Your data matches 5 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001060
Mapping
Mp00114: Permutations —connectivity set⟶ Binary words
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St001060: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,2,3] => 11 => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3
[2,1,3] => 01 => [2,1] => ([(0,2),(1,2)],3)
 => 2
[1,2,3,4] => 111 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 3
[1,2,4,3] => 110 => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
 => 3
[1,3,2,4] => 101 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 2
[2,1,3,4] => 011 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
[2,1,4,3] => 010 => [2,2] => ([(1,3),(2,3)],4)
 => 2
[2,3,1,4] => 001 => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 3
[3,1,2,4] => 001 => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 3
[3,2,1,4] => 001 => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 3
[1,2,3,4,5] => 1111 => [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)
 => 3
[1,2,3,5,4] => 1110 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
[1,2,4,3,5] => 1101 => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[1,3,2,4,5] => 1011 => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[1,3,2,5,4] => 1010 => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[1,3,4,2,5] => 1001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[1,4,2,3,5] => 1001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[1,4,3,2,5] => 1001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[2,1,3,4,5] => 0111 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[2,1,3,5,4] => 0110 => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[2,1,4,3,5] => 0101 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[2,3,1,4,5] => 0011 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[2,3,1,5,4] => 0010 => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => 3
[2,3,4,1,5] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 4
[2,4,1,3,5] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 4
[2,4,3,1,5] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 4
[3,1,2,4,5] => 0011 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[3,1,2,5,4] => 0010 => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => 3
[3,1,4,2,5] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 4
[3,2,1,4,5] => 0011 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[3,2,1,5,4] => 0010 => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => 3
[3,2,4,1,5] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 4
[3,4,1,2,5] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 4
[3,4,2,1,5] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 4
[4,1,2,3,5] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 4
[4,1,3,2,5] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 4
[4,2,1,3,5] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 4
[4,2,3,1,5] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 4
[4,3,1,2,5] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 4
[4,3,2,1,5] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 4
[1,2,3,4,5,6] => 11111 => [1,1,1,1,1,1] => ([(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)
 => 2
[1,2,3,4,6,5] => 11110 => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
[1,2,3,5,4,6] => 11101 => [1,1,1,2,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
[1,2,4,3,5,6] => 11011 => [1,1,2,1,1] => ([(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)
 => 2
[1,2,4,3,6,5] => 11010 => [1,1,2,2] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
[1,2,4,5,3,6] => 11001 => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
[1,2,5,3,4,6] => 11001 => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
[1,2,5,4,3,6] => 11001 => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
[1,3,2,4,6,5] => 10110 => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
[1,3,2,5,4,6] => 10101 => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
Description
The distinguishing index of a graph. This is the smallest number of colours such that there is a colouring of the edges which is not preserved by any automorphism. If the graph has a connected component which is a single edge, or at least two isolated vertices, this statistic is undefined.
Matching statistic: St001645
(load all 18 compositions to match this statistic)
Mapping
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
Mp00088: Permutations —Kreweras complement⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St001645: Graphs ⟶ ℤResult quality: 49% ●values known / values provided: 49%●distinct values known / distinct values provided: 100%
Values
[1,2,3] => [1,2,3] => [2,3,1] => ([(0,2),(1,2)],3)
 => 4 = 3 + 1
[2,1,3] => [2,1,3] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
 => 3 = 2 + 1
[1,2,3,4] => [1,2,3,4] => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
 => ? = 3 + 1
[1,2,4,3] => [1,2,4,3] => [2,3,1,4] => ([(1,3),(2,3)],4)
 => ? = 3 + 1
[1,3,2,4] => [1,3,2,4] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 2 + 1
