Your data matches 3 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000777
Mapping
Mp00201: Dyck paths —Ringel⟶ Permutations
Mp00088: Permutations —Kreweras complement⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000777: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0,1,0]
 => [3,1,2] => [3,1,2] => ([(0,2),(1,2)],3)
 => 3
[1,0,1,0,1,0]
 => [4,1,2,3] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 3
[1,1,0,0,1,0]
 => [2,4,1,3] => [4,2,1,3] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 4
[1,1,0,1,0,0]
 => [4,3,1,2] => [4,1,3,2] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 4
[1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => [3,4,5,1,2] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 4
[1,0,1,1,0,0,1,0]
 => [3,1,5,2,4] => [3,5,2,1,4] => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => 5
[1,0,1,1,0,1,0,0]
 => [5,1,4,2,3] => [3,5,1,4,2] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 5
[1,1,0,0,1,0,1,0]
 => [2,5,1,3,4] => [4,2,5,1,3] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 5
[1,1,0,1,0,0,1,0]
 => [5,3,1,2,4] => [4,5,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 3
[1,1,0,1,0,1,0,0]
 => [5,4,1,2,3] => [4,5,1,3,2] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => 5
[1,1,1,0,0,0,1,0]
 => [2,3,5,1,4] => [5,2,3,1,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 5
[1,1,1,0,0,1,0,0]
 => [2,5,4,1,3] => [5,2,1,4,3] => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => 4
[1,1,1,0,1,0,0,0]
 => [5,3,4,1,2] => [5,1,3,4,2] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 5
[1,0,1,0,1,0,1,0,1,0]
 => [6,1,2,3,4,5] => [3,4,5,6,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 4
[1,0,1,0,1,1,0,0,1,0]
 => [4,1,2,6,3,5] => [3,4,6,2,1,5] => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 5
[1,0,1,0,1,1,0,1,0,0]
 => [6,1,2,5,3,4] => [3,4,6,1,5,2] => ([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
 => 6
[1,0,1,1,0,0,1,0,1,0]
 => [3,1,6,2,4,5] => [3,5,2,6,1,4] => ([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 6
[1,0,1,1,0,1,0,0,1,0]
 => [6,1,4,2,3,5] => [3,5,6,4,1,2] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => 6
[1,0,1,1,0,1,0,1,0,0]
 => [6,1,5,2,3,4] => [3,5,6,1,4,2] => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 5
[1,0,1,1,1,0,0,0,1,0]
 => [3,1,4,6,2,5] => [3,6,2,4,1,5] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => 6
[1,0,1,1,1,0,0,1,0,0]
 => [3,1,6,5,2,4] => [3,6,2,1,5,4] => ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => 6
[1,0,1,1,1,0,1,0,0,0]
 => [6,1,4,5,2,3] => [3,6,1,4,5,2] => ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 6
[1,1,0,0,1,0,1,0,1,0]
 => [2,6,1,3,4,5] => [4,2,5,6,1,3] => ([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
 => 6
[1,1,0,0,1,1,0,0,1,0]
 => [2,4,1,6,3,5] => [4,2,6,3,1,5] => ([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 6
[1,1,0,0,1,1,0,1,0,0]
 => [2,6,1,5,3,4] => [4,2,6,1,5,3] => ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)
 => 5
[1,1,0,1,0,0,1,0,1,0]
