Your data matches 3 different statistics following compositions of up to 3 maps.
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Matching statistic: St001629
(load all 2 compositions to match this statistic)
Mapping
Mp00054: Parking functions —to inverse des composition⟶ Integer compositions
Mp00133: Integer compositions —delta morphism⟶ Integer compositions
St001629: Integer compositions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,1,1] => [1,1,1] => [3] => 1
[1,1,2] => [1,1,1] => [3] => 1
[1,3,1] => [1,1,1] => [3] => 1
[1,2,2] => [1,1,1] => [3] => 1
[1,2,3] => [1,1,1] => [3] => 1
[1,1,1,1] => [1,1,1,1] => [4] => 1
[1,1,1,2] => [1,1,1,1] => [4] => 1
[1,1,2,1] => [1,1,2] => [2,1] => 0
[1,2,1,1] => [1,2,1] => [1,1,1] => 1
[2,1,1,1] => [2,1,1] => [1,2] => 0
[1,1,1,3] => [1,1,2] => [2,1] => 0
[1,1,3,1] => [1,1,1,1] => [4] => 1
[1,3,1,1] => [1,2,1] => [1,1,1] => 1
[3,1,1,1] => [2,1,1] => [1,2] => 0
[1,1,1,4] => [1,1,2] => [2,1] => 0
[1,1,4,1] => [1,2,1] => [1,1,1] => 1
[1,4,1,1] => [1,1,1,1] => [4] => 1
[4,1,1,1] => [2,1,1] => [1,2] => 0
[1,1,2,2] => [1,1,1,1] => [4] => 1
[1,2,1,2] => [1,2,1] => [1,1,1] => 1
[1,2,2,1] => [1,1,2] => [2,1] => 0
[2,1,1,2] => [2,1,1] => [1,2] => 0
[2,2,1,1] => [1,2,1] => [1,1,1] => 1
[1,1,2,3] => [1,1,1,1] => [4] => 1
[1,1,3,2] => [1,1,2] => [2,1] => 0
[1,2,1,3] => [1,2,1] => [1,1,1] => 1
[1,2,3,1] => [1,1,2] => [2,1] => 0
[1,3,1,2] => [1,2,1] => [1,1,1] => 1
[2,1,1,3] => [2,1,1] => [1,2] => 0
[2,3,1,1] => [1,2,1] => [1,1,1] => 1
[3,1,1,2] => [2,1,1] => [1,2] => 0
[1,1,2,4] => [1,1,2] => [2,1] => 0
[1,1,4,2] => [1,2,1] => [1,1,1] => 1
[1,2,4,1] => [1,2,1] => [1,1,1] => 1
[1,4,1,2] => [1,1,1,1] => [4] => 1
[1,4,2,1] => [1,1,2] => [2,1] => 0
[2,1,4,1] => [2,1,1] => [1,2] => 0
[4,1,1,2] => [2,1,1] => [1,2] => 0
[4,2,1,1] => [1,2,1] => [1,1,1] => 1
[1,1,3,3] => [1,2,1] => [1,1,1] => 1
[1,3,1,3] => [1,1,1,1] => [4] => 1
[1,3,3,1] => [1,1,2] => [2,1] => 0
[3,1,1,3] => [2,1,1] => [1,2] => 0
[3,3,1,1] => [1,2,1] => [1,1,1] => 1
[1,1,3,4] => [1,2,1] => [1,1,1] => 1
[1,3,1,4] => [1,1,2] => [2,1] => 0
[1,3,4,1] => [1,1,1,1] => [4] => 1
[1,4,1,3] => [1,1,2] => [2,1] => 0
[1,4,3,1] => [1,2,1] => [1,1,1] => 1
[3,1,4,1] => [2,1,1] => [1,2] => 0
Description
The coefficient of the integer composition in the quasisymmetric expansion of the relabelling action of the symmetric group on cycles.