[2,1,3,4] => [2,1,3,4] => [3,2,4,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 2 + 1
[2,1,4,3] => [2,1,4,3] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
 => ? = 2 + 1
[2,3,1,4] => [3,2,1,4] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 3 + 1
[3,1,2,4] => [3,2,1,4] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 3 + 1
[3,2,1,4] => [3,2,1,4] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 3 + 1
[1,2,3,4,5] => [1,2,3,4,5] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ? = 3 + 1
[1,2,3,5,4] => [1,2,3,5,4] => [2,3,4,1,5] => ([(1,4),(2,4),(3,4)],5)
 => ? = 3 + 1
[1,2,4,3,5] => [1,2,4,3,5] => [2,3,5,4,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 2 + 1
[1,3,2,4,5] => [1,3,2,4,5] => [2,4,3,5,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 2 + 1
[1,3,2,5,4] => [1,3,2,5,4] => [2,4,3,1,5] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 2 + 1
[1,3,4,2,5] => [1,4,3,2,5] => [2,5,4,3,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 2 + 1
[1,4,2,3,5] => [1,4,3,2,5] => [2,5,4,3,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 2 + 1
[1,4,3,2,5] => [1,4,3,2,5] => [2,5,4,3,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 2 + 1
[2,1,3,4,5] => [2,1,3,4,5] => [3,2,4,5,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 2 + 1
[2,1,3,5,4] => [2,1,3,5,4] => [3,2,4,1,5] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 2 + 1
[2,1,4,3,5] => [2,1,4,3,5] => [3,2,5,4,1] => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ? = 2 + 1
[2,3,1,4,5] => [3,2,1,4,5] => [4,3,2,5,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 2 + 1
[2,3,1,5,4] => [3,2,1,5,4] => [4,3,2,1,5] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 3 + 1
[2,3,4,1,5] => [4,2,3,1,5] => [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
[2,4,1,3,5] => [3,4,1,2,5] => [4,5,2,3,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 5 = 4 + 1
[2,4,3,1,5] => [4,3,2,1,5] => [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
[3,1,2,4,5] => [3,2,1,4,5] => [4,3,2,5,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 2 + 1
[3,1,2,5,4] => [3,2,1,5,4] => [4,3,2,1,5] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 3 + 1
[3,1,4,2,5] => [4,2,3,1,5] => [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
[3,2,1,4,5] => [3,2,1,4,5] => [4,3,2,5,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 2 + 1
[3,2,1,5,4] => [3,2,1,5,4] => [4,3,2,1,5] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 3 + 1
[3,2,4,1,5] => [4,2,3,1,5] => [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
[3,4,1,2,5] => [4,3,2,1,5] => [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
[3,4,2,1,5] => [4,3,2,1,5] => [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
[4,1,2,3,5] => [4,2,3,1,5] => [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
[4,1,3,2,5] => [4,2,3,1,5] => [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
[4,2,1,3,5] => [4,3,2,1,5] => [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
[4,2,3,1,5] => [4,3,2,1,5] => [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
[4,3,1,2,5] => [4,3,2,1,5] => [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
[4,3,2,1,5] => [4,3,2,1,5] => [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
[1,2,3,4,5,6] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 2 + 1
[1,2,3,4,6,5] => [1,2,3,4,6,5] => [2,3,4,5,1,6] => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 3 + 1
[1,2,3,5,4,6] => [1,2,3,5,4,6] => [2,3,4,6,5,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2 + 1
[1,2,4,3,5,6] => [1,2,4,3,5,6] => [2,3,5,4,6,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2 + 1
[1,2,4,3,6,5] => [1,2,4,3,6,5] => [2,3,5,4,1,6] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2 + 1
[1,2,4,5,3,6] => [1,2,5,4,3,6] => [2,3,6,5,4,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2 + 1
[1,2,5,3,4,6] => [1,2,5,4,3,6] => [2,3,6,5,4,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2 + 1
[1,2,5,4,3,6] => [1,2,5,4,3,6] => [2,3,6,5,4,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2 + 1
[1,3,2,4,6,5] => [1,3,2,4,6,5] => [2,4,3,5,1,6] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2 + 1
[1,3,2,5,4,6] => [1,3,2,5,4,6] => [2,4,3,6,5,1] => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ? = 2 + 1
[1,3,4,2,5,6] => [1,4,3,2,5,6] => [2,5,4,3,6,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2 + 1
[1,3,4,2,6,5] => [1,4,3,2,6,5] => [2,5,4,3,1,6] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2 + 1
[1,3,4,5,2,6] => [1,5,3,4,2,6] => [2,6,4,5,3,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 + 1
[1,3,5,2,4,6] => [1,4,5,2,3,6] => [2,5,6,3,4,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 3 + 1
[1,3,5,4,2,6] => [1,5,4,3,2,6] => [2,6,5,4,3,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 + 1
[1,4,2,3,5,6] => [1,4,3,2,5,6] => [2,5,4,3,6,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2 + 1
[1,4,2,3,6,5] => [1,4,3,2,6,5] => [2,5,4,3,1,6] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2 + 1