 => [6,3,1,2,4,5] => [4,5,3,6,1,2] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => 6
[1,1,0,1,0,1,0,0,1,0]
 => [6,4,1,2,3,5] => [4,5,6,3,1,2] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 4
[1,1,0,1,0,1,0,1,0,0]
 => [5,6,1,2,3,4] => [4,5,6,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
 => 3
[1,1,0,1,1,0,0,0,1,0]
 => [4,3,1,6,2,5] => [4,6,3,2,1,5] => ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 5
[1,1,0,1,1,0,0,1,0,0]
 => [6,3,1,5,2,4] => [4,6,3,1,5,2] => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => 6
[1,1,0,1,1,0,1,0,0,0]
 => [6,4,1,5,2,3] => [4,6,1,3,5,2] => ([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => 6
[1,1,1,0,0,0,1,0,1,0]
 => [2,3,6,1,4,5] => [5,2,3,6,1,4] => ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 6
[1,1,1,0,0,1,0,0,1,0]
 => [2,6,4,1,3,5] => [5,2,6,4,1,3] => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => 6
[1,1,1,0,0,1,0,1,0,0]
 => [2,6,5,1,3,4] => [5,2,6,1,4,3] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => 5
[1,1,1,0,1,0,0,0,1,0]
 => [6,3,4,1,2,5] => [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)
 => 3
[1,1,1,0,1,0,0,1,0,0]
 => [6,3,5,1,2,4] => [5,6,3,1,4,2] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => 5
[1,1,1,0,1,0,1,0,0,0]
 => [6,5,4,1,2,3] => [5,6,1,4,3,2] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => 5
[1,1,1,1,0,0,0,0,1,0]
 => [2,3,4,6,1,5] => [6,2,3,4,1,5] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 5
[1,1,1,1,0,0,0,1,0,0]
 => [2,3,6,5,1,4] => [6,2,3,1,5,4] => ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 6
[1,1,1,1,0,0,1,0,0,0]
 => [2,6,4,5,1,3] => [6,2,1,4,5,3] => ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 6
[1,1,1,1,0,1,0,0,0,0]
 => [6,3,4,5,1,2] => [6,1,3,4,5,2] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 5
[1,0,1,0,1,0,1,0,1,0,1,0]
 => [7,1,2,3,4,5,6] => [3,4,5,6,7,1,2] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => 4
[1,0,1,0,1,0,1,1,0,0,1,0]
 => [5,1,2,3,7,4,6] => [3,4,5,7,2,1,6] => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 6
[1,0,1,0,1,0,1,1,0,1,0,0]
 => [7,1,2,3,6,4,5] => [3,4,5,7,1,6,2] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6)],7)
 => 6
[1,0,1,0,1,1,0,0,1,0,1,0]
 => [4,1,2,7,3,5,6] => [3,4,6,2,7,1,5] => ([(0,3),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6),(5,6)],7)
 => 7
[1,0,1,0,1,1,0,1,0,0,1,0]
 => [7,1,2,5,3,4,6] => [3,4,6,7,5,1,2] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
 => 5
[1,0,1,0,1,1,0,1,0,1,0,0]
 => [7,1,2,6,3,4,5] => [3,4,6,7,1,5,2] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => 7
[1,0,1,0,1,1,1,0,0,0,1,0]
 => [4,1,2,5,7,3,6] => [3,4,7,2,5,1,6] => ([(0,5),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => 7
[1,0,1,0,1,1,1,0,0,1,0,0]
 => [4,1,2,7,6,3,5] => [3,4,7,2,1,6,5] => ([(0,1),(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7
[1,0,1,0,1,1,1,0,1,0,0,0]
 => [7,1,2,5,6,3,4] => [3,4,7,1,5,6,2] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
 => 6
Description
The number of distinct eigenvalues of the distance Laplacian of a connected graph.
