Identifier
- St000224: Permutations ⟶ ℤ
Values
=>
[1]=>0
[1,2]=>0
[2,1]=>1
[1,2,3]=>0
[1,3,2]=>1
[2,1,3]=>1
[2,3,1]=>2
[3,1,2]=>3
[3,2,1]=>2
[1,2,3,4]=>0
[1,2,4,3]=>1
[1,3,2,4]=>1
[1,3,4,2]=>2
[1,4,2,3]=>3
[1,4,3,2]=>2
[2,1,3,4]=>1
[2,1,4,3]=>2
[2,3,1,4]=>2
[2,3,4,1]=>3
[2,4,1,3]=>4
[2,4,3,1]=>3
[3,1,2,4]=>3
[3,1,4,2]=>4
[3,2,1,4]=>2
[3,2,4,1]=>3
[3,4,1,2]=>4
[3,4,2,1]=>5
[4,1,2,3]=>6
[4,1,3,2]=>4
[4,2,1,3]=>5
[4,2,3,1]=>3
[4,3,1,2]=>5
[4,3,2,1]=>4
[1,2,3,4,5]=>0
[1,2,3,5,4]=>1
[1,2,4,3,5]=>1
[1,2,4,5,3]=>2
[1,2,5,3,4]=>3
[1,2,5,4,3]=>2
[1,3,2,4,5]=>1
[1,3,2,5,4]=>2
[1,3,4,2,5]=>2
[1,3,4,5,2]=>3
[1,3,5,2,4]=>4
[1,3,5,4,2]=>3
[1,4,2,3,5]=>3
[1,4,2,5,3]=>4
[1,4,3,2,5]=>2
[1,4,3,5,2]=>3
[1,4,5,2,3]=>4
[1,4,5,3,2]=>5
[1,5,2,3,4]=>6
[1,5,2,4,3]=>4
[1,5,3,2,4]=>5
[1,5,3,4,2]=>3
[1,5,4,2,3]=>5
[1,5,4,3,2]=>4
[2,1,3,4,5]=>1
[2,1,3,5,4]=>2
[2,1,4,3,5]=>2
[2,1,4,5,3]=>3
[2,1,5,3,4]=>4
[2,1,5,4,3]=>3
[2,3,1,4,5]=>2
[2,3,1,5,4]=>3
[2,3,4,1,5]=>3
[2,3,4,5,1]=>4
[2,3,5,1,4]=>5
[2,3,5,4,1]=>4
[2,4,1,3,5]=>4
[2,4,1,5,3]=>5
[2,4,3,1,5]=>3
[2,4,3,5,1]=>4
[2,4,5,1,3]=>5
[2,4,5,3,1]=>6
[2,5,1,3,4]=>7
[2,5,1,4,3]=>5
[2,5,3,1,4]=>6
[2,5,3,4,1]=>4
[2,5,4,1,3]=>6
[2,5,4,3,1]=>5
[3,1,2,4,5]=>3
[3,1,2,5,4]=>4
[3,1,4,2,5]=>4
[3,1,4,5,2]=>5
[3,1,5,2,4]=>6
[3,1,5,4,2]=>5
[3,2,1,4,5]=>2
[3,2,1,5,4]=>3
[3,2,4,1,5]=>3
[3,2,4,5,1]=>4
[3,2,5,1,4]=>5
[3,2,5,4,1]=>4
[3,4,1,2,5]=>4
[3,4,1,5,2]=>5
[3,4,2,1,5]=>5
[3,4,2,5,1]=>6
[3,4,5,1,2]=>7
[3,4,5,2,1]=>6
[3,5,1,2,4]=>7
[3,5,1,4,2]=>5
[3,5,2,1,4]=>8
[3,5,2,4,1]=>6
[3,5,4,1,2]=>6
[3,5,4,2,1]=>7
[4,1,2,3,5]=>6
[4,1,2,5,3]=>7
[4,1,3,2,5]=>4
[4,1,3,5,2]=>5
[4,1,5,2,3]=>6
[4,1,5,3,2]=>8
[4,2,1,3,5]=>5
[4,2,1,5,3]=>6
[4,2,3,1,5]=>3
[4,2,3,5,1]=>4