[1,4,2,5,3,6] => [1,5,3,4,2,6] => [2,6,4,5,3,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 + 1
[1,4,3,2,5,6] => [1,4,3,2,5,6] => [2,5,4,3,6,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2 + 1
[1,4,3,2,6,5] => [1,4,3,2,6,5] => [2,5,4,3,1,6] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2 + 1
[1,4,3,5,2,6] => [1,5,3,4,2,6] => [2,6,4,5,3,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 + 1
[1,4,5,2,3,6] => [1,5,4,3,2,6] => [2,6,5,4,3,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 + 1
[1,4,5,3,2,6] => [1,5,4,3,2,6] => [2,6,5,4,3,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 + 1
[1,5,2,3,4,6] => [1,5,3,4,2,6] => [2,6,4,5,3,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 + 1
[1,5,2,4,3,6] => [1,5,3,4,2,6] => [2,6,4,5,3,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 + 1
[1,5,3,2,4,6] => [1,5,4,3,2,6] => [2,6,5,4,3,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 + 1
[1,5,3,4,2,6] => [1,5,4,3,2,6] => [2,6,5,4,3,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 + 1
[1,5,4,2,3,6] => [1,5,4,3,2,6] => [2,6,5,4,3,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 + 1
[2,3,4,5,1,6] => [5,2,3,4,1,6] => [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
[2,3,5,1,4,6] => [4,2,5,1,3,6] => [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
[2,3,5,4,1,6] => [5,2,4,3,1,6] => [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
[2,4,1,5,3,6] => [3,5,1,4,2,6] => [4,6,2,5,3,1] => ([(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
[2,4,3,5,1,6] => [5,3,2,4,1,6] => [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
[2,4,5,1,3,6] => [4,5,3,1,2,6] => [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
[2,4,5,3,1,6] => [5,4,3,2,1,6] => [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
[2,5,1,3,4,6] => [3,5,1,4,2,6] => [4,6,2,5,3,1] => ([(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
[2,5,1,4,3,6] => [3,5,1,4,2,6] => [4,6,2,5,3,1] => ([(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
[2,5,3,1,4,6] => [4,5,3,1,2,6] => [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
[2,5,3,4,1,6] => [5,4,3,2,1,6] => [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
[2,5,4,1,3,6] => [4,5,3,1,2,6] => [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
[2,5,4,3,1,6] => [5,4,3,2,1,6] => [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
[3,1,4,5,2,6] => [5,2,3,4,1,6] => [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
[3,1,5,2,4,6] => [4,2,5,1,3,6] => [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
[3,1,5,4,2,6] => [5,2,4,3,1,6] => [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
[3,2,4,5,1,6] => [5,2,3,4,1,6] => [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
[3,2,5,1,4,6] => [4,2,5,1,3,6] => [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
[3,2,5,4,1,6] => [5,2,4,3,1,6] => [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
[3,4,1,5,2,6] => [5,3,2,4,1,6] => [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
[3,4,2,5,1,6] => [5,3,2,4,1,6] => [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
[3,4,5,1,2,6] => [5,4,3,2,1,6] => [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
[3,4,5,2,1,6] => [5,4,3,2,1,6] => [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
[3,5,1,2,4,6] => [4,5,3,1,2,6] => [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
[3,5,1,4,2,6] => [5,4,3,2,1,6] => [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
[3,5,2,1,4,6] => [4,5,3,1,2,6] => [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
[3,5,2,4,1,6] => [5,4,3,2,1,6] => [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
[3,5,4,1,2,6] => [5,4,3,2,1,6] => [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
[3,5,4,2,1,6] => [5,4,3,2,1,6] => [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
[4,1,2,5,3,6] => [5,2,3,4,1,6] => [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
[4,1,3,5,2,6] => [5,2,3,4,1,6] => [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
[4,1,5,2,3,6] => [5,2,4,3,1,6] => [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
Description
The pebbling number of a connected graph.
Matching statistic: St001232
(load all 28 compositions to match this statistic)
Mapping
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 43% ●values known / values provided: 43%●distinct values known / distinct values provided: 75%
Values
[1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
 => ? = 3
[2,1,3] => [2,1,3] => [1,2,3] => [1,0,1,0,1,0]
 => ? = 2
[1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => ? = 3
[1,2,4,3] => [1,2,4,3] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => ? = 3
[1,3,2,4] => [1,3,2,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => ? = 2
[2,1,3,4] => [2,1,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => ? = 2
[2,1,4,3] => [2,1,4,3] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => ? = 2
[2,3,1,4] => [3,2,1,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
 => 3
[3,1,2,4] => [3,2,1,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