Matching statistic: St001629
(load all 2 compositions to match this statistic)
Mapping
Mp00129: Dyck paths —to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶ Permutations
Mp00248: Permutations —DEX composition⟶ Integer compositions
Mp00133: Integer compositions —delta morphism⟶ Integer compositions
St001629: Integer compositions ⟶ ℤResult quality: 15% ●values known / values provided: 15%●distinct values known / distinct values provided: 33%
Values
[1,0,1,0]
 => [2,1] => [2] => [1] => ? = 3 - 6
[1,0,1,0,1,0]
 => [2,3,1] => [3] => [1] => ? = 3 - 6
[1,1,0,0,1,0]
 => [1,3,2] => [1,2] => [1,1] => ? = 4 - 6
[1,1,0,1,0,0]
 => [3,1,2] => [3] => [1] => ? = 4 - 6
[1,0,1,0,1,0,1,0]
 => [2,3,4,1] => [4] => [1] => ? = 4 - 6
[1,0,1,1,0,0,1,0]
 => [2,1,4,3] => [2,2] => [2] => ? = 5 - 6
[1,0,1,1,0,1,0,0]
 => [2,4,1,3] => [4] => [1] => ? = 5 - 6
[1,1,0,0,1,0,1,0]
 => [1,3,4,2] => [1,3] => [1,1] => ? = 5 - 6
[1,1,0,1,0,0,1,0]
 => [3,1,4,2] => [2,2] => [2] => ? = 3 - 6
[1,1,0,1,0,1,0,0]
 => [3,4,1,2] => [4] => [1] => ? = 5 - 6
[1,1,1,0,0,0,1,0]
 => [1,2,4,3] => [2,2] => [2] => ? = 5 - 6
[1,1,1,0,0,1,0,0]
 => [1,4,2,3] => [1,3] => [1,1] => ? = 4 - 6
[1,1,1,0,1,0,0,0]
 => [4,1,2,3] => [4] => [1] => ? = 5 - 6
[1,0,1,0,1,0,1,0,1,0]
 => [2,3,4,5,1] => [5] => [1] => ? = 4 - 6
[1,0,1,0,1,1,0,0,1,0]
 => [2,3,1,5,4] => [3,2] => [1,1] => ? = 5 - 6
[1,0,1,0,1,1,0,1,0,0]
 => [2,3,5,1,4] => [5] => [1] => ? = 6 - 6
[1,0,1,1,0,0,1,0,1,0]
 => [2,1,4,5,3] => [2,3] => [1,1] => ? = 6 - 6
[1,0,1,1,0,1,0,0,1,0]
 => [2,4,1,5,3] => [3,2] => [1,1] => ? = 6 - 6
[1,0,1,1,0,1,0,1,0,0]
 => [2,4,5,1,3] => [5] => [1] => ? = 5 - 6
[1,0,1,1,1,0,0,0,1,0]
 => [2,1,3,5,4] => [3,2] => [1,1] => ? = 6 - 6
[1,0,1,1,1,0,0,1,0,0]
 => [2,1,5,3,4] => [2,3] => [1,1] => ? = 6 - 6
[1,0,1,1,1,0,1,0,0,0]
 => [2,5,1,3,4] => [5] => [1] => ? = 6 - 6
[1,1,0,0,1,0,1,0,1,0]
 => [1,3,4,5,2] => [1,4] => [1,1] => ? = 6 - 6
[1,1,0,0,1,1,0,0,1,0]
 => [1,3,2,5,4] => [1,2,2] => [1,2] => 0 = 6 - 6
[1,1,0,0,1,1,0,1,0,0]
 => [1,3,5,2,4] => [1,4] => [1,1] => ? = 5 - 6
[1,1,0,1,0,0,1,0,1,0]
 => [3,1,4,5,2] => [2,3] => [1,1] => ? = 6 - 6
[1,1,0,1,0,1,0,0,1,0]
 => [3,4,1,5,2] => [3,2] => [1,1] => ? = 4 - 6
[1,1,0,1,0,1,0,1,0,0]
 => [3,4,5,1,2] => [5] => [1] => ? = 3 - 6
[1,1,0,1,1,0,0,0,1,0]
 => [3,1,2,5,4] => [3,2] => [1,1] => ? = 5 - 6
[1,1,0,1,1,0,0,1,0,0]
 => [3,1,5,2,4] => [2,3] => [1,1] => ? = 6 - 6
[1,1,0,1,1,0,1,0,0,0]
 => [3,5,1,2,4] => [5] => [1] => ? = 6 - 6
[1,1,1,0,0,0,1,0,1,0]
 => [1,2,4,5,3] => [2,3] => [1,1] => ? = 6 - 6
[1,1,1,0,0,1,0,0,1,0]
 => [1,4,2,5,3] => [1,2,2] => [1,2] => 0 = 6 - 6
[1,1,1,0,0,1,0,1,0,0]
 => [1,4,5,2,3] => [1,4] => [1,1] => ? = 5 - 6
[1,1,1,0,1,0,0,0,1,0]
 => [4,1,2,5,3] => [3,2] => [1,1] => ? = 3 - 6
[1,1,1,0,1,0,0,1,0,0]
 => [4,1,5,2,3] => [2,3] => [1,1] => ? = 5 - 6
[1,1,1,0,1,0,1,0,0,0]
 => [4,5,1,2,3] => [5] => [1] => ? = 5 - 6
[1,1,1,1,0,0,0,0,1,0]
 => [1,2,3,5,4] => [3,2] => [1,1] => ? = 5 - 6
[1,1,1,1,0,0,0,1,0,0]
 => [1,2,5,3,4] => [2,3] => [1,1] => ? = 6 - 6
[1,1,1,1,0,0,1,0,0,0]
 => [1,5,2,3,4] => [1,4] => [1,1] => ? = 6 - 6
[1,1,1,1,0,1,0,0,0,0]
 => [5,1,2,3,4] => [5] => [1] => ? = 5 - 6
[1,0,1,0,1,0,1,0,1,0,1,0]
 => [2,3,4,5,6,1] => [6] => [1] => ? = 4 - 6
[1,0,1,0,1,0,1,1,0,0,1,0]