Matching statistic: St001232
Mapping
Mp00054: Parking functions —to inverse des composition⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00121: Dyck paths —Cori-Le Borgne involution⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 7% ●values known / values provided: 7%●distinct values known / distinct values provided: 50%
Values
[1,1,1] => [1,1,1] => [1,0,1,0,1,0]
 => [1,0,1,0,1,0]
 => ? = 1 + 3
[1,1,2] => [1,1,1] => [1,0,1,0,1,0]
 => [1,0,1,0,1,0]
 => ? = 1 + 3
[1,3,1] => [1,1,1] => [1,0,1,0,1,0]
 => [1,0,1,0,1,0]
 => ? = 1 + 3
[1,2,2] => [1,1,1] => [1,0,1,0,1,0]
 => [1,0,1,0,1,0]
 => ? = 1 + 3
[1,2,3] => [1,1,1] => [1,0,1,0,1,0]
 => [1,0,1,0,1,0]
 => ? = 1 + 3
[1,1,1,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => ? = 1 + 3
[1,1,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => ? = 1 + 3
[1,1,2,1] => [1,1,2] => [1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,0]
 => ? = 0 + 3
[1,2,1,1] => [1,2,1] => [1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,0,1,0]
 => ? = 1 + 3
[2,1,1,1] => [2,1,1] => [1,1,0,0,1,0,1,0]
 => [1,1,0,0,1,0,1,0]
 => ? = 0 + 3
[1,1,1,3] => [1,1,2] => [1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,0]
 => ? = 0 + 3
[1,1,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => ? = 1 + 3
[1,3,1,1] => [1,2,1] => [1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,0,1,0]
 => ? = 1 + 3
[3,1,1,1] => [2,1,1] => [1,1,0,0,1,0,1,0]
 => [1,1,0,0,1,0,1,0]
 => ? = 0 + 3
[1,1,1,4] => [1,1,2] => [1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,0]
 => ? = 0 + 3
[1,1,4,1] => [1,2,1] => [1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,0,1,0]
 => ? = 1 + 3
[1,4,1,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => ? = 1 + 3
[4,1,1,1] => [2,1,1] => [1,1,0,0,1,0,1,0]
 => [1,1,0,0,1,0,1,0]
 => ? = 0 + 3
[1,1,2,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => ? = 1 + 3
[1,2,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,0,1,0]
 => ? = 1 + 3
[1,2,2,1] => [1,1,2] => [1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,0]
 => ? = 0 + 3
[2,1,1,2] => [2,1,1] => [1,1,0,0,1,0,1,0]
 => [1,1,0,0,1,0,1,0]
 => ? = 0 + 3
[2,2,1,1] => [1,2,1] => [1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,0,1,0]
 => ? = 1 + 3
[1,1,2,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => ? = 1 + 3
[1,1,3,2] => [1,1,2] => [1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,0]
 => ? = 0 + 3
[1,2,1,3] => [1,2,1] => [1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,0,1,0]
 => ? = 1 + 3
[1,2,3,1] => [1,1,2] => [1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,0]
 => ? = 0 + 3
[1,3,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,0,1,0]
 => ? = 1 + 3
[2,1,1,3] => [2,1,1] => [1,1,0,0,1,0,1,0]
 => [1,1,0,0,1,0,1,0]
 => ? = 0 + 3
[2,3,1,1] => [1,2,1] => [1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,0,1,0]
 => ? = 1 + 3
[3,1,1,2] => [2,1,1] => [1,1,0,0,1,0,1,0]
 => [1,1,0,0,1,0,1,0]
 => ? = 0 + 3
[1,1,2,4] => [1,1,2] => [1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,0]
 => ? = 0 + 3
[1,1,4,2] => [1,2,1] => [1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,0,1,0]
 => ? = 1 + 3
[1,2,4,1] => [1,2,1] => [1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,0,1,0]
 => ? = 1 + 3
[1,4,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => ? = 1 + 3
[1,4,2,1] => [1,1,2] => [1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,0]
 => ? = 0 + 3
[2,1,4,1] => [2,1,1] => [1,1,0,0,1,0,1,0]
