Identifier
- St000988: Permutations ⟶ ℤ
Values
=>
[1,2]=>1
[2,1]=>1
[1,2,3]=>1
[1,3,2]=>2
[2,1,3]=>1
[2,3,1]=>1
[3,1,2]=>2
[3,2,1]=>1
[1,2,3,4]=>1
[1,2,4,3]=>2
[1,3,2,4]=>2
[1,3,4,2]=>3
[1,4,2,3]=>1
[1,4,3,2]=>2
[2,1,3,4]=>1
[2,1,4,3]=>3
[2,3,1,4]=>1
[2,3,4,1]=>1
[2,4,1,3]=>3
[2,4,3,1]=>2
[3,1,2,4]=>2
[3,1,4,2]=>3
[3,2,1,4]=>1
[3,2,4,1]=>1
[3,4,1,2]=>3
[3,4,2,1]=>1
[4,1,2,3]=>2
[4,1,3,2]=>1
[4,2,1,3]=>3
[4,2,3,1]=>2
[4,3,1,2]=>2
[4,3,2,1]=>1
[1,2,3,4,5]=>1
[1,2,3,5,4]=>2
[1,2,4,3,5]=>2
[1,2,4,5,3]=>6
[1,2,5,3,4]=>2
[1,2,5,4,3]=>2
[1,3,2,4,5]=>2
[1,3,2,5,4]=>7
[1,3,4,2,5]=>3
[1,3,4,5,2]=>4
[1,3,5,2,4]=>7
[1,3,5,4,2]=>7
[1,4,2,3,5]=>1
[1,4,2,5,3]=>6
[1,4,3,2,5]=>2
[1,4,3,5,2]=>3
[1,4,5,2,3]=>6
[1,4,5,3,2]=>4
[1,5,2,3,4]=>2
[1,5,2,4,3]=>2
[1,5,3,2,4]=>7
[1,5,3,4,2]=>7
[1,5,4,2,3]=>1
[1,5,4,3,2]=>2
[2,1,3,4,5]=>1
[2,1,3,5,4]=>4
[2,1,4,3,5]=>3
[2,1,4,5,3]=>4
[2,1,5,3,4]=>4
[2,1,5,4,3]=>6
[2,3,1,4,5]=>1
[2,3,1,5,4]=>3
[2,3,4,1,5]=>1
[2,3,4,5,1]=>1
[2,3,5,1,4]=>3
[2,3,5,4,1]=>2
[2,4,1,3,5]=>3
[2,4,1,5,3]=>2
[2,4,3,1,5]=>2
[2,4,3,5,1]=>2
[2,4,5,1,3]=>4
[2,4,5,3,1]=>3
[2,5,1,3,4]=>4
[2,5,1,4,3]=>6
[2,5,3,1,4]=>1
[2,5,3,4,1]=>1
[2,5,4,1,3]=>6
[2,5,4,3,1]=>2
[3,1,2,4,5]=>2
[3,1,2,5,4]=>7
[3,1,4,2,5]=>3
[3,1,4,5,2]=>4
[3,1,5,2,4]=>1
[3,1,5,4,2]=>7
[3,2,1,4,5]=>1
[3,2,1,5,4]=>4
[3,2,4,1,5]=>1
[3,2,4,5,1]=>1
[3,2,5,1,4]=>4
[3,2,5,4,1]=>3
[3,4,1,2,5]=>3
[3,4,1,5,2]=>4
[3,4,2,1,5]=>1
[3,4,2,5,1]=>1
[3,4,5,1,2]=>4
[3,4,5,2,1]=>1
[3,5,1,2,4]=>7
[3,5,1,4,2]=>1
[3,5,2,1,4]=>4
[3,5,2,4,1]=>3
[3,5,4,1,2]=>7
[3,5,4,2,1]=>2
[4,1,2,3,5]=>2
[4,1,2,5,3]=>6
[4,1,3,2,5]=>1
[4,1,3,5,2]=>1
[4,1,5,2,3]=>6
[4,1,5,3,2]=>4
[4,2,1,3,5]=>3
[4,2,1,5,3]=>4
[4,2,3,1,5]=>2
[4,2,3,5,1]=>2
[4,2,5,1,3]=>2
[4,2,5,3,1]=>3
[4,3,1,2,5]=>2
[4,3,1,5,2]=>3
[4,3,2,1,5]=>1
[4,3,2,5,1]=>1
[4,3,5,1,2]=>3
[4,3,5,2,1]=>1
[4,5,1,2,3]=>6
[4,5,1,3,2]=>4
[4,5,2,1,3]=>4
[4,5,2,3,1]=>3
[4,5,3,1,2]=>4
[4,5,3,2,1]=>1
[5,1,2,3,4]=>2
[5,1,2,4,3]=>1
[5,1,3,2,4]=>7
[5,1,3,4,2]=>7
[5,1,4,2,3]=>2
[5,1,4,3,2]=>2
[5,2,1,3,4]=>4
[5,2,1,4,3]=>6
[5,2,3,1,4]=>3
[5,2,3,4,1]=>2
[5,2,4,1,3]=>6
[5,2,4,3,1]=>1
[5,3,1,2,4]=>7
[5,3,1,4,2]=>7
[5,3,2,1,4]=>4
[5,3,2,4,1]=>3
[5,3,4,1,2]=>7
[5,3,4,2,1]=>2
[5,4,1,2,3]=>2
[5,4,1,3,2]=>2
[5,4,2,1,3]=>6
[5,4,2,3,1]=>2
[5,4,3,1,2]=>2
[5,4,3,2,1]=>1
[1,2,3,4,5,6]=>1
[1,2,3,4,6,5]=>2
[1,2,3,5,4,6]=>2
[1,2,3,5,6,4]=>7
[1,2,3,6,4,5]=>2
[1,2,3,6,5,4]=>2
[1,2,4,3,5,6]=>2
[1,2,4,3,6,5]=>12
[1,2,4,5,3,6]=>6
[1,2,4,5,6,3]=>4
[1,2,4,6,3,5]=>12
[1,2,4,6,5,3]=>16
[1,2,5,3,4,6]=>2
[1,2,5,3,6,4]=>7
[1,2,5,4,3,6]=>2
[1,2,5,4,6,3]=>9
[1,2,5,6,3,4]=>3
[1,2,5,6,4,3]=>6
[1,2,6,3,4,5]=>1
[1,2,6,3,5,4]=>2
[1,2,6,4,3,5]=>12
[1,2,6,4,5,3]=>16
[1,2,6,5,3,4]=>2
[1,2,6,5,4,3]=>2
[1,3,2,4,5,6]=>2
[1,3,2,4,6,5]=>4
[1,3,2,5,4,6]=>7
[1,3,2,5,6,4]=>4
[1,3,2,6,4,5]=>4