[4,2,5,1,3]=>5
[4,2,5,3,1]=>7
[4,3,1,2,5]=>5
[4,3,1,5,2]=>6
[4,3,2,1,5]=>4
[4,3,2,5,1]=>5
[4,3,5,1,2]=>6
[4,3,5,2,1]=>7
[4,5,1,2,3]=>8
[4,5,1,3,2]=>8
[4,5,2,1,3]=>7
[4,5,2,3,1]=>9
[4,5,3,1,2]=>6
[4,5,3,2,1]=>7
[5,1,2,3,4]=>10
[5,1,2,4,3]=>7
[5,1,3,2,4]=>8
[5,1,3,4,2]=>5
[5,1,4,2,3]=>8
[5,1,4,3,2]=>6
[5,2,1,3,4]=>9
[5,2,1,4,3]=>6
[5,2,3,1,4]=>7
[5,2,3,4,1]=>4
[5,2,4,1,3]=>7
[5,2,4,3,1]=>5
[5,3,1,2,4]=>9
[5,3,1,4,2]=>6
[5,3,2,1,4]=>8
[5,3,2,4,1]=>5
[5,3,4,1,2]=>7
[5,3,4,2,1]=>6
[5,4,1,2,3]=>8
[5,4,1,3,2]=>8
[5,4,2,1,3]=>9
[5,4,2,3,1]=>7
[5,4,3,1,2]=>7
[5,4,3,2,1]=>6
[1,2,3,4,5,6]=>0
[1,2,3,4,6,5]=>1
[1,2,3,5,4,6]=>1
[1,2,3,5,6,4]=>2
[1,2,3,6,4,5]=>3
[1,2,3,6,5,4]=>2
[1,2,4,3,5,6]=>1
[1,2,4,3,6,5]=>2
[1,2,4,5,3,6]=>2
[1,2,4,5,6,3]=>3
[1,2,4,6,3,5]=>4
[1,2,4,6,5,3]=>3
[1,2,5,3,4,6]=>3
[1,2,5,3,6,4]=>4
[1,2,5,4,3,6]=>2
[1,2,5,4,6,3]=>3
[1,2,5,6,3,4]=>4
[1,2,5,6,4,3]=>5
[1,2,6,3,4,5]=>6
[1,2,6,3,5,4]=>4
[1,2,6,4,3,5]=>5
[1,2,6,4,5,3]=>3
[1,2,6,5,3,4]=>5
[1,2,6,5,4,3]=>4
[1,3,2,4,5,6]=>1
[1,3,2,4,6,5]=>2
[1,3,2,5,4,6]=>2
[1,3,2,5,6,4]=>3
[1,3,2,6,4,5]=>4
[1,3,2,6,5,4]=>3
[1,3,4,2,5,6]=>2
[1,3,4,2,6,5]=>3
[1,3,4,5,2,6]=>3
[1,3,4,5,6,2]=>4
[1,3,4,6,2,5]=>5
[1,3,4,6,5,2]=>4
[1,3,5,2,4,6]=>4
[1,3,5,2,6,4]=>5
[1,3,5,4,2,6]=>3
[1,3,5,4,6,2]=>4
[1,3,5,6,2,4]=>5
[1,3,5,6,4,2]=>6
[1,3,6,2,4,5]=>7
[1,3,6,2,5,4]=>5
[1,3,6,4,2,5]=>6
[1,3,6,4,5,2]=>4
[1,3,6,5,2,4]=>6
[1,3,6,5,4,2]=>5
[1,4,2,3,5,6]=>3
[1,4,2,3,6,5]=>4
[1,4,2,5,3,6]=>4
[1,4,2,5,6,3]=>5
[1,4,2,6,3,5]=>6
[1,4,2,6,5,3]=>5
[1,4,3,2,5,6]=>2
[1,4,3,2,6,5]=>3
[1,4,3,5,2,6]=>3
[1,4,3,5,6,2]=>4
[1,4,3,6,2,5]=>5
[1,4,3,6,5,2]=>4
[1,4,5,2,3,6]=>4
[1,4,5,2,6,3]=>5
[1,4,5,3,2,6]=>5
[1,4,5,3,6,2]=>6
[1,4,5,6,2,3]=>7