 => [2,3,4,1,6,5] => [4,2] => [1,1] => ? = 6 - 6
[1,0,1,0,1,0,1,1,0,1,0,0]
 => [2,3,4,6,1,5] => [6] => [1] => ? = 6 - 6
[1,0,1,0,1,1,0,0,1,0,1,0]
 => [2,3,1,5,6,4] => [3,3] => [2] => ? = 7 - 6
[1,0,1,0,1,1,0,1,0,0,1,0]
 => [2,3,5,1,6,4] => [4,2] => [1,1] => ? = 5 - 6
[1,0,1,0,1,1,0,1,0,1,0,0]
 => [2,3,5,6,1,4] => [6] => [1] => ? = 7 - 6
[1,0,1,0,1,1,1,0,0,0,1,0]
 => [2,3,1,4,6,5] => [4,2] => [1,1] => ? = 7 - 6
[1,0,1,0,1,1,1,0,0,1,0,0]
 => [2,3,1,6,4,5] => [3,3] => [2] => ? = 7 - 6
[1,0,1,0,1,1,1,0,1,0,0,0]
 => [2,3,6,1,4,5] => [6] => [1] => ? = 6 - 6
[1,0,1,1,0,0,1,0,1,0,1,0]
 => [2,1,4,5,6,3] => [2,4] => [1,1] => ? = 7 - 6
[1,0,1,1,0,0,1,1,0,0,1,0]
 => [2,1,4,3,6,5] => [2,2,2] => [3] => 1 = 7 - 6
[1,0,1,1,0,0,1,1,0,1,0,0]
 => [2,1,4,6,3,5] => [2,4] => [1,1] => ? = 7 - 6
[1,0,1,1,1,0,0,1,0,0,1,0]
 => [2,1,5,3,6,4] => [2,2,2] => [3] => 1 = 7 - 6
[1,1,0,0,1,0,1,1,0,0,1,0]
 => [1,3,4,2,6,5] => [1,3,2] => [1,1,1] => 1 = 7 - 6
[1,1,0,0,1,1,0,0,1,0,1,0]
 => [1,3,2,5,6,4] => [1,2,3] => [1,1,1] => 1 = 7 - 6
[1,1,0,0,1,1,0,1,0,0,1,0]
 => [1,3,5,2,6,4] => [1,3,2] => [1,1,1] => 1 = 7 - 6
[1,1,0,0,1,1,1,0,0,0,1,0]
 => [1,3,2,4,6,5] => [1,3,2] => [1,1,1] => 1 = 7 - 6
[1,1,0,0,1,1,1,0,0,1,0,0]
 => [1,3,2,6,4,5] => [1,2,3] => [1,1,1] => 1 = 7 - 6
[1,1,0,1,0,0,1,1,0,0,1,0]
 => [3,1,4,2,6,5] => [2,2,2] => [3] => 1 = 7 - 6
[1,1,0,1,1,0,0,1,0,0,1,0]
 => [3,1,5,2,6,4] => [2,2,2] => [3] => 1 = 7 - 6
[1,1,1,0,0,0,1,1,0,0,1,0]
 => [1,2,4,3,6,5] => [2,2,2] => [3] => 1 = 7 - 6
[1,1,1,0,0,1,0,0,1,0,1,0]
 => [1,4,2,5,6,3] => [1,2,3] => [1,1,1] => 1 = 7 - 6
[1,1,1,0,0,1,0,1,0,0,1,0]
 => [1,4,5,2,6,3] => [1,3,2] => [1,1,1] => 1 = 7 - 6
[1,1,1,0,0,1,1,0,0,0,1,0]
 => [1,4,2,3,6,5] => [1,3,2] => [1,1,1] => 1 = 7 - 6
[1,1,1,0,0,1,1,0,0,1,0,0]
 => [1,4,2,6,3,5] => [1,2,3] => [1,1,1] => 1 = 7 - 6
[1,1,1,0,1,0,0,1,0,0,1,0]
 => [4,1,5,2,6,3] => [2,2,2] => [3] => 1 = 7 - 6
[1,1,1,1,0,0,0,1,0,0,1,0]
 => [1,2,5,3,6,4] => [2,2,2] => [3] => 1 = 7 - 6
[1,1,1,1,0,0,1,0,0,0,1,0]
 => [1,5,2,3,6,4] => [1,3,2] => [1,1,1] => 1 = 7 - 6
[1,1,1,1,0,0,1,0,0,1,0,0]
 => [1,5,2,6,3,4] => [1,2,3] => [1,1,1] => 1 = 7 - 6
Description
The coefficient of the integer composition in the quasisymmetric expansion of the relabelling action of the symmetric group on cycles.
Matching statistic: St001645
Mapping
Mp00296: Dyck paths —Knuth-Krattenthaler⟶ Dyck paths
Mp00102: Dyck paths —rise composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St001645: Graphs ⟶ ℤResult quality: 11% ●values known / values provided: 11%●distinct values known / distinct values provided: 50%
Values
[1,0,1,0]
 => [1,1,0,0]
 => [2] => ([],2)
 => ? = 3 - 1
[1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => [3] => ([],3)
 => ? = 3 - 1
[1,1,0,0,1,0]
 => [1,0,1,0,1,0]
 => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3 = 4 - 1
[1,1,0,1,0,0]
 => [1,0,1,1,0,0]
 => [1,2] => ([(1,2)],3)
 => ? = 4 - 1
[1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => [4] => ([],4)
 => ? = 4 - 1
[1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,0,0]
 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 5 - 1
[1,0,1,1,0,1,0,0]
 => [1,1,0,1,1,0,0,0]
 => [2,2] => ([(1,3),(2,3)],4)
 => ? = 5 - 1
[1,1,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 5 - 1