[1,3,2,6,5,4]=>16
[1,3,4,2,5,6]=>3
[1,3,4,2,6,5]=>3
[1,3,4,5,2,6]=>4
[1,3,4,5,6,2]=>5
[1,3,4,6,2,5]=>3
[1,3,4,6,5,2]=>5
[1,3,5,2,4,6]=>7
[1,3,5,2,6,4]=>6
[1,3,5,4,2,6]=>7
[1,3,5,4,6,2]=>4
[1,3,5,6,2,4]=>9
[1,3,5,6,4,2]=>3
[1,3,6,2,4,5]=>3
[1,3,6,2,5,4]=>16
[1,3,6,4,2,5]=>4
[1,3,6,4,5,2]=>9
[1,3,6,5,2,4]=>16
[1,3,6,5,4,2]=>12
[1,4,2,3,5,6]=>1
[1,4,2,3,6,5]=>12
[1,4,2,5,3,6]=>6
[1,4,2,5,6,3]=>6
[1,4,2,6,3,5]=>2
[1,4,2,6,5,3]=>16
[1,4,3,2,5,6]=>2
[1,4,3,2,6,5]=>5
[1,4,3,5,2,6]=>3
[1,4,3,5,6,2]=>4
[1,4,3,6,2,5]=>9
[1,4,3,6,5,2]=>3
[1,4,5,2,3,6]=>6
[1,4,5,2,6,3]=>6
[1,4,5,3,2,6]=>4
[1,4,5,3,6,2]=>5
[1,4,5,6,2,3]=>6
[1,4,5,6,3,2]=>3
[1,4,6,2,3,5]=>12
[1,4,6,2,5,3]=>4
[1,4,6,3,2,5]=>5
[1,4,6,3,5,2]=>3
[1,4,6,5,2,3]=>16
[1,4,6,5,3,2]=>4
[1,5,2,3,4,6]=>2
[1,5,2,3,6,4]=>3
[1,5,2,4,3,6]=>2
[1,5,2,4,6,3]=>9
[1,5,2,6,3,4]=>7
[1,5,2,6,4,3]=>6
[1,5,3,2,4,6]=>7
[1,5,3,2,6,4]=>9
[1,5,3,4,2,6]=>7
[1,5,3,4,6,2]=>5
[1,5,3,6,2,4]=>9
[1,5,3,6,4,2]=>3
[1,5,4,2,3,6]=>1
[1,5,4,2,6,3]=>9
[1,5,4,3,2,6]=>2
[1,5,4,3,6,2]=>3
[1,5,4,6,2,3]=>9
[1,5,4,6,3,2]=>5
[1,5,6,2,3,4]=>7
[1,5,6,2,4,3]=>4
[1,5,6,3,2,4]=>1
[1,5,6,3,4,2]=>8
[1,5,6,4,2,3]=>4
[1,5,6,4,3,2]=>4
[1,6,2,3,4,5]=>2
[1,6,2,3,5,4]=>2
[1,6,2,4,3,5]=>12
[1,6,2,4,5,3]=>16
[1,6,2,5,3,4]=>1
[1,6,2,5,4,3]=>2
[1,6,3,2,4,5]=>3
[1,6,3,2,5,4]=>16
[1,6,3,4,2,5]=>1
[1,6,3,4,5,2]=>9
[1,6,3,5,2,4]=>16
[1,6,3,5,4,2]=>12
[1,6,4,2,3,5]=>12
[1,6,4,2,5,3]=>16
[1,6,4,3,2,5]=>9
[1,6,4,3,5,2]=>3
[1,6,4,5,2,3]=>16
[1,6,4,5,3,2]=>3
[1,6,5,2,3,4]=>2
[1,6,5,2,4,3]=>2
[1,6,5,3,2,4]=>16
[1,6,5,3,4,2]=>12
[1,6,5,4,2,3]=>1
[1,6,5,4,3,2]=>2
[2,1,3,4,5,6]=>1
[2,1,3,4,6,5]=>4
[2,1,3,5,4,6]=>4
[2,1,3,5,6,4]=>9
[2,1,3,6,4,5]=>4
[2,1,3,6,5,4]=>6
[2,1,4,3,5,6]=>3
[2,1,4,3,6,5]=>3
[2,1,4,5,3,6]=>4
[2,1,4,5,6,3]=>5
[2,1,4,6,3,5]=>3
[2,1,4,6,5,3]=>9
[2,1,5,3,4,6]=>4
[2,1,5,3,6,4]=>9
[2,1,5,4,3,6]=>6
[2,1,5,4,6,3]=>8
[2,1,5,6,3,4]=>9
[2,1,5,6,4,3]=>9
[2,1,6,3,4,5]=>1
[2,1,6,3,5,4]=>6
[2,1,6,4,3,5]=>8
[2,1,6,4,5,3]=>9
[2,1,6,5,3,4]=>6
[2,1,6,5,4,3]=>7
[2,3,1,4,5,6]=>1
[2,3,1,4,6,5]=>5
[2,3,1,5,4,6]=>3
[2,3,1,5,6,4]=>8
[2,3,1,6,4,5]=>5
[2,3,1,6,5,4]=>9
[2,3,4,1,5,6]=>1
[2,3,4,1,6,5]=>3
[2,3,4,5,1,6]=>1
[2,3,4,5,6,1]=>1
[2,3,4,6,1,5]=>3
[2,3,4,6,5,1]=>2
[2,3,5,1,4,6]=>3
[2,3,5,1,6,4]=>2
[2,3,5,4,1,6]=>2
[2,3,5,4,6,1]=>2
[2,3,5,6,1,4]=>8
[2,3,5,6,4,1]=>6
[2,3,6,1,4,5]=>5
[2,3,6,1,5,4]=>9
[2,3,6,4,1,5]=>2
[2,3,6,4,5,1]=>2
[2,3,6,5,1,4]=>9
[2,3,6,5,4,1]=>2
[2,4,1,3,5,6]=>3
[2,4,1,3,6,5]=>8
[2,4,1,5,3,6]=>2
[2,4,1,5,6,3]=>5
[2,4,1,6,3,5]=>8
[2,4,1,6,5,3]=>6
[2,4,3,1,5,6]=>2
[2,4,3,1,6,5]=>4
[2,4,3,5,1,6]=>2
[2,4,3,5,6,1]=>2
[2,4,3,6,1,5]=>5
[2,4,3,6,5,1]=>7
[2,4,5,1,3,6]=>4
[2,4,5,1,6,3]=>5
[2,4,5,3,1,6]=>3
[2,4,5,3,6,1]=>3
[2,4,5,6,1,3]=>5
[2,4,5,6,3,1]=>4
[2,4,6,1,3,5]=>3
[2,4,6,1,5,3]=>6
[2,4,6,3,1,5]=>4
[2,4,6,3,5,1]=>7