[1,4,5,6,3,2]=>6
[1,4,6,2,3,5]=>7
[1,4,6,2,5,3]=>5
[1,4,6,3,2,5]=>8
[1,4,6,3,5,2]=>6
[1,4,6,5,2,3]=>6
[1,4,6,5,3,2]=>7
[1,5,2,3,4,6]=>6
[1,5,2,3,6,4]=>7
[1,5,2,4,3,6]=>4
[1,5,2,4,6,3]=>5
[1,5,2,6,3,4]=>6
[1,5,2,6,4,3]=>8
[1,5,3,2,4,6]=>5
[1,5,3,2,6,4]=>6
[1,5,3,4,2,6]=>3
[1,5,3,4,6,2]=>4
[1,5,3,6,2,4]=>5
[1,5,3,6,4,2]=>7
[1,5,4,2,3,6]=>5
[1,5,4,2,6,3]=>6
[1,5,4,3,2,6]=>4
[1,5,4,3,6,2]=>5
[1,5,4,6,2,3]=>6
[1,5,4,6,3,2]=>7
[1,5,6,2,3,4]=>8
[1,5,6,2,4,3]=>8
[1,5,6,3,2,4]=>7
[1,5,6,3,4,2]=>9
[1,5,6,4,2,3]=>6
[1,5,6,4,3,2]=>7
[1,6,2,3,4,5]=>10
[1,6,2,3,5,4]=>7
[1,6,2,4,3,5]=>8
[1,6,2,4,5,3]=>5
[1,6,2,5,3,4]=>8
[1,6,2,5,4,3]=>6
[1,6,3,2,4,5]=>9
[1,6,3,2,5,4]=>6
[1,6,3,4,2,5]=>7
[1,6,3,4,5,2]=>4
[1,6,3,5,2,4]=>7
[1,6,3,5,4,2]=>5
[1,6,4,2,3,5]=>9
[1,6,4,2,5,3]=>6
[1,6,4,3,2,5]=>8
[1,6,4,3,5,2]=>5
[1,6,4,5,2,3]=>7
[1,6,4,5,3,2]=>6
[1,6,5,2,3,4]=>8
[1,6,5,2,4,3]=>8
[1,6,5,3,2,4]=>9
[1,6,5,3,4,2]=>7
[1,6,5,4,2,3]=>7
[1,6,5,4,3,2]=>6
[2,1,3,4,5,6]=>1
[2,1,3,4,6,5]=>2
[2,1,3,5,4,6]=>2
[2,1,3,5,6,4]=>3
[2,1,3,6,4,5]=>4
[2,1,3,6,5,4]=>3
[2,1,4,3,5,6]=>2
[2,1,4,3,6,5]=>3
[2,1,4,5,3,6]=>3
[2,1,4,5,6,3]=>4
[2,1,4,6,3,5]=>5
[2,1,4,6,5,3]=>4
[2,1,5,3,4,6]=>4
[2,1,5,3,6,4]=>5
[2,1,5,4,3,6]=>3
[2,1,5,4,6,3]=>4
[2,1,5,6,3,4]=>5
[2,1,5,6,4,3]=>6
[2,1,6,3,4,5]=>7
[2,1,6,3,5,4]=>5
[2,1,6,4,3,5]=>6
[2,1,6,4,5,3]=>4
[2,1,6,5,3,4]=>6
[2,1,6,5,4,3]=>5
[2,3,1,4,5,6]=>2
[2,3,1,4,6,5]=>3
[2,3,1,5,4,6]=>3
[2,3,1,5,6,4]=>4
[2,3,1,6,4,5]=>5
[2,3,1,6,5,4]=>4
[2,3,4,1,5,6]=>3
[2,3,4,1,6,5]=>4
[2,3,4,5,1,6]=>4
[2,3,4,5,6,1]=>5
[2,3,4,6,1,5]=>6
[2,3,4,6,5,1]=>5
[2,3,5,1,4,6]=>5
[2,3,5,1,6,4]=>6
[2,3,5,4,1,6]=>4
[2,3,5,4,6,1]=>5
[2,3,5,6,1,4]=>6
[2,3,5,6,4,1]=>7
[2,3,6,1,4,5]=>8