[1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,1,0,0]
 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 3 - 1
[1,1,0,1,0,1,0,0]
 => [1,0,1,1,1,0,0,0]
 => [1,3] => ([(2,3)],4)
 => ? = 5 - 1
[1,1,1,0,0,0,1,0]
 => [1,1,0,1,0,0,1,0]
 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 5 - 1
[1,1,1,0,0,1,0,0]
 => [1,1,0,0,1,0,1,0]
 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 4 - 1
[1,1,1,0,1,0,0,0]
 => [1,1,0,0,1,1,0,0]
 => [2,2] => ([(1,3),(2,3)],4)
 => ? = 5 - 1
[1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => [5] => ([],5)
 => ? = 4 - 1
[1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 5 - 1
[1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,0,1,1,0,0,0,0]
 => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => ? = 6 - 1
[1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,1,0,0,1,0,0]
 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 6 - 1
[1,0,1,1,0,1,0,0,1,0]
 => [1,1,0,1,1,0,1,0,0,0]
 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 6 - 1
[1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,1,1,0,0,0,0]
 => [2,3] => ([(2,4),(3,4)],5)
 => ? = 5 - 1
[1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 6 - 1
[1,0,1,1,1,0,0,1,0,0]
 => [1,1,1,0,0,1,0,1,0,0]
 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 6 - 1
[1,0,1,1,1,0,1,0,0,0]
 => [1,1,1,0,0,1,1,0,0,0]
 => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => ? = 6 - 1
[1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 6 - 1
[1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 5 = 6 - 1
[1,1,0,0,1,1,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 5 - 1
[1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 6 - 1
[1,1,0,1,0,1,0,0,1,0]
 => [1,0,1,1,1,0,1,0,0,0]
 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 4 - 1
[1,1,0,1,0,1,0,1,0,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,4] => ([(3,4)],5)
 => ? = 3 - 1
[1,1,0,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 5 - 1
[1,1,0,1,1,0,0,1,0,0]
 => [1,0,1,0,1,1,0,1,0,0]
 => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 6 - 1
[1,1,0,1,1,0,1,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,3] => ([(2,3),(2,4),(3,4)],5)
 => ? = 6 - 1
[1,1,1,0,0,0,1,0,1,0]
 => [1,1,0,1,1,0,0,0,1,0]
 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 6 - 1
[1,1,1,0,0,1,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 5 = 6 - 1
[1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 5 - 1
[1,1,1,0,1,0,0,0,1,0]
 => [1,1,0,0,1,0,1,1,0,0]
 => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 3 - 1
[1,1,1,0,1,0,0,1,0,0]
 => [1,1,0,0,1,1,0,1,0,0]
 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 5 - 1
[1,1,1,0,1,0,1,0,0,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => [2,3] => ([(2,4),(3,4)],5)
 => ? = 5 - 1
[1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,0,1,0,0,0,1,0]
 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 5 - 1
[1,1,1,1,0,0,0,1,0,0]
 => [1,1,1,0,0,1,0,0,1,0]
 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 6 - 1
[1,1,1,1,0,0,1,0,0,0]
 => [1,1,1,0,0,0,1,0,1,0]
 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 6 - 1
[1,1,1,1,0,1,0,0,0,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => ? = 5 - 1