[2,4,6,5,1,3]=>4
[2,4,6,5,3,1]=>7
[2,5,1,3,4,6]=>4
[2,5,1,3,6,4]=>9
[2,5,1,4,3,6]=>6
[2,5,1,4,6,3]=>8
[2,5,1,6,3,4]=>1
[2,5,1,6,4,3]=>9
[2,5,3,1,4,6]=>1
[2,5,3,1,6,4]=>8
[2,5,3,4,1,6]=>1
[2,5,3,4,6,1]=>1
[2,5,3,6,1,4]=>8
[2,5,3,6,4,1]=>6
[2,5,4,1,3,6]=>6
[2,5,4,1,6,3]=>2
[2,5,4,3,1,6]=>2
[2,5,4,3,6,1]=>2
[2,5,4,6,1,3]=>8
[2,5,4,6,3,1]=>3
[2,5,6,1,3,4]=>9
[2,5,6,1,4,3]=>9
[2,5,6,3,1,4]=>8
[2,5,6,3,4,1]=>6
[2,5,6,4,1,3]=>9
[2,5,6,4,3,1]=>4
[2,6,1,3,4,5]=>4
[2,6,1,3,5,4]=>4
[2,6,1,4,3,5]=>1
[2,6,1,4,5,3]=>4
[2,6,1,5,3,4]=>4
[2,6,1,5,4,3]=>3
[2,6,3,1,4,5]=>5
[2,6,3,1,5,4]=>9
[2,6,3,4,1,5]=>2
[2,6,3,4,5,1]=>2
[2,6,3,5,1,4]=>9
[2,6,3,5,4,1]=>2
[2,6,4,1,3,5]=>8
[2,6,4,1,5,3]=>9
[2,6,4,3,1,5]=>5
[2,6,4,3,5,1]=>7
[2,6,4,5,1,3]=>9
[2,6,4,5,3,1]=>7
[2,6,5,1,3,4]=>6
[2,6,5,1,4,3]=>7
[2,6,5,3,1,4]=>1
[2,6,5,3,4,1]=>1
[2,6,5,4,1,3]=>7
[2,6,5,4,3,1]=>2
[3,1,2,4,5,6]=>2
[3,1,2,4,6,5]=>3
[3,1,2,5,4,6]=>7
[3,1,2,5,6,4]=>9
[3,1,2,6,4,5]=>3
[3,1,2,6,5,4]=>16
[3,1,4,2,5,6]=>3
[3,1,4,2,6,5]=>3
[3,1,4,5,2,6]=>4
[3,1,4,5,6,2]=>5
[3,1,4,6,2,5]=>3
[3,1,4,6,5,2]=>9
[3,1,5,2,4,6]=>1
[3,1,5,2,6,4]=>6
[3,1,5,4,2,6]=>7
[3,1,5,4,6,2]=>5
[3,1,5,6,2,4]=>6
[3,1,5,6,4,2]=>8
[3,1,6,2,4,5]=>3
[3,1,6,2,5,4]=>4
[3,1,6,4,2,5]=>4
[3,1,6,4,5,2]=>9
[3,1,6,5,2,4]=>4
[3,1,6,5,4,2]=>12
[3,2,1,4,5,6]=>1
[3,2,1,4,6,5]=>3
[3,2,1,5,4,6]=>4
[3,2,1,5,6,4]=>5
[3,2,1,6,4,5]=>2
[3,2,1,6,5,4]=>4
[3,2,4,1,5,6]=>1
[3,2,4,1,6,5]=>5
[3,2,4,5,1,6]=>1
[3,2,4,5,6,1]=>1
[3,2,4,6,1,5]=>5
[3,2,4,6,5,1]=>4
[3,2,5,1,4,6]=>4
[3,2,5,1,6,4]=>5
[3,2,5,4,1,6]=>3
[3,2,5,4,6,1]=>3
[3,2,5,6,1,4]=>5
[3,2,5,6,4,1]=>4
[3,2,6,1,4,5]=>3
[3,2,6,1,5,4]=>6
[3,2,6,4,1,5]=>5
[3,2,6,4,5,1]=>4
[3,2,6,5,1,4]=>6
[3,2,6,5,4,1]=>6
[3,4,1,2,5,6]=>3
[3,4,1,2,6,5]=>3
[3,4,1,5,2,6]=>4
[3,4,1,5,6,2]=>5
[3,4,1,6,2,5]=>1
[3,4,1,6,5,2]=>5
[3,4,2,1,5,6]=>1
[3,4,2,1,6,5]=>4
[3,4,2,5,1,6]=>1
[3,4,2,5,6,1]=>1
[3,4,2,6,1,5]=>4
[3,4,2,6,5,1]=>3
[3,4,5,1,2,6]=>4
[3,4,5,1,6,2]=>5
[3,4,5,2,1,6]=>1
[3,4,5,2,6,1]=>1
[3,4,5,6,1,2]=>5
[3,4,5,6,2,1]=>1
[3,4,6,1,2,5]=>3
[3,4,6,1,5,2]=>1
[3,4,6,2,1,5]=>4
[3,4,6,2,5,1]=>3
[3,4,6,5,1,2]=>9
[3,4,6,5,2,1]=>2
[3,5,1,2,4,6]=>7
[3,5,1,2,6,4]=>9
[3,5,1,4,2,6]=>1
[3,5,1,4,6,2]=>1
[3,5,1,6,2,4]=>6
[3,5,1,6,4,2]=>8
[3,5,2,1,4,6]=>4
[3,5,2,1,6,4]=>5
[3,5,2,4,1,6]=>3
[3,5,2,4,6,1]=>3
[3,5,2,6,1,4]=>5
[3,5,2,6,4,1]=>2
[3,5,4,1,2,6]=>7
[3,5,4,1,6,2]=>4
[3,5,4,2,1,6]=>2
[3,5,4,2,6,1]=>2
[3,5,4,6,1,2]=>5
[3,5,4,6,2,1]=>2
[3,5,6,1,2,4]=>4
[3,5,6,1,4,2]=>8
[3,5,6,2,1,4]=>5
[3,5,6,2,4,1]=>4
[3,5,6,4,1,2]=>3
[3,5,6,4,2,1]=>3
[3,6,1,2,4,5]=>4
[3,6,1,2,5,4]=>16
[3,6,1,4,2,5]=>4
[3,6,1,4,5,2]=>5
[3,6,1,5,2,4]=>4
[3,6,1,5,4,2]=>2
[3,6,2,1,4,5]=>2
[3,6,2,1,5,4]=>6
[3,6,2,4,1,5]=>5
[3,6,2,4,5,1]=>4
[3,6,2,5,1,4]=>4
[3,6,2,5,4,1]=>6
[3,6,4,1,2,5]=>4
[3,6,4,1,5,2]=>9
[3,6,4,2,1,5]=>1
[3,6,4,2,5,1]=>1