 => [1,1,0,0,1,0,1,0]
 => ? = 0 + 3
[4,1,1,2] => [2,1,1] => [1,1,0,0,1,0,1,0]
 => [1,1,0,0,1,0,1,0]
 => ? = 0 + 3
[4,2,1,1] => [1,2,1] => [1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,0,1,0]
 => ? = 1 + 3
[1,1,3,3] => [1,2,1] => [1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,0,1,0]
 => ? = 1 + 3
[1,3,1,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => ? = 1 + 3
[1,3,3,1] => [1,1,2] => [1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,0]
 => ? = 0 + 3
[3,1,1,3] => [2,1,1] => [1,1,0,0,1,0,1,0]
 => [1,1,0,0,1,0,1,0]
 => ? = 0 + 3
[3,3,1,1] => [1,2,1] => [1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,0,1,0]
 => ? = 1 + 3
[1,1,3,4] => [1,2,1] => [1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,0,1,0]
 => ? = 1 + 3
[1,3,1,4] => [1,1,2] => [1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,0]
 => ? = 0 + 3
[1,3,4,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => ? = 1 + 3
[1,4,1,3] => [1,1,2] => [1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,0]
 => ? = 0 + 3
[1,4,3,1] => [1,2,1] => [1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,0,1,0]
 => ? = 1 + 3
[3,1,4,1] => [2,1,1] => [1,1,0,0,1,0,1,0]
 => [1,1,0,0,1,0,1,0]
 => ? = 0 + 3
[2,1,2,1,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3 = 0 + 3
[2,1,3,1,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3 = 0 + 3
[3,1,2,1,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3 = 0 + 3
[2,1,4,1,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3 = 0 + 3
[4,1,2,1,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3 = 0 + 3
[2,1,1,5,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3 = 0 + 3
[5,1,2,1,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3 = 0 + 3
[3,1,3,1,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3 = 0 + 3
[3,1,4,1,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3 = 0 + 3
[4,1,3,1,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3 = 0 + 3
[3,1,1,5,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3 = 0 + 3
[5,1,3,1,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3 = 0 + 3
[4,1,4,1,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3 = 0 + 3
[4,1,1,5,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3 = 0 + 3
[5,1,1,4,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3 = 0 + 3
[2,1,2,1,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3 = 0 + 3
[2,1,2,1,3] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3 = 0 + 3
[2,1,3,1,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3 = 0 + 3
[3,1,2,1,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3 = 0 + 3
[3,2,2,1,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3 = 0 + 3
[2,1,2,1,4] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3 = 0 + 3
[2,1,4,1,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3 = 0 + 3
[4,1,2,1,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3 = 0 + 3
[4,2,2,1,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3 = 0 + 3
[2,1,1,5,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3 = 0 + 3
[2,1,2,5,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3 = 0 + 3
[2,5,2,1,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3 = 0 + 3
[5,1,2,1,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3 = 0 + 3
[2,1,3,1,3] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3 = 0 + 3
[3,1,2,1,3] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3 = 0 + 3
[3,1,3,1,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3 = 0 + 3