 => 3
[3,2,1,4] => [3,2,1,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
 => 3
[1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
 => ? = 3
[1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
 => ? = 3
[1,2,4,3,5] => [1,2,4,3,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
 => ? = 2
[1,3,2,4,5] => [1,3,2,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
 => ? = 2
[1,3,2,5,4] => [1,3,2,5,4] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
 => ? = 2
[1,3,4,2,5] => [1,4,3,2,5] => [1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0]
 => ? = 2
[1,4,2,3,5] => [1,4,3,2,5] => [1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0]
 => ? = 2
[1,4,3,2,5] => [1,4,3,2,5] => [1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0]
 => ? = 2
[2,1,3,4,5] => [2,1,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
 => ? = 2
[2,1,3,5,4] => [2,1,3,5,4] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
 => ? = 2
[2,1,4,3,5] => [2,1,4,3,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
 => ? = 2
[2,3,1,4,5] => [3,2,1,4,5] => [1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0]
 => ? = 2
[2,3,1,5,4] => [3,2,1,5,4] => [1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0]
 => ? = 3
[2,3,4,1,5] => [4,2,3,1,5] => [1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0]
 => 4
[2,4,1,3,5] => [3,4,1,2,5] => [1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0]
 => ? = 4
[2,4,3,1,5] => [4,3,2,1,5] => [1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0]
 => 4
[3,1,2,4,5] => [3,2,1,4,5] => [1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0]
 => ? = 2
[3,1,2,5,4] => [3,2,1,5,4] => [1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0]
 => ? = 3
[3,1,4,2,5] => [4,2,3,1,5] => [1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0]
 => 4
[3,2,1,4,5] => [3,2,1,4,5] => [1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0]
 => ? = 2
[3,2,1,5,4] => [3,2,1,5,4] => [1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0]
 => ? = 3
[3,2,4,1,5] => [4,2,3,1,5] => [1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0]
 => 4
[3,4,1,2,5] => [4,3,2,1,5] => [1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0]
 => 4
[3,4,2,1,5] => [4,3,2,1,5] => [1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0]
 => 4
[4,1,2,3,5] => [4,2,3,1,5] => [1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0]
 => 4
[4,1,3,2,5] => [4,2,3,1,5] => [1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0]
 => 4
[4,2,1,3,5] => [4,3,2,1,5] => [1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0]
 => 4
[4,2,3,1,5] => [4,3,2,1,5] => [1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0]
 => 4
[4,3,1,2,5] => [4,3,2,1,5] => [1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0]
 => 4
[4,3,2,1,5] => [4,3,2,1,5] => [1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0]
 => 4
[1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 2
[1,2,3,4,6,5] => [1,2,3,4,6,5] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 3
[1,2,3,5,4,6] => [1,2,3,5,4,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 2
[1,2,4,3,5,6] => [1,2,4,3,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 2
[1,2,4,3,6,5] => [1,2,4,3,6,5] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 2
[1,2,4,5,3,6] => [1,2,5,4,3,6] => [1,2,3,5,4,6] => [1,0,1,0,1,0,1,1,0,0,1,0]
 => ? = 2
[1,2,5,3,4,6] => [1,2,5,4,3,6] => [1,2,3,5,4,6] => [1,0,1,0,1,0,1,1,0,0,1,0]
 => ? = 2
[1,2,5,4,3,6] => [1,2,5,4,3,6] => [1,2,3,5,4,6] => [1,0,1,0,1,0,1,1,0,0,1,0]
 => ? = 2
[1,3,2,4,6,5] => [1,3,2,4,6,5] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 2
[1,3,2,5,4,6] => [1,3,2,5,4,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 2
[1,3,4,2,5,6] => [1,4,3,2,5,6] => [1,2,4,3,5,6] => [1,0,1,0,1,1,0,0,1,0,1,0]
 => ? = 2
[1,3,4,2,6,5] => [1,4,3,2,6,5] => [1,2,4,3,5,6] => [1,0,1,0,1,1,0,0,1,0,1,0]
 => ? = 2
[1,3,4,5,2,6] => [1,5,3,4,2,6] => [1,2,5,3,4,6] => [1,0,1,0,1,1,1,0,0,0,1,0]
 => ? = 3
[1,3,5,2,4,6] => [1,4,5,2,3,6] => [1,2,4,3,5,6] => [1,0,1,0,1,1,0,0,1,0,1,0]
 => ? = 3
[1,3,5,4,2,6] => [1,5,4,3,2,6] => [1,2,5,3,4,6] => [1,0,1,0,1,1,1,0,0,0,1,0]
 => ? = 3
[1,4,2,3,5,6] => [1,4,3,2,5,6] => [1,2,4,3,5,6] => [1,0,1,0,1,1,0,0,1,0,1,0]
 => ? = 2
[1,4,2,3,6,5] => [1,4,3,2,6,5] => [1,2,4,3,5,6] => [1,0,1,0,1,1,0,0,1,0,1,0]
 => ? = 2
[1,4,2,5,3,6] => [1,5,3,4,2,6] => [1,2,5,3,4,6] => [1,0,1,0,1,1,1,0,0,0,1,0]
 => ? = 3
[1,4,3,2,5,6] => [1,4,3,2,5,6] => [1,2,4,3,5,6] => [1,0,1,0,1,1,0,0,1,0,1,0]
 => ? = 2
[1,4,3,2,6,5] => [1,4,3,2,6,5] => [1,2,4,3,5,6] => [1,0,1,0,1,1,0,0,1,0,1,0]
 => ? = 2
[1,4,3,5,2,6] => [1,5,3,4,2,6] => [1,2,5,3,4,6] => [1,0,1,0,1,1,1,0,0,0,1,0]
 => ? = 3
[1,4,5,2,3,6] => [1,5,4,3,2,6] => [1,2,5,3,4,6] => [1,0,1,0,1,1,1,0,0,0,1,0]
 => ? = 3
[1,4,5,3,2,6] => [1,5,4,3,2,6] => [1,2,5,3,4,6] => [1,0,1,0,1,1,1,0,0,0,1,0]
 => ? = 3
[1,5,2,3,4,6] => [1,5,3,4,2,6] => [1,2,5,3,4,6] => [1,0,1,0,1,1,1,0,0,0,1,0]
 => ? = 3
[1,5,2,4,3,6] => [1,5,3,4,2,6] => [1,2,5,3,4,6] => [1,0,1,0,1,1,1,0,0,0,1,0]