[3,6,4,5,1,2]=>9
[3,6,4,5,2,1]=>1
[3,6,5,1,2,4]=>16
[3,6,5,1,4,2]=>1
[3,6,5,2,1,4]=>4
[3,6,5,2,4,1]=>6
[3,6,5,4,1,2]=>12
[3,6,5,4,2,1]=>2
[4,1,2,3,5,6]=>2
[4,1,2,3,6,5]=>12
[4,1,2,5,3,6]=>6
[4,1,2,5,6,3]=>4
[4,1,2,6,3,5]=>1
[4,1,2,6,5,3]=>16
[4,1,3,2,5,6]=>1
[4,1,3,2,6,5]=>9
[4,1,3,5,2,6]=>1
[4,1,3,5,6,2]=>1
[4,1,3,6,2,5]=>9
[4,1,3,6,5,2]=>4
[4,1,5,2,3,6]=>6
[4,1,5,2,6,3]=>4
[4,1,5,3,2,6]=>4
[4,1,5,3,6,2]=>5
[4,1,5,6,2,3]=>6
[4,1,5,6,3,2]=>2
[4,1,6,2,3,5]=>2
[4,1,6,2,5,3]=>4
[4,1,6,3,2,5]=>5
[4,1,6,3,5,2]=>4
[4,1,6,5,2,3]=>16
[4,1,6,5,3,2]=>4
[4,2,1,3,5,6]=>3
[4,2,1,3,6,5]=>3
[4,2,1,5,3,6]=>4
[4,2,1,5,6,3]=>5
[4,2,1,6,3,5]=>8
[4,2,1,6,5,3]=>4
[4,2,3,1,5,6]=>2
[4,2,3,1,6,5]=>5
[4,2,3,5,1,6]=>2
[4,2,3,5,6,1]=>2
[4,2,3,6,1,5]=>4
[4,2,3,6,5,1]=>7
[4,2,5,1,3,6]=>2
[4,2,5,1,6,3]=>5
[4,2,5,3,1,6]=>3
[4,2,5,3,6,1]=>3
[4,2,5,6,1,3]=>5
[4,2,5,6,3,1]=>4
[4,2,6,1,3,5]=>8
[4,2,6,1,5,3]=>6
[4,2,6,3,1,5]=>1
[4,2,6,3,5,1]=>1
[4,2,6,5,1,3]=>9
[4,2,6,5,3,1]=>7
[4,3,1,2,5,6]=>2
[4,3,1,2,6,5]=>9
[4,3,1,5,2,6]=>3
[4,3,1,5,6,2]=>4
[4,3,1,6,2,5]=>1
[4,3,1,6,5,2]=>3
[4,3,2,1,5,6]=>1
[4,3,2,1,6,5]=>5
[4,3,2,5,1,6]=>1
[4,3,2,5,6,1]=>1
[4,3,2,6,1,5]=>5
[4,3,2,6,5,1]=>4
[4,3,5,1,2,6]=>3
[4,3,5,1,6,2]=>4
[4,3,5,2,1,6]=>1
[4,3,5,2,6,1]=>1
[4,3,5,6,1,2]=>4
[4,3,5,6,2,1]=>1
[4,3,6,1,2,5]=>5
[4,3,6,1,5,2]=>1
[4,3,6,2,1,5]=>5
[4,3,6,2,5,1]=>4
[4,3,6,5,1,2]=>3
[4,3,6,5,2,1]=>3
[4,5,1,2,3,6]=>6
[4,5,1,2,6,3]=>6
[4,5,1,3,2,6]=>4
[4,5,1,3,6,2]=>5
[4,5,1,6,2,3]=>6
[4,5,1,6,3,2]=>3
[4,5,2,1,3,6]=>4
[4,5,2,1,6,3]=>5
[4,5,2,3,1,6]=>3
[4,5,2,3,6,1]=>3
[4,5,2,6,1,3]=>5
[4,5,2,6,3,1]=>4
[4,5,3,1,2,6]=>4
[4,5,3,1,6,2]=>5
[4,5,3,2,1,6]=>1
[4,5,3,2,6,1]=>1
[4,5,3,6,1,2]=>5
[4,5,3,6,2,1]=>1
[4,5,6,1,2,3]=>4
[4,5,6,1,3,2]=>2
[4,5,6,2,1,3]=>5
[4,5,6,2,3,1]=>4
[4,5,6,3,1,2]=>3
[4,5,6,3,2,1]=>1
[4,6,1,2,3,5]=>12
[4,6,1,2,5,3]=>4
[4,6,1,3,2,5]=>9
[4,6,1,3,5,2]=>4
[4,6,1,5,2,3]=>4
[4,6,1,5,3,2]=>3
[4,6,2,1,3,5]=>8
[4,6,2,1,5,3]=>6
[4,6,2,3,1,5]=>5
[4,6,2,3,5,1]=>7
[4,6,2,5,1,3]=>6
[4,6,2,5,3,1]=>1
[4,6,3,1,2,5]=>9
[4,6,3,1,5,2]=>3
[4,6,3,2,1,5]=>5
[4,6,3,2,5,1]=>4
[4,6,3,5,1,2]=>3
[4,6,3,5,2,1]=>3
[4,6,5,1,2,3]=>16
[4,6,5,1,3,2]=>3
[4,6,5,2,1,3]=>9
[4,6,5,2,3,1]=>7
[4,6,5,3,1,2]=>3
[4,6,5,3,2,1]=>2
[5,1,2,3,4,6]=>2
[5,1,2,3,6,4]=>7
[5,1,2,4,3,6]=>1
[5,1,2,4,6,3]=>1
[5,1,2,6,3,4]=>7
[5,1,2,6,4,3]=>6
[5,1,3,2,4,6]=>7
[5,1,3,2,6,4]=>9
[5,1,3,4,2,6]=>7
[5,1,3,4,6,2]=>5
[5,1,3,6,2,4]=>9
[5,1,3,6,4,2]=>8
[5,1,4,2,3,6]=>2
[5,1,4,2,6,3]=>9
[5,1,4,3,2,6]=>2
[5,1,4,3,6,2]=>2
[5,1,4,6,2,3]=>9
[5,1,4,6,3,2]=>5
[5,1,6,2,3,4]=>3
[5,1,6,2,4,3]=>4
[5,1,6,3,2,4]=>4
[5,1,6,3,4,2]=>1
[5,1,6,4,2,3]=>4
[5,1,6,4,3,2]=>4
[5,2,1,3,4,6]=>4
[5,2,1,3,6,4]=>9
[5,2,1,4,3,6]=>6
[5,2,1,4,6,3]=>8
[5,2,1,6,3,4]=>9
[5,2,1,6,4,3]=>9
[5,2,3,1,4,6]=>3
[5,2,3,1,6,4]=>8
[5,2,3,4,1,6]=>2