[3,2,3,1,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3 = 0 + 3
[2,1,3,1,4] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3 = 0 + 3
[2,1,4,1,3] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3 = 0 + 3
[3,1,2,1,4] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3 = 0 + 3
[3,1,4,1,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3 = 0 + 3
[3,2,4,1,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3 = 0 + 3
[4,1,2,1,3] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3 = 0 + 3
[4,1,3,1,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3 = 0 + 3
[4,2,3,1,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3 = 0 + 3
[2,1,1,5,3] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3 = 0 + 3
[2,1,3,5,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3 = 0 + 3
[2,5,3,1,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3 = 0 + 3
[3,1,1,5,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3 = 0 + 3
[3,1,2,5,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3 = 0 + 3
[3,5,2,1,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3 = 0 + 3
[5,1,2,1,3] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3 = 0 + 3
[5,1,3,1,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3 = 0 + 3
[2,1,1,4,4] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3 = 0 + 3
[2,4,4,1,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3 = 0 + 3
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
Matching statistic: St001645
(load all 2 compositions to match this statistic)
Mapping
Mp00054: Parking functions —to inverse des composition⟶ Integer compositions
Mp00039: Integer compositions —complement⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St001645: Graphs ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 25%
Values
[1,1,1] => [1,1,1] => [3] => ([],3)
 => ? = 1 + 6
[1,1,2] => [1,1,1] => [3] => ([],3)
 => ? = 1 + 6
[1,3,1] => [1,1,1] => [3] => ([],3)
 => ? = 1 + 6
[1,2,2] => [1,1,1] => [3] => ([],3)
 => ? = 1 + 6
[1,2,3] => [1,1,1] => [3] => ([],3)
 => ? = 1 + 6
[1,1,1,1] => [1,1,1,1] => [4] => ([],4)
 => ? = 1 + 6
[1,1,1,2] => [1,1,1,1] => [4] => ([],4)
 => ? = 1 + 6
[1,1,2,1] => [1,1,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => ? = 0 + 6
[1,2,1,1] => [1,2,1] => [2,2] => ([(1,3),(2,3)],4)
 => ? = 1 + 6
[2,1,1,1] => [2,1,1] => [1,3] => ([(2,3)],4)
 => ? = 0 + 6
[1,1,1,3] => [1,1,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => ? = 0 + 6
[1,1,3,1] => [1,1,1,1] => [4] => ([],4)
 => ? = 1 + 6
[1,3,1,1] => [1,2,1] => [2,2] => ([(1,3),(2,3)],4)
 => ? = 1 + 6
[3,1,1,1] => [2,1,1] => [1,3] => ([(2,3)],4)
 => ? = 0 + 6
[1,1,1,4] => [1,1,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => ? = 0 + 6
[1,1,4,1] => [1,2,1] => [2,2] => ([(1,3),(2,3)],4)
 => ? = 1 + 6
[1,4,1,1] => [1,1,1,1] => [4] => ([],4)
 => ? = 1 + 6
[4,1,1,1] => [2,1,1] => [1,3] => ([(2,3)],4)
 => ? = 0 + 6
[1,1,2,2] => [1,1,1,1] => [4] => ([],4)
 => ? = 1 + 6
[1,2,1,2] => [1,2,1] => [2,2] => ([(1,3),(2,3)],4)
 => ? = 1 + 6
[1,2,2,1] => [1,1,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => ? = 0 + 6
[2,1,1,2] => [2,1,1] => [1,3] => ([(2,3)],4)
 => ? = 0 + 6
[2,2,1,1] => [1,2,1] => [2,2] => ([(1,3),(2,3)],4)
 => ? = 1 + 6
[1,1,2,3] => [1,1,1,1] => [4] => ([],4)
 => ? = 1 + 6
[1,1,3,2] => [1,1,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => ? = 0 + 6
[1,2,1,3] => [1,2,1] => [2,2] => ([(1,3),(2,3)],4)
 => ? = 1 + 6
[1,2,3,1] => [1,1,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => ? = 0 + 6