 => ? = 3
[2,3,4,5,1,6] => [5,2,3,4,1,6] => [1,5,2,3,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => 5
[2,3,5,4,1,6] => [5,2,4,3,1,6] => [1,5,2,3,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => 5
[2,4,1,5,3,6] => [3,5,1,4,2,6] => [1,3,2,5,4,6] => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 5
[2,4,3,5,1,6] => [5,3,2,4,1,6] => [1,5,2,3,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => 5
[2,4,5,3,1,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => 5
[2,5,1,3,4,6] => [3,5,1,4,2,6] => [1,3,2,5,4,6] => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 5
[2,5,1,4,3,6] => [3,5,1,4,2,6] => [1,3,2,5,4,6] => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 5
[2,5,3,4,1,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => 5
[2,5,4,3,1,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => 5
[3,1,4,5,2,6] => [5,2,3,4,1,6] => [1,5,2,3,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => 5
[3,1,5,4,2,6] => [5,2,4,3,1,6] => [1,5,2,3,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => 5
[3,2,4,5,1,6] => [5,2,3,4,1,6] => [1,5,2,3,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => 5
[3,2,5,4,1,6] => [5,2,4,3,1,6] => [1,5,2,3,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => 5
[3,4,1,5,2,6] => [5,3,2,4,1,6] => [1,5,2,3,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => 5
[3,4,2,5,1,6] => [5,3,2,4,1,6] => [1,5,2,3,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => 5
[3,4,5,1,2,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => 5
[3,4,5,2,1,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => 5
[3,5,1,4,2,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => 5
[3,5,2,4,1,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => 5
[3,5,4,1,2,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => 5
[3,5,4,2,1,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => 5
[4,1,2,5,3,6] => [5,2,3,4,1,6] => [1,5,2,3,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => 5
[4,1,3,5,2,6] => [5,2,3,4,1,6] => [1,5,2,3,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => 5
[4,1,5,2,3,6] => [5,2,4,3,1,6] => [1,5,2,3,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => 5
[4,1,5,3,2,6] => [5,2,4,3,1,6] => [1,5,2,3,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => 5
[4,2,1,5,3,6] => [5,3,2,4,1,6] => [1,5,2,3,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => 5
[4,2,3,5,1,6] => [5,3,2,4,1,6] => [1,5,2,3,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => 5
[4,2,5,1,3,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => 5
[4,2,5,3,1,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => 5
[4,3,1,5,2,6] => [5,3,2,4,1,6] => [1,5,2,3,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => 5
[4,3,2,5,1,6] => [5,3,2,4,1,6] => [1,5,2,3,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => 5
[4,3,5,1,2,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => 5
[4,3,5,2,1,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => 5
[4,5,1,2,3,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => 5
[4,5,1,3,2,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => 5
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
Matching statistic: St000264
Mapping
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000264: Graphs ⟶ ℤResult quality: 19% ●values known / values provided: 19%●distinct values known / distinct values provided: 25%
Values
[1,2,3] => [1,2,3] => [1,2,3] => ([],3)
 => ? = 3 - 2
[2,1,3] => [2,1,3] => [1,2,3] => ([],3)
 => ? = 2 - 2
[1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([],4)
 => ? = 3 - 2
[1,2,4,3] => [1,2,4,3] => [1,2,3,4] => ([],4)
 => ? = 3 - 2
[1,3,2,4] => [1,3,2,4] => [1,2,3,4] => ([],4)
 => ? = 2 - 2
[2,1,3,4] => [2,1,3,4] => [1,2,3,4] => ([],4)
 => ? = 2 - 2
[2,1,4,3] => [2,1,4,3] => [1,2,3,4] => ([],4)
 => ? = 2 - 2
[2,3,1,4] => [3,2,1,4] => [1,3,2,4] => ([(2,3)],4)
 => ? = 3 - 2
[3,1,2,4] => [3,2,1,4] => [1,3,2,4] => ([(2,3)],4)
 => ? = 3 - 2
[3,2,1,4] => [3,2,1,4] => [1,3,2,4] => ([(2,3)],4)
 => ? = 3 - 2
[1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([],5)
 => ? = 3 - 2
[1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,4,5] => ([],5)
 => ? = 3 - 2
[1,2,4,3,5] => [1,2,4,3,5] => [1,2,3,4,5] => ([],5)
 => ? = 2 - 2
[1,3,2,4,5] => [1,3,2,4,5] => [1,2,3,4,5] => ([],5)
 => ? = 2 - 2
[1,3,2,5,4] => [1,3,2,5,4] => [1,2,3,4,5] => ([],5)
 => ? = 2 - 2
[1,3,4,2,5] => [1,4,3,2,5] => [1,2,4,3,5] => ([(3,4)],5)
 => ? = 2 - 2
[1,4,2,3,5] => [1,4,3,2,5] => [1,2,4,3,5] => ([(3,4)],5)
 => ? = 2 - 2
[1,4,3,2,5] => [1,4,3,2,5] => [1,2,4,3,5] => ([(3,4)],5)
 => ? = 2 - 2
[2,1,3,4,5] => [2,1,3,4,5] => [1,2,3,4,5] => ([],5)
 => ? = 2 - 2
[2,1,3,5,4] => [2,1,3,5,4] => [1,2,3,4,5] => ([],5)
 => ? = 2 - 2
[2,1,4,3,5] => [2,1,4,3,5] => [1,2,3,4,5] => ([],5)
 => ? = 2 - 2
[2,3,1,4,5] => [3,2,1,4,5] => [1,3,2,4,5] => ([(3,4)],5)
 => ? = 2 - 2
[2,3,1,5,4] => [3,2,1,5,4] => [1,3,2,4,5] => ([(3,4)],5)
 => ? = 3 - 2
[2,3,4,1,5] => [4,2,3,1,5] => [1,4,2,3,5] => ([(2,4),(3,4)],5)
 => ? = 4 - 2
[2,4,1,3,5] => [3,4,1,2,5] => [1,3,2,4,5] => ([(3,4)],5)