[5,2,3,4,6,1]=>2
[5,2,3,6,1,4]=>2
[5,2,3,6,4,1]=>6
[5,2,4,1,3,6]=>6
[5,2,4,1,6,3]=>8
[5,2,4,3,1,6]=>1
[5,2,4,3,6,1]=>1
[5,2,4,6,1,3]=>8
[5,2,4,6,3,1]=>1
[5,2,6,1,3,4]=>9
[5,2,6,1,4,3]=>1
[5,2,6,3,1,4]=>8
[5,2,6,3,4,1]=>6
[5,2,6,4,1,3]=>9
[5,2,6,4,3,1]=>4
[5,3,1,2,4,6]=>7
[5,3,1,2,6,4]=>4
[5,3,1,4,2,6]=>7
[5,3,1,4,6,2]=>4
[5,3,1,6,2,4]=>6
[5,3,1,6,4,2]=>3
[5,3,2,1,4,6]=>4
[5,3,2,1,6,4]=>5
[5,3,2,4,1,6]=>3
[5,3,2,4,6,1]=>3
[5,3,2,6,1,4]=>5
[5,3,2,6,4,1]=>4
[5,3,4,1,2,6]=>7
[5,3,4,1,6,2]=>5
[5,3,4,2,1,6]=>2
[5,3,4,2,6,1]=>2
[5,3,4,6,1,2]=>4
[5,3,4,6,2,1]=>2
[5,3,6,1,2,4]=>6
[5,3,6,1,4,2]=>8
[5,3,6,2,1,4]=>5
[5,3,6,2,4,1]=>2
[5,3,6,4,1,2]=>8
[5,3,6,4,2,1]=>3
[5,4,1,2,3,6]=>2
[5,4,1,2,6,3]=>9
[5,4,1,3,2,6]=>2
[5,4,1,3,6,2]=>2
[5,4,1,6,2,3]=>9
[5,4,1,6,3,2]=>5
[5,4,2,1,3,6]=>6
[5,4,2,1,6,3]=>8
[5,4,2,3,1,6]=>2
[5,4,2,3,6,1]=>2
[5,4,2,6,1,3]=>2
[5,4,2,6,3,1]=>3
[5,4,3,1,2,6]=>2
[5,4,3,1,6,2]=>3
[5,4,3,2,1,6]=>1
[5,4,3,2,6,1]=>1
[5,4,3,6,1,2]=>3
[5,4,3,6,2,1]=>1
[5,4,6,1,2,3]=>9
[5,4,6,1,3,2]=>5
[5,4,6,2,1,3]=>8
[5,4,6,2,3,1]=>3
[5,4,6,3,1,2]=>5
[5,4,6,3,2,1]=>1
[5,6,1,2,3,4]=>7
[5,6,1,2,4,3]=>6
[5,6,1,3,2,4]=>9
[5,6,1,3,4,2]=>8
[5,6,1,4,2,3]=>6
[5,6,1,4,3,2]=>1
[5,6,2,1,3,4]=>9
[5,6,2,1,4,3]=>9
[5,6,2,3,1,4]=>8
[5,6,2,3,4,1]=>6
[5,6,2,4,1,3]=>9
[5,6,2,4,3,1]=>4
[5,6,3,1,2,4]=>9
[5,6,3,1,4,2]=>3
[5,6,3,2,1,4]=>5
[5,6,3,2,4,1]=>4
[5,6,3,4,1,2]=>3
[5,6,3,4,2,1]=>3
[5,6,4,1,2,3]=>6
[5,6,4,1,3,2]=>4
[5,6,4,2,1,3]=>9
[5,6,4,2,3,1]=>4
[5,6,4,3,1,2]=>4
[5,6,4,3,2,1]=>1
[6,1,2,3,4,5]=>2
[6,1,2,3,5,4]=>1
[6,1,2,4,3,5]=>12
[6,1,2,4,5,3]=>16
[6,1,2,5,3,4]=>2
[6,1,2,5,4,3]=>2
[6,1,3,2,4,5]=>3
[6,1,3,2,5,4]=>16
[6,1,3,4,2,5]=>3
[6,1,3,4,5,2]=>9
[6,1,3,5,2,4]=>16
[6,1,3,5,4,2]=>12
[6,1,4,2,3,5]=>12
[6,1,4,2,5,3]=>16
[6,1,4,3,2,5]=>9
[6,1,4,3,5,2]=>1
[6,1,4,5,2,3]=>16
[6,1,4,5,3,2]=>3
[6,1,5,2,3,4]=>2
[6,1,5,2,4,3]=>1
[6,1,5,3,2,4]=>16
[6,1,5,3,4,2]=>12
[6,1,5,4,2,3]=>2
[6,1,5,4,3,2]=>2
[6,2,1,3,4,5]=>4
[6,2,1,3,5,4]=>4
[6,2,1,4,3,5]=>8
[6,2,1,4,5,3]=>1
[6,2,1,5,3,4]=>4
[6,2,1,5,4,3]=>7
[6,2,3,1,4,5]=>5
[6,2,3,1,5,4]=>9
[6,2,3,4,1,5]=>3
[6,2,3,4,5,1]=>2
[6,2,3,5,1,4]=>9
[6,2,3,5,4,1]=>1
[6,2,4,1,3,5]=>3
[6,2,4,1,5,3]=>9
[6,2,4,3,1,5]=>5
[6,2,4,3,5,1]=>7
[6,2,4,5,1,3]=>9
[6,2,4,5,3,1]=>7
[6,2,5,1,3,4]=>6
[6,2,5,1,4,3]=>7
[6,2,5,3,1,4]=>9
[6,2,5,3,4,1]=>2
[6,2,5,4,1,3]=>3
[6,2,5,4,3,1]=>2
[6,3,1,2,4,5]=>4
[6,3,1,2,5,4]=>16
[6,3,1,4,2,5]=>3
[6,3,1,4,5,2]=>5
[6,3,1,5,2,4]=>4
[6,3,1,5,4,2]=>12
[6,3,2,1,4,5]=>3
[6,3,2,1,5,4]=>6
[6,3,2,4,1,5]=>5
[6,3,2,4,5,1]=>4
[6,3,2,5,1,4]=>6
[6,3,2,5,4,1]=>6
[6,3,4,1,2,5]=>3
[6,3,4,1,5,2]=>9
[6,3,4,2,1,5]=>4
[6,3,4,2,5,1]=>3
[6,3,4,5,1,2]=>5
[6,3,4,5,2,1]=>2
[6,3,5,1,2,4]=>16
[6,3,5,1,4,2]=>2
[6,3,5,2,1,4]=>6
[6,3,5,2,4,1]=>6
[6,3,5,4,1,2]=>12
[6,3,5,4,2,1]=>1
[6,4,1,2,3,5]=>12
[6,4,1,2,5,3]=>16
