4,1,2] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => 7 = 1 + 6
[6,7,2,5,3,4,1] => [3,7,1,6,2,5,4] => [6,5,3,7,4,2,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 1 + 6
[6,7,2,5,4,1,3] => [3,7,2,6,5,1,4] => [4,6,3,7,1,5,2] => ([(0,1),(0,4),(0,6),(1,3),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => 7 = 1 + 6
[6,7,3,5,1,4,2] => [3,7,2,6,1,5,4] => [5,6,3,7,4,1,2] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => 7 = 1 + 6
[6,7,3,5,2,4,1] => [3,7,2,6,1,5,4] => [5,6,3,7,4,1,2] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => 7 = 1 + 6
[6,7,3,5,4,1,2] => [3,7,2,6,5,1,4] => [4,6,3,7,1,5,2] => ([(0,1),(0,4),(0,6),(1,3),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => 7 = 1 + 6
[6,7,4,5,1,3,2] => [3,7,2,6,1,5,4] => [5,6,3,7,4,1,2] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => 7 = 1 + 6
[6,7,4,5,2,3,1] => [3,7,2,6,1,5,4] => [5,6,3,7,4,1,2] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => 7 = 1 + 6
[6,7,4,5,3,1,2] => [3,7,2,6,5,1,4] => [4,6,3,7,1,5,2] => ([(0,1),(0,4),(0,6),(1,3),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => 7 = 1 + 6
Description
The pebbling number of a connected graph.