[1,3,1,2] => [1,2,1] => [2,2] => ([(1,3),(2,3)],4)
 => ? = 1 + 6
[2,1,1,3] => [2,1,1] => [1,3] => ([(2,3)],4)
 => ? = 0 + 6
[2,3,1,1] => [1,2,1] => [2,2] => ([(1,3),(2,3)],4)
 => ? = 1 + 6
[3,1,1,2] => [2,1,1] => [1,3] => ([(2,3)],4)
 => ? = 0 + 6
[1,1,2,4] => [1,1,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => ? = 0 + 6
[1,1,4,2] => [1,2,1] => [2,2] => ([(1,3),(2,3)],4)
 => ? = 1 + 6
[1,2,4,1] => [1,2,1] => [2,2] => ([(1,3),(2,3)],4)
 => ? = 1 + 6
[1,4,1,2] => [1,1,1,1] => [4] => ([],4)
 => ? = 1 + 6
[1,4,2,1] => [1,1,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => ? = 0 + 6
[2,1,4,1] => [2,1,1] => [1,3] => ([(2,3)],4)
 => ? = 0 + 6
[4,1,1,2] => [2,1,1] => [1,3] => ([(2,3)],4)
 => ? = 0 + 6
[4,2,1,1] => [1,2,1] => [2,2] => ([(1,3),(2,3)],4)
 => ? = 1 + 6
[1,1,3,3] => [1,2,1] => [2,2] => ([(1,3),(2,3)],4)
 => ? = 1 + 6
[1,3,1,3] => [1,1,1,1] => [4] => ([],4)
 => ? = 1 + 6
[1,3,3,1] => [1,1,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => ? = 0 + 6
[3,1,1,3] => [2,1,1] => [1,3] => ([(2,3)],4)
 => ? = 0 + 6
[3,3,1,1] => [1,2,1] => [2,2] => ([(1,3),(2,3)],4)
 => ? = 1 + 6
[1,1,3,4] => [1,2,1] => [2,2] => ([(1,3),(2,3)],4)
 => ? = 1 + 6
[1,3,1,4] => [1,1,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => ? = 0 + 6
[1,3,4,1] => [1,1,1,1] => [4] => ([],4)
 => ? = 1 + 6
[1,4,1,3] => [1,1,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => ? = 0 + 6
[1,4,3,1] => [1,2,1] => [2,2] => ([(1,3),(2,3)],4)
 => ? = 1 + 6
[3,1,4,1] => [2,1,1] => [1,3] => ([(2,3)],4)
 => ? = 0 + 6
[1,1,4,3,2,1] => [1,1,4] => [3,1,1,1] => ([(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 = 0 + 6
[1,1,3,2,1,5] => [1,1,4] => [3,1,1,1] => ([(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 = 0 + 6
[1,1,3,2,1,6] => [1,1,4] => [3,1,1,1] => ([(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 = 0 + 6
[1,1,2,1,5,4] => [1,1,4] => [3,1,1,1] => ([(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 = 0 + 6
[1,1,2,1,4,6] => [1,1,4] => [3,1,1,1] => ([(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 = 0 + 6
[1,1,2,1,6,5] => [1,1,4] => [3,1,1,1] => ([(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 = 0 + 6
[1,1,1,5,4,3] => [1,1,4] => [3,1,1,1] => ([(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 = 0 + 6
[1,1,1,4,3,6] => [1,1,4] => [3,1,1,1] => ([(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 = 0 + 6
[1,1,1,3,6,5] => [1,1,4] => [3,1,1,1] => ([(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 = 0 + 6
[1,1,1,6,5,4] => [1,1,4] => [3,1,1,1] => ([(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 = 0 + 6
[1,2,4,3,2,1] => [1,1,4] => [3,1,1,1] => ([(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 = 0 + 6
[1,2,3,2,5,1] => [1,1,4] => [3,1,1,1] => ([(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 = 0 + 6
[1,2,3,2,1,6] => [1,1,4] => [3,1,1,1] => ([(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 = 0 + 6
[1,2,2,5,4,1] => [1,1,4] => [3,1,1,1] => ([(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 = 0 + 6
[1,2,2,4,1,6] => [1,1,4] => [3,1,1,1] => ([(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 = 0 + 6
[1,2,2,1,6,5] => [1,1,4] => [3,1,1,1] => ([(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 = 0 + 6
[1,3,4,3,2,1] => [1,1,4] => [3,1,1,1] => ([(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 = 0 + 6
[1,3,3,5,2,1] => [1,1,4] => [3,1,1,1] => ([(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 = 0 + 6