[6,4,1,3,2,5]=>9
[6,4,1,3,5,2]=>4
[6,4,1,5,2,3]=>16
[6,4,1,5,3,2]=>3
[6,4,2,1,3,5]=>3
[6,4,2,1,5,3]=>9
[6,4,2,3,1,5]=>4
[6,4,2,3,5,1]=>7
[6,4,2,5,1,3]=>6
[6,4,2,5,3,1]=>7
[6,4,3,1,2,5]=>5
[6,4,3,1,5,2]=>3
[6,4,3,2,1,5]=>5
[6,4,3,2,5,1]=>4
[6,4,3,5,1,2]=>3
[6,4,3,5,2,1]=>3
[6,4,5,1,2,3]=>16
[6,4,5,1,3,2]=>4
[6,4,5,2,1,3]=>4
[6,4,5,2,3,1]=>7
[6,4,5,3,1,2]=>4
[6,4,5,3,2,1]=>2
[6,5,1,2,3,4]=>2
[6,5,1,2,4,3]=>2
[6,5,1,3,2,4]=>16
[6,5,1,3,4,2]=>12
[6,5,1,4,2,3]=>2
[6,5,1,4,3,2]=>1
[6,5,2,1,3,4]=>6
[6,5,2,1,4,3]=>3
[6,5,2,3,1,4]=>9
[6,5,2,3,4,1]=>2
[6,5,2,4,1,3]=>7
[6,5,2,4,3,1]=>2
[6,5,3,1,2,4]=>16
[6,5,3,1,4,2]=>12
[6,5,3,2,1,4]=>4
[6,5,3,2,4,1]=>6
[6,5,3,4,1,2]=>12
[6,5,3,4,2,1]=>2
[6,5,4,1,2,3]=>2
[6,5,4,1,3,2]=>2
[6,5,4,2,1,3]=>7
[6,5,4,2,3,1]=>2
[6,5,4,3,1,2]=>2
[6,5,4,3,2,1]=>1
[1,2,3,4,5,6,7]=>1
[1,2,3,4,5,7,6]=>2
[1,2,3,4,6,5,7]=>2
[1,2,3,4,6,7,5]=>15
[1,2,3,4,7,5,6]=>2
[1,2,3,4,7,6,5]=>2
[1,2,3,5,4,6,7]=>2
[1,2,3,5,4,7,6]=>13
[1,2,3,5,6,4,7]=>7
[1,2,3,5,6,7,4]=>19
[1,2,3,5,7,4,6]=>13
[1,2,3,5,7,6,4]=>20
[1,2,3,6,4,5,7]=>2
[1,2,3,6,4,7,5]=>15
[1,2,3,6,5,4,7]=>2
[1,2,3,6,5,7,4]=>19
[1,2,3,6,7,4,5]=>15
[1,2,3,6,7,5,4]=>8
[1,2,3,7,4,5,6]=>2
[1,2,3,7,4,6,5]=>2
[1,2,3,7,5,4,6]=>13
[1,2,3,7,5,6,4]=>20
[1,2,3,7,6,4,5]=>2
[1,2,3,7,6,5,4]=>2
[1,2,4,3,5,6,7]=>2
[1,2,4,3,5,7,6]=>4
[1,2,4,3,6,5,7]=>12
[1,2,4,3,6,7,5]=>8
[1,2,4,3,7,5,6]=>4
[1,2,4,3,7,6,5]=>16
[1,2,4,5,3,6,7]=>6
[1,2,4,5,3,7,6]=>9
[1,2,4,5,6,3,7]=>4
[1,2,4,5,6,7,3]=>8
[1,2,4,5,7,3,6]=>6
[1,2,4,5,7,6,3]=>6
[1,2,4,6,3,5,7]=>12
[1,2,4,6,3,7,5]=>32
[1,2,4,6,5,3,7]=>16
[1,2,4,6,5,7,3]=>4
[1,2,4,6,7,3,5]=>32
[1,2,4,6,7,5,3]=>27
[1,2,4,7,3,5,6]=>14
[1,2,4,7,3,6,5]=>10
[1,2,4,7,5,3,6]=>6
[1,2,4,7,5,6,3]=>4
[1,2,4,7,6,3,5]=>16
[1,2,4,7,6,5,3]=>16
[1,2,5,3,4,6,7]=>2
[1,2,5,3,4,7,6]=>13
[1,2,5,3,6,4,7]=>7
[1,2,5,3,6,7,4]=>19
[1,2,5,3,7,4,6]=>2
[1,2,5,3,7,6,4]=>20
[1,2,5,4,3,6,7]=>2
[1,2,5,4,3,7,6]=>26
[1,2,5,4,6,3,7]=>9
[1,2,5,4,6,7,3]=>14
[1,2,5,4,7,3,6]=>26
[1,2,5,4,7,6,3]=>27
[1,2,5,6,3,4,7]=>3
[1,2,5,6,3,7,4]=>19
[1,2,5,6,4,3,7]=>6
[1,2,5,6,4,7,3]=>15
[1,2,5,6,7,3,4]=>19
[1,2,5,6,7,4,3]=>14
[1,2,5,7,3,4,6]=>5
[1,2,5,7,3,6,4]=>6
[1,2,5,7,4,3,6]=>26
[1,2,5,7,4,6,3]=>27
[1,2,5,7,6,3,4]=>20
[1,2,5,7,6,4,3]=>6
[1,2,6,3,4,5,7]=>1
[1,2,6,3,4,7,5]=>15
[1,2,6,3,5,4,7]=>2
[1,2,6,3,5,7,4]=>19
[1,2,6,3,7,4,5]=>15
[1,2,6,3,7,5,4]=>8
[1,2,6,4,3,5,7]=>12
[1,2,6,4,3,7,5]=>32
[1,2,6,4,5,3,7]=>16
[1,2,6,4,5,7,3]=>15
[1,2,6,4,7,3,5]=>5
[1,2,6,4,7,5,3]=>27
[1,2,6,5,3,4,7]=>2
[1,2,6,5,3,7,4]=>19
[1,2,6,5,4,3,7]=>2
[1,2,6,5,4,7,3]=>9
[1,2,6,5,7,3,4]=>19
[1,2,6,5,7,4,3]=>15
[1,2,6,7,3,4,5]=>15
[1,2,6,7,3,5,4]=>12
[1,2,6,7,4,3,5]=>8
[1,2,6,7,4,5,3]=>27
[1,2,6,7,5,3,4]=>12
[1,2,6,7,5,4,3]=>6
[1,2,7,3,4,5,6]=>2
[1,2,7,3,4,6,5]=>2
[1,2,7,3,5,4,6]=>5
[1,2,7,3,5,6,4]=>10