 => ? = 4 - 2
[2,4,3,1,5] => [4,3,2,1,5] => [1,4,2,3,5] => ([(2,4),(3,4)],5)
 => ? = 4 - 2
[3,1,2,4,5] => [3,2,1,4,5] => [1,3,2,4,5] => ([(3,4)],5)
 => ? = 2 - 2
[3,1,2,5,4] => [3,2,1,5,4] => [1,3,2,4,5] => ([(3,4)],5)
 => ? = 3 - 2
[3,1,4,2,5] => [4,2,3,1,5] => [1,4,2,3,5] => ([(2,4),(3,4)],5)
 => ? = 4 - 2
[3,2,1,4,5] => [3,2,1,4,5] => [1,3,2,4,5] => ([(3,4)],5)
 => ? = 2 - 2
[3,2,1,5,4] => [3,2,1,5,4] => [1,3,2,4,5] => ([(3,4)],5)
 => ? = 3 - 2
[3,2,4,1,5] => [4,2,3,1,5] => [1,4,2,3,5] => ([(2,4),(3,4)],5)
 => ? = 4 - 2
[3,4,1,2,5] => [4,3,2,1,5] => [1,4,2,3,5] => ([(2,4),(3,4)],5)
 => ? = 4 - 2
[3,4,2,1,5] => [4,3,2,1,5] => [1,4,2,3,5] => ([(2,4),(3,4)],5)
 => ? = 4 - 2
[4,1,2,3,5] => [4,2,3,1,5] => [1,4,2,3,5] => ([(2,4),(3,4)],5)
 => ? = 4 - 2
[4,1,3,2,5] => [4,2,3,1,5] => [1,4,2,3,5] => ([(2,4),(3,4)],5)
 => ? = 4 - 2
[4,2,1,3,5] => [4,3,2,1,5] => [1,4,2,3,5] => ([(2,4),(3,4)],5)
 => ? = 4 - 2
[4,2,3,1,5] => [4,3,2,1,5] => [1,4,2,3,5] => ([(2,4),(3,4)],5)
 => ? = 4 - 2
[4,3,1,2,5] => [4,3,2,1,5] => [1,4,2,3,5] => ([(2,4),(3,4)],5)
 => ? = 4 - 2
[4,3,2,1,5] => [4,3,2,1,5] => [1,4,2,3,5] => ([(2,4),(3,4)],5)
 => ? = 4 - 2
[1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([],6)
 => ? = 2 - 2
[1,2,3,4,6,5] => [1,2,3,4,6,5] => [1,2,3,4,5,6] => ([],6)
 => ? = 3 - 2
[1,2,3,5,4,6] => [1,2,3,5,4,6] => [1,2,3,4,5,6] => ([],6)
 => ? = 2 - 2
[1,2,4,3,5,6] => [1,2,4,3,5,6] => [1,2,3,4,5,6] => ([],6)
 => ? = 2 - 2
[1,2,4,3,6,5] => [1,2,4,3,6,5] => [1,2,3,4,5,6] => ([],6)
 => ? = 2 - 2
[1,2,4,5,3,6] => [1,2,5,4,3,6] => [1,2,3,5,4,6] => ([(4,5)],6)
 => ? = 2 - 2
[1,2,5,3,4,6] => [1,2,5,4,3,6] => [1,2,3,5,4,6] => ([(4,5)],6)
 => ? = 2 - 2
[1,2,5,4,3,6] => [1,2,5,4,3,6] => [1,2,3,5,4,6] => ([(4,5)],6)
 => ? = 2 - 2
[1,3,2,4,6,5] => [1,3,2,4,6,5] => [1,2,3,4,5,6] => ([],6)
 => ? = 2 - 2
[1,3,2,5,4,6] => [1,3,2,5,4,6] => [1,2,3,4,5,6] => ([],6)
 => ? = 2 - 2
[2,4,5,3,1,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => ([(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 5 - 2
[2,5,3,4,1,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => ([(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 5 - 2
[2,5,4,3,1,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => ([(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 5 - 2
[3,4,5,1,2,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => ([(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 5 - 2
[3,4,5,2,1,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => ([(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 5 - 2
[3,5,1,4,2,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => ([(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 5 - 2
[3,5,2,4,1,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => ([(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 5 - 2
[3,5,4,1,2,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => ([(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 5 - 2
[3,5,4,2,1,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => ([(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 5 - 2
[4,2,5,1,3,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => ([(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 5 - 2
[4,2,5,3,1,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => ([(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 5 - 2
[4,3,5,1,2,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => ([(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 5 - 2
[4,3,5,2,1,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => ([(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 5 - 2
[4,5,1,2,3,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => ([(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 5 - 2
[4,5,1,3,2,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => ([(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 5 - 2
[4,5,2,1,3,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => ([(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 5 - 2
[4,5,2,3,1,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => ([(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 5 - 2
[4,5,3,1,2,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => ([(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 5 - 2
[4,5,3,2,1,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => ([(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 5 - 2
[5,2,3,1,4,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => ([(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 5 - 2
[5,2,3,4,1,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => ([(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 5 - 2
[5,2,4,1,3,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => ([(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 5 - 2
[5,2,4,3,1,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => ([(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 5 - 2
[5,3,1,2,4,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => ([(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 5 - 2