[1,3,3,2,1,6] => [1,1,4] => [3,1,1,1] => ([(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 = 0 + 6
[1,4,4,3,2,1] => [1,1,4] => [3,1,1,1] => ([(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 = 0 + 6
[1,1,5,4,3,2] => [1,1,4] => [3,1,1,1] => ([(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 = 0 + 6
[1,2,5,4,3,1] => [1,1,4] => [3,1,1,1] => ([(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 = 0 + 6
[1,3,5,4,2,1] => [1,1,4] => [3,1,1,1] => ([(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 = 0 + 6
[1,4,5,3,2,1] => [1,1,4] => [3,1,1,1] => ([(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 = 0 + 6
[1,1,4,3,2,6] => [1,1,4] => [3,1,1,1] => ([(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 = 0 + 6
[1,2,4,3,1,6] => [1,1,4] => [3,1,1,1] => ([(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 = 0 + 6
[1,3,4,2,1,6] => [1,1,4] => [3,1,1,1] => ([(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 = 0 + 6
[1,6,4,3,2,1] => [1,1,4] => [3,1,1,1] => ([(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 = 0 + 6
[1,5,5,3,2,1] => [1,1,4] => [3,1,1,1] => ([(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 = 0 + 6
[1,1,3,2,6,5] => [1,1,4] => [3,1,1,1] => ([(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 = 0 + 6
[1,2,3,1,6,5] => [1,1,4] => [3,1,1,1] => ([(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 = 0 + 6
[1,5,3,2,1,6] => [1,1,4] => [3,1,1,1] => ([(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 = 0 + 6
[1,6,3,2,1,5] => [1,1,4] => [3,1,1,1] => ([(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 = 0 + 6
[1,4,5,4,2,1] => [1,1,4] => [3,1,1,1] => ([(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 = 0 + 6
[1,4,4,2,1,6] => [1,1,4] => [3,1,1,1] => ([(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 = 0 + 6
[1,5,5,2,1,4] => [1,1,4] => [3,1,1,1] => ([(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 = 0 + 6
[1,1,2,6,5,4] => [1,1,4] => [3,1,1,1] => ([(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 = 0 + 6
[1,4,2,1,6,5] => [1,1,4] => [3,1,1,1] => ([(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 = 0 + 6
[1,5,2,1,6,4] => [1,1,4] => [3,1,1,1] => ([(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 = 0 + 6
[1,6,2,1,5,4] => [1,1,4] => [3,1,1,1] => ([(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 = 0 + 6
[1,3,5,4,3,1] => [1,1,4] => [3,1,1,1] => ([(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 = 0 + 6
[1,3,4,3,1,6] => [1,1,4] => [3,1,1,1] => ([(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 = 0 + 6
[1,3,3,1,6,5] => [1,1,4] => [3,1,1,1] => ([(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 = 0 + 6
[1,4,5,4,1,3] => [1,1,4] => [3,1,1,1] => ([(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 = 0 + 6
[1,4,4,1,6,3] => [1,1,4] => [3,1,1,1] => ([(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 = 0 + 6
[1,5,5,1,4,3] => [1,1,4] => [3,1,1,1] => ([(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 = 0 + 6
[1,3,1,6,5,4] => [1,1,4] => [3,1,1,1] => ([(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 = 0 + 6
[1,4,1,6,5,3] => [1,1,4] => [3,1,1,1] => ([(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 = 0 + 6
[1,5,1,6,4,3] => [1,1,4] => [3,1,1,1] => ([(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 = 0 + 6
[1,6,1,5,4,3] => [1,1,4] => [3,1,1,1] => ([(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 = 0 + 6
Description
The pebbling number of a connected graph.