[1,2,7,3,6,4,5]=>2
[1,2,7,3,6,5,4]=>2
[1,2,7,4,3,5,6]=>14
[1,2,7,4,3,6,5]=>16
[1,2,7,4,5,3,6]=>9
[1,2,7,4,5,6,3]=>5
[1,2,7,4,6,3,5]=>5
[1,2,7,4,6,5,3]=>5
[1,2,7,5,3,4,6]=>13
[1,2,7,5,3,6,4]=>20
[1,2,7,5,4,3,6]=>26
[1,2,7,5,4,6,3]=>6
[1,2,7,5,6,3,4]=>20
[1,2,7,5,6,4,3]=>6
[1,2,7,6,3,4,5]=>1
[1,2,7,6,3,5,4]=>2
[1,2,7,6,4,3,5]=>10
[1,2,7,6,4,5,3]=>10
[1,2,7,6,5,3,4]=>2
[1,2,7,6,5,4,3]=>2
[1,3,2,4,5,6,7]=>2
[1,3,2,4,5,7,6]=>4
[1,3,2,4,6,5,7]=>4
[1,3,2,4,6,7,5]=>30
[1,3,2,4,7,5,6]=>4
[1,3,2,4,7,6,5]=>6
[1,3,2,5,4,6,7]=>7
[1,3,2,5,4,7,6]=>38
[1,3,2,5,6,4,7]=>4
[1,3,2,5,6,7,4]=>10
[1,3,2,5,7,4,6]=>38
[1,3,2,5,7,6,4]=>27
[1,3,2,6,4,5,7]=>4
[1,3,2,6,4,7,5]=>30
[1,3,2,6,5,4,7]=>16
[1,3,2,6,5,7,4]=>34
[1,3,2,6,7,4,5]=>30
[1,3,2,6,7,5,4]=>14
[1,3,2,7,4,5,6]=>8
[1,3,2,7,4,6,5]=>6
[1,3,2,7,5,4,6]=>38
[1,3,2,7,5,6,4]=>27
[1,3,2,7,6,4,5]=>6
[1,3,2,7,6,5,4]=>20
[1,3,4,2,5,6,7]=>3
[1,3,4,2,5,7,6]=>8
[1,3,4,2,6,5,7]=>3
[1,3,4,2,6,7,5]=>29
[1,3,4,2,7,5,6]=>10
[1,3,4,2,7,6,5]=>27
[1,3,4,5,2,6,7]=>4
[1,3,4,5,2,7,6]=>18
[1,3,4,5,6,2,7]=>5
[1,3,4,5,6,7,2]=>6
[1,3,4,5,7,2,6]=>18
[1,3,4,5,7,6,2]=>23
[1,3,4,6,2,5,7]=>3
[1,3,4,6,2,7,5]=>10
[1,3,4,6,5,2,7]=>5
[1,3,4,6,5,7,2]=>17
[1,3,4,6,7,2,5]=>29
[1,3,4,6,7,5,2]=>18
[1,3,4,7,2,5,6]=>10
[1,3,4,7,2,6,5]=>27
[1,3,4,7,5,2,6]=>18
[1,3,4,7,5,6,2]=>23
[1,3,4,7,6,2,5]=>27
[1,3,4,7,6,5,2]=>26
[1,3,5,2,4,6,7]=>7
[1,3,5,2,4,7,6]=>38
[1,3,5,2,6,4,7]=>6
[1,3,5,2,6,7,4]=>7
[1,3,5,2,7,4,6]=>38
[1,3,5,2,7,6,4]=>7
[1,3,5,4,2,6,7]=>7
[1,3,5,4,2,7,6]=>43
[1,3,5,4,6,2,7]=>4
[1,3,5,4,6,7,2]=>11
[1,3,5,4,7,2,6]=>43
[1,3,5,4,7,6,2]=>43
[1,3,5,6,2,4,7]=>9
[1,3,5,6,2,7,4]=>7
[1,3,5,6,4,2,7]=>3
[1,3,5,6,4,7,2]=>17
[1,3,5,6,7,2,4]=>10
[1,3,5,6,7,4,2]=>24
[1,3,5,7,2,4,6]=>38
[1,3,5,7,2,6,4]=>7
[1,3,5,7,4,2,6]=>43
[1,3,5,7,4,6,2]=>43
[1,3,5,7,6,2,4]=>27
[1,3,5,7,6,4,2]=>38
[1,3,6,2,4,5,7]=>3
[1,3,6,2,4,7,5]=>30
[1,3,6,2,5,4,7]=>16
[1,3,6,2,5,7,4]=>34
[1,3,6,2,7,4,5]=>30
[1,3,6,2,7,5,4]=>14
[1,3,6,4,2,5,7]=>4
[1,3,6,4,2,7,5]=>29
[1,3,6,4,5,2,7]=>9
[1,3,6,4,5,7,2]=>17
[1,3,6,4,7,2,5]=>29
[1,3,6,4,7,5,2]=>18
[1,3,6,5,2,4,7]=>16
[1,3,6,5,2,7,4]=>34
[1,3,6,5,4,2,7]=>12
[1,3,6,5,4,7,2]=>4
[1,3,6,5,7,2,4]=>34
[1,3,6,5,7,4,2]=>3
[1,3,6,7,2,4,5]=>30
[1,3,6,7,2,5,4]=>17
[1,3,6,7,4,2,5]=>29
[1,3,6,7,4,5,2]=>14
[1,3,6,7,5,2,4]=>17
[1,3,6,7,5,4,2]=>19
[1,3,7,2,4,5,6]=>8
[1,3,7,2,4,6,5]=>4
[1,3,7,2,5,4,6]=>38
[1,3,7,2,5,6,4]=>4
[1,3,7,2,6,4,5]=>6
[1,3,7,2,6,5,4]=>20
[1,3,7,4,2,5,6]=>8
[1,3,7,4,2,6,5]=>27
[1,3,7,4,5,2,6]=>5
[1,3,7,4,5,6,2]=>23
[1,3,7,4,6,2,5]=>27
[1,3,7,4,6,5,2]=>26
[1,3,7,5,2,4,6]=>38
[1,3,7,5,2,6,4]=>27
[1,3,7,5,4,2,6]=>43
[1,3,7,5,4,6,2]=>43
[1,3,7,5,6,2,4]=>27
[1,3,7,5,6,4,2]=>38
[1,3,7,6,2,4,5]=>7
[1,3,7,6,2,5,4]=>10
[1,3,7,6,4,2,5]=>4
[1,3,7,6,4,5,2]=>26
[1,3,7,6,5,2,4]=>20
[1,3,7,6,5,4,2]=>13