[5,3,1,4,2,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => ([(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 5 - 2
[5,3,2,1,4,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => ([(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 5 - 2
[5,3,2,4,1,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => ([(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 5 - 2
[5,3,4,1,2,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => ([(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 5 - 2
[5,3,4,2,1,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => ([(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 5 - 2
[5,4,1,2,3,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => ([(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 5 - 2
[5,4,1,3,2,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => ([(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 5 - 2
[5,4,2,1,3,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => ([(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 5 - 2
[5,4,2,3,1,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => ([(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 5 - 2
[5,4,3,1,2,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => ([(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 5 - 2
[5,4,3,2,1,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => ([(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 5 - 2
Description
The girth of a graph, which is not a tree. This is the length of the shortest cycle in the graph.
Matching statistic: St000741
Mapping
Mp00064: Permutations —reverse⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00156: Graphs —line graph⟶ Graphs
St000741: Graphs ⟶ ℤResult quality: 11% ●values known / values provided: 11%●distinct values known / distinct values provided: 100%
Values
[1,2,3] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 2 = 3 - 1
[2,1,3] => [3,1,2] => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 1 = 2 - 1
[1,2,3,4] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(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
[1,2,4,3] => [3,4,2,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ? = 3 - 1
[1,3,2,4] => [4,2,3,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ? = 2 - 1
[2,1,3,4] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ? = 2 - 1
[2,1,4,3] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ? = 2 - 1
[2,3,1,4] => [4,1,3,2] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2 = 3 - 1
[3,1,2,4] => [4,2,1,3] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2 = 3 - 1
[3,2,1,4] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 2 = 3 - 1
[1,2,3,4,5] => [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)
 => ([(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,3),(1,6),(1,7),(1,8),(1,9),(2,3),(2,4),(2,5),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(4,9),(5,6),(5,8),(6,7),(6,8),(7,9),(8,9)],10)
 => ? = 3 - 1
[1,2,3,5,4] => [4,5,3,2,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,4),(0,5),(0,7),(0,8),(1,2),(1,3),(1,7),(1,8),(2,3),(2,5),(2,6),(2,8),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,8),(6,7),(6,8),(7,8)],9)
 => ? = 3 - 1
[1,2,4,3,5] => [5,3,4,2,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,4),(0,5),(0,7),(0,8),(1,2),(1,3),(1,7),(1,8),(2,3),(2,5),(2,6),(2,8),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,8),(6,7),(6,8),(7,8)],9)
 => ? = 2 - 1
[1,3,2,4,5] => [5,4,2,3,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,4),(0,5),(0,7),(0,8),(1,2),(1,3),(1,7),(1,8),(2,3),(2,5),(2,6),(2,8),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,8),(6,7),(6,8),(7,8)],9)
 => ? = 2 - 1
[1,3,2,5,4] => [4,5,2,3,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(2,5),(2,7),(3,4),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2 - 1
[1,3,4,2,5] => [5,2,4,3,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,5),(1,6),(1,7),(2,3),(2,4),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2 - 1
[1,4,2,3,5] => [5,3,2,4,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,5),(1,6),(1,7),(2,3),(2,4),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2 - 1
[1,4,3,2,5] => [5,2,3,4,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ? = 2 - 1
[2,1,3,4,5] => [5,4,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,4),(0,5),(0,7),(0,8),(1,2),(1,3),(1,7),(1,8),(2,3),(2,5),(2,6),(2,8),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,8),(6,7),(6,8),(7,8)],9)
 => ? = 2 - 1
[2,1,3,5,4] => [4,5,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(2,5),(2,7),(3,4),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2 - 1
[2,1,4,3,5] => [5,3,4,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(2,5),(2,7),(3,4),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2 - 1
[2,3,1,4,5] => [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),(0,5),(0,6),(1,2),(1,5),(1,6),(1,7),(2,3),(2,4),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2 - 1