[1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [6] => ([],6)
 => ? = 4 - 1
[1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,0,1,0,1,0,0,0,0]
 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 6 - 1
[1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,1,0,1,1,0,0,0,0,0]
 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 6 - 1
[1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,1,0,0,1,0,0,0]
 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 7 - 1
[1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,1,1,0,1,1,0,1,0,0,0,0]
 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 5 - 1
[1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,1,1,1,0,0,0,0,0]
 => [3,3] => ([(2,5),(3,5),(4,5)],6)
 => ? = 7 - 1
[1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,1,0,0,1,0,0,0]
 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 7 - 1
[1,0,1,0,1,1,1,0,0,1,0,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 7 - 1
[1,0,1,0,1,1,1,0,1,0,0,0]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 6 - 1
[1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,1,1,1,0,0,0,1,0,0]
 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 7 - 1
[1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => [2,1,1,1,1] => ([(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 = 7 - 1
[1,0,1,1,0,0,1,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,0,1,0,0]
 => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 7 - 1
[1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,1,0,1,1,1,0,0,1,0,0,0]
 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 5 - 1
[1,0,1,1,1,0,0,1,0,0,1,0]
 => [1,1,1,0,0,1,0,1,0,1,0,0]
 => [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 = 7 - 1
[1,1,0,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,2,1,1,1] => ([(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 = 7 - 1
[1,1,0,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,2,1,1,1] => ([(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 = 7 - 1
[1,1,0,0,1,1,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,2,1,1,1] => ([(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 = 7 - 1
[1,1,0,1,0,0,1,1,0,0,1,0]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,2,1,1,1] => ([(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 = 7 - 1
[1,1,1,0,0,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0]
 => [2,1,1,1,1] => ([(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 = 7 - 1
[1,1,1,0,0,1,1,0,0,0,1,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => [2,1,1,1,1] => ([(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 = 7 - 1
[1,1,1,0,0,1,1,0,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0]
 => [2,1,1,1,1] => ([(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 = 7 - 1
[1,1,1,1,0,0,0,1,0,0,1,0]
 => [1,1,1,0,0,1,0,1,0,0,1,0]
 => [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 = 7 - 1
[1,1,1,1,0,0,1,0,0,0,1,0]
 => [1,1,1,0,0,1,0,0,1,0,1,0]
 => [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 = 7 - 1
[1,1,1,1,0,0,1,0,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => [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 = 7 - 1
Description
The pebbling number of a connected graph.