[1,4,2,3,5,6,7]=>1
[1,4,2,3,5,7,6]=>14
[1,4,2,3,6,5,7]=>12
[1,4,2,3,6,7,5]=>32
[1,4,2,3,7,5,6]=>14
[1,4,2,3,7,6,5]=>5
[1,4,2,5,3,6,7]=>6
[1,4,2,5,3,7,6]=>6
[1,4,2,5,6,3,7]=>6
[1,4,2,5,6,7,3]=>5
[1,4,2,5,7,3,6]=>6
[1,4,2,5,7,6,3]=>5
[1,4,2,6,3,5,7]=>2
[1,4,2,6,3,7,5]=>32
[1,4,2,6,5,3,7]=>16
[1,4,2,6,5,7,3]=>11
[1,4,2,6,7,3,5]=>32
[1,4,2,6,7,5,3]=>27
[1,4,2,7,3,5,6]=>14
[1,4,2,7,3,6,5]=>4
[1,4,2,7,5,3,6]=>6
[1,4,2,7,5,6,3]=>11
[1,4,2,7,6,3,5]=>4
[1,4,2,7,6,5,3]=>16
[1,4,3,2,5,6,7]=>2
[1,4,3,2,5,7,6]=>10
[1,4,3,2,6,5,7]=>5
[1,4,3,2,6,7,5]=>11
[1,4,3,2,7,5,6]=>2
[1,4,3,2,7,6,5]=>6
[1,4,3,5,2,6,7]=>3
[1,4,3,5,2,7,6]=>17
[1,4,3,5,6,2,7]=>4
[1,4,3,5,6,7,2]=>5
[1,4,3,5,7,2,6]=>17
[1,4,3,5,7,6,2]=>4
[1,4,3,6,2,5,7]=>9
[1,4,3,6,2,7,5]=>24
[1,4,3,6,5,2,7]=>3
[1,4,3,6,5,7,2]=>12
[1,4,3,6,7,2,5]=>11
[1,4,3,6,7,5,2]=>17
[1,4,3,7,2,5,6]=>10
[1,4,3,7,2,6,5]=>6
[1,4,3,7,5,2,6]=>17
[1,4,3,7,5,6,2]=>5
[1,4,3,7,6,2,5]=>5
[1,4,3,7,6,5,2]=>6
[1,4,5,2,3,6,7]=>6
[1,4,5,2,3,7,6]=>9
[1,4,5,2,6,3,7]=>6
[1,4,5,2,6,7,3]=>8
[1,4,5,2,7,3,6]=>4
[1,4,5,2,7,6,3]=>6
[1,4,5,3,2,6,7]=>4
[1,4,5,3,2,7,6]=>5
[1,4,5,3,6,2,7]=>5
[1,4,5,3,6,7,2]=>6
[1,4,5,3,7,2,6]=>4
[1,4,5,3,7,6,2]=>17
[1,4,5,6,2,3,7]=>6
[1,4,5,6,2,7,3]=>2
[1,4,5,6,3,2,7]=>3
[1,4,5,6,3,7,2]=>4
[1,4,5,6,7,2,3]=>5
[1,4,5,6,7,3,2]=>6
[1,4,5,7,2,3,6]=>6
[1,4,5,7,2,6,3]=>3
[1,4,5,7,3,2,6]=>4
[1,4,5,7,3,6,2]=>17
[1,4,5,7,6,2,3]=>6
[1,4,5,7,6,3,2]=>10
[1,4,6,2,3,5,7]=>12
[1,4,6,2,3,7,5]=>32
[1,4,6,2,5,3,7]=>4
[1,4,6,2,5,7,3]=>15
[1,4,6,2,7,3,5]=>32
[1,4,6,2,7,5,3]=>15
[1,4,6,3,2,5,7]=>5
[1,4,6,3,2,7,5]=>24
[1,4,6,3,5,2,7]=>3
[1,4,6,3,5,7,2]=>12
[1,4,6,3,7,2,5]=>3
[1,4,6,3,7,5,2]=>8
[1,4,6,5,2,3,7]=>16
[1,4,6,5,2,7,3]=>11
[1,4,6,5,3,2,7]=>4
[1,4,6,5,3,7,2]=>9
search for individual values
searching the database for the individual values of this statistic
/
search for generating function
searching the database for statistics with the same generating function
Description
The orbit size of a permutation under Foata's bijection.
References
[1] Foata bijection Mp00067
Code
def foata_bijection(elt):
L = list(elt)
M = []
for e in L:
M.append(e)
k = len(M)
if k <= 1:
continue
a = M[-2]
M_prime = [0]*k
if a > e:
index_list = [-1] + [i for i in range(k - 1) if M[i] > e]
else:
index_list = [-1] + [i for i in range(k - 1) if M[i] < e]
for j in range(1, len(index_list)):
start = index_list[j-1] + 1
end = index_list[j]
M_prime[start] = M[end]
for x in range(start + 1, end + 1):
M_prime[x] = M[x-1]
M_prime[k-1] = e
M = M_prime
return Permutations()(M)
def statistic(pi):
l = 1
pi_new = pi
while True:
pi_new = foata_bijection(pi_new)
if pi_new == pi:
return l
l += 1
Created
Sep 24, 2017 at 11:48 by Martin Rubey
Updated
Sep 24, 2017 at 11:48 by Martin Rubey
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!