[2,3,1,5,4] => [4,5,1,3,2] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
 => ? = 3 - 1
[2,3,4,1,5] => [5,1,4,3,2] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ? = 4 - 1
[2,4,1,3,5] => [5,3,1,4,2] => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 4 - 1
[2,4,3,1,5] => [5,1,3,4,2] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 4 - 1
[3,1,2,4,5] => [5,4,2,1,3] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,5),(1,6),(1,7),(2,3),(2,4),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2 - 1
[3,1,2,5,4] => [4,5,2,1,3] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
 => ? = 3 - 1
[3,1,4,2,5] => [5,2,4,1,3] => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 4 - 1
[3,2,1,4,5] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ? = 2 - 1
[3,2,1,5,4] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ? = 3 - 1
[3,2,4,1,5] => [5,1,4,2,3] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 4 - 1
[3,4,1,2,5] => [5,2,1,4,3] => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 4 - 1
[3,4,2,1,5] => [5,1,2,4,3] => ([(0,4),(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)
 => 3 = 4 - 1
[4,1,2,3,5] => [5,3,2,1,4] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ? = 4 - 1
[4,1,3,2,5] => [5,2,3,1,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 4 - 1
[4,2,1,3,5] => [5,3,1,2,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 4 - 1
[4,2,3,1,5] => [5,1,3,2,4] => ([(0,4),(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)
 => 3 = 4 - 1
[4,3,1,2,5] => [5,2,1,3,4] => ([(0,4),(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)
 => 3 = 4 - 1
[4,3,2,1,5] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 3 = 4 - 1
[1,2,3,4,5,6] => [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)
 => ?
 => ? = 2 - 1
[1,2,3,4,6,5] => [5,6,4,3,2,1] => ([(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)
 => ?
 => ? = 3 - 1
[1,2,3,5,4,6] => [6,4,5,3,2,1] => ([(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)
 => ?
 => ? = 2 - 1
[1,2,4,3,5,6] => [6,5,3,4,2,1] => ([(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)
 => ?
 => ? = 2 - 1
[1,2,4,3,6,5] => [5,6,3,4,2,1] => ([(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)
 => ?
 => ? = 2 - 1
[1,2,4,5,3,6] => [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)
 => ?
 => ? = 2 - 1
[1,2,5,3,4,6] => [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)
 => ?
 => ? = 2 - 1
[1,2,5,4,3,6] => [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)
 => ?
 => ? = 2 - 1
[1,3,2,4,6,5] => [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)
 => ?
 => ? = 2 - 1
[1,3,2,5,4,6] => [6,4,5,2,3,1] => ([(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)
 => ?
 => ? = 2 - 1
[1,3,4,2,5,6] => [6,5,2,4,3,1] => ([(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)
 => ?
 => ? = 2 - 1
[1,3,4,2,6,5] => [5,6,2,4,3,1] => ([(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 - 1
[1,3,4,5,2,6] => [6,2,5,4,3,1] => ([(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 - 1
[1,3,5,2,4,6] => [6,4,2,5,3,1] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ?
 => ? = 3 - 1
[1,3,5,4,2,6] => [6,2,4,5,3,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ?
 => ? = 3 - 1
[1,4,2,3,5,6] => [6,5,3,2,4,1] => ([(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)
 => ?
 => ? = 2 - 1
[1,4,2,3,6,5] => [5,6,3,2,4,1] => ([(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 - 1
[1,4,2,5,3,6] => [6,3,5,2,4,1] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ?
 => ? = 3 - 1
[1,4,3,2,5,6] => [6,5,2,3,4,1] => ([(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)
 => ?
 => ? = 2 - 1
[1,4,3,2,6,5] => [5,6,2,3,4,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ?
 => ? = 2 - 1
[1,4,3,5,2,6] => [6,2,5,3,4,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ?
 => ? = 3 - 1
[1,4,5,2,3,6] => [6,3,2,5,4,1] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ?
 => ? = 3 - 1
[1,4,5,3,2,6] => [6,2,3,5,4,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(0,6),(0,7),(0,8),(1,3),(1,4),(1,7),(1,8),(1,9),(2,3),(2,4),(2,5),(2,6),(2,9),(3,5),(3,6),(3,9),(4,7),(4,8),(4,9),(5,6),(5,8),(5,9),(6,7),(6,9),(7,8),(7,9),(8,9)],10)
 => ? = 3 - 1
[1,5,2,3,4,6] => [6,4,3,2,5,1] => ([(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 - 1
[4,5,3,2,1,6] => [6,1,2,3,5,4] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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)
 => 4 = 5 - 1
[5,3,4,2,1,6] => [6,1,2,4,3,5] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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)
 => 4 = 5 - 1
[5,4,2,3,1,6] => [6,1,3,2,4,5] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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)
 => 4 = 5 - 1
[5,4,3,1,2,6] => [6,2,1,3,4,5] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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)
 => 4 = 5 - 1
[5,4,3,2,1,6] => [6,1,2,3,4,5] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4 = 5 - 1
Description
The Colin de Verdière graph invariant.