Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000741
Mp00254: Permutations Inverse fireworks mapPermutations
Mp00086: Permutations first fundamental transformationPermutations
Mp00160: Permutations graph of inversionsGraphs
St000741: Graphs ⟶ ℤResult quality: 100% values known / values provided: 100%distinct values known / distinct values provided: 100%
Values
[1] => [1] => [1] => ([],1)
=> 0
[1,2] => [1,2] => [1,2] => ([],2)
=> 1
[2,1] => [2,1] => [2,1] => ([(0,1)],2)
=> 1
[1,2,3] => [1,2,3] => [1,2,3] => ([],3)
=> 1
[3,1,2] => [3,1,2] => [2,3,1] => ([(0,2),(1,2)],3)
=> 2
[3,2,1] => [3,2,1] => [3,1,2] => ([(0,2),(1,2)],3)
=> 2
[1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([],4)
=> 1
[1,4,2,3] => [1,4,2,3] => [1,3,4,2] => ([(1,3),(2,3)],4)
=> 1
[1,4,3,2] => [1,4,3,2] => [1,4,2,3] => ([(1,3),(2,3)],4)
=> 1
[2,4,1,3] => [2,4,1,3] => [3,2,4,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 2
[2,4,3,1] => [1,4,3,2] => [1,4,2,3] => ([(1,3),(2,3)],4)
=> 1
[3,1,2,4] => [3,1,2,4] => [2,3,1,4] => ([(1,3),(2,3)],4)
=> 1
[3,2,1,4] => [3,2,1,4] => [3,1,2,4] => ([(1,3),(2,3)],4)
=> 1
[3,4,1,2] => [2,4,1,3] => [3,2,4,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 2
[3,4,2,1] => [1,4,3,2] => [1,4,2,3] => ([(1,3),(2,3)],4)
=> 1
[4,1,2,3] => [4,1,2,3] => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
=> 2
[4,1,3,2] => [4,1,3,2] => [3,4,2,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 2
[4,2,1,3] => [4,2,1,3] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
=> 1
[4,2,3,1] => [4,1,3,2] => [3,4,2,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 2
[4,3,1,2] => [4,3,1,2] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
=> 1
[4,3,2,1] => [4,3,2,1] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4)
=> 2
[1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([],5)
=> 1
[1,2,5,3,4] => [1,2,5,3,4] => [1,2,4,5,3] => ([(2,4),(3,4)],5)
=> 1
[1,2,5,4,3] => [1,2,5,4,3] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
=> 1
[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
[1,3,5,4,2] => [1,2,5,4,3] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
=> 1
[1,4,2,3,5] => [1,4,2,3,5] => [1,3,4,2,5] => ([(2,4),(3,4)],5)
=> 1
[1,4,3,2,5] => [1,4,3,2,5] => [1,4,2,3,5] => ([(2,4),(3,4)],5)
=> 1
[1,4,5,2,3] => [1,3,5,2,4] => [1,4,3,5,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[1,4,5,3,2] => [1,2,5,4,3] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
=> 1
[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
[1,5,3,2,4] => [1,5,3,2,4] => [1,4,2,5,3] => ([(1,4),(2,3),(3,4)],5)
=> 1
[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
[1,5,4,2,3] => [1,5,4,2,3] => [1,3,5,2,4] => ([(1,4),(2,3),(3,4)],5)
=> 1
[2,1,5,3,4] => [2,1,5,3,4] => [2,1,4,5,3] => ([(0,1),(2,4),(3,4)],5)
=> 1
[2,1,5,4,3] => [2,1,5,4,3] => [2,1,5,3,4] => ([(0,1),(2,4),(3,4)],5)
=> 1
[2,3,5,1,4] => [1,3,5,2,4] => [1,4,3,5,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[2,3,5,4,1] => [1,2,5,4,3] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
=> 1
[2,4,1,3,5] => [2,4,1,3,5] => [3,2,4,1,5] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[2,4,3,1,5] => [1,4,3,2,5] => [1,4,2,3,5] => ([(2,4),(3,4)],5)
=> 1
[2,4,5,1,3] => [1,3,5,2,4] => [1,4,3,5,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[2,4,5,3,1] => [1,2,5,4,3] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
=> 1
[2,5,1,3,4] => [2,5,1,3,4] => [3,2,4,5,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[2,5,1,4,3] => [2,5,1,4,3] => [4,2,5,3,1] => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[2,5,3,1,4] => [1,5,3,2,4] => [1,4,2,5,3] => ([(1,4),(2,3),(3,4)],5)
=> 1
[2,5,3,4,1] => [1,5,2,4,3] => [1,4,5,3,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[2,5,4,1,3] => [2,5,4,1,3] => [3,2,5,1,4] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> 2
[3,1,2,4,5] => [3,1,2,4,5] => [2,3,1,4,5] => ([(2,4),(3,4)],5)
=> 1
[3,1,2,5,4] => [3,1,2,5,4] => [2,3,1,5,4] => ([(0,1),(2,4),(3,4)],5)
=> 1
[3,1,5,4,2] => [2,1,5,4,3] => [2,1,5,3,4] => ([(0,1),(2,4),(3,4)],5)
=> 1
Description
The Colin de Verdière graph invariant.