[2,3,6,1,5,4]=>6
[2,3,6,4,1,5]=>7
[2,3,6,4,5,1]=>5
[2,3,6,5,1,4]=>7
[2,3,6,5,4,1]=>6
[2,4,1,3,5,6]=>4
[2,4,1,3,6,5]=>5
[2,4,1,5,3,6]=>5
[2,4,1,5,6,3]=>6
[2,4,1,6,3,5]=>7
[2,4,1,6,5,3]=>6
[2,4,3,1,5,6]=>3
[2,4,3,1,6,5]=>4
[2,4,3,5,1,6]=>4
[2,4,3,5,6,1]=>5
[2,4,3,6,1,5]=>6
[2,4,3,6,5,1]=>5
[2,4,5,1,3,6]=>5
[2,4,5,1,6,3]=>6
[2,4,5,3,1,6]=>6
[2,4,5,3,6,1]=>7
[2,4,5,6,1,3]=>8
[2,4,5,6,3,1]=>7
[2,4,6,1,3,5]=>8
[2,4,6,1,5,3]=>6
[2,4,6,3,1,5]=>9
[2,4,6,3,5,1]=>7
[2,4,6,5,1,3]=>7
[2,4,6,5,3,1]=>8
[2,5,1,3,4,6]=>7
[2,5,1,3,6,4]=>8
[2,5,1,4,3,6]=>5
[2,5,1,4,6,3]=>6
[2,5,1,6,3,4]=>7
[2,5,1,6,4,3]=>9
[2,5,3,1,4,6]=>6
[2,5,3,1,6,4]=>7
[2,5,3,4,1,6]=>4
[2,5,3,4,6,1]=>5
[2,5,3,6,1,4]=>6
[2,5,3,6,4,1]=>8
[2,5,4,1,3,6]=>6
[2,5,4,1,6,3]=>7
[2,5,4,3,1,6]=>5
[2,5,4,3,6,1]=>6
[2,5,4,6,1,3]=>7
[2,5,4,6,3,1]=>8
[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]=>10
[2,5,6,4,1,3]=>7
[2,5,6,4,3,1]=>8
[2,6,1,3,4,5]=>11
[2,6,1,3,5,4]=>8
[2,6,1,4,3,5]=>9
[2,6,1,4,5,3]=>6
[2,6,1,5,3,4]=>9
[2,6,1,5,4,3]=>7
[2,6,3,1,4,5]=>10
[2,6,3,1,5,4]=>7
[2,6,3,4,1,5]=>8
[2,6,3,4,5,1]=>5
[2,6,3,5,1,4]=>8
[2,6,3,5,4,1]=>6
[2,6,4,1,3,5]=>10
[2,6,4,1,5,3]=>7
[2,6,4,3,1,5]=>9
[2,6,4,3,5,1]=>6
[2,6,4,5,1,3]=>8
[2,6,4,5,3,1]=>7
[2,6,5,1,3,4]=>9
[2,6,5,1,4,3]=>9
[2,6,5,3,1,4]=>10
[2,6,5,3,4,1]=>8
[2,6,5,4,1,3]=>8
[2,6,5,4,3,1]=>7
[3,1,2,4,5,6]=>3
[3,1,2,4,6,5]=>4
[3,1,2,5,4,6]=>4
[3,1,2,5,6,4]=>5
[3,1,2,6,4,5]=>6
[3,1,2,6,5,4]=>5
[3,1,4,2,5,6]=>4
[3,1,4,2,6,5]=>5
[3,1,4,5,2,6]=>5
[3,1,4,5,6,2]=>6
[3,1,4,6,2,5]=>7
[3,1,4,6,5,2]=>6
[3,1,5,2,4,6]=>6
[3,1,5,2,6,4]=>7
[3,1,5,4,2,6]=>5
[3,1,5,4,6,2]=>6
[3,1,5,6,2,4]=>7
[3,1,5,6,4,2]=>8
[3,1,6,2,4,5]=>9
[3,1,6,2,5,4]=>7
[3,1,6,4,2,5]=>8
[3,1,6,4,5,2]=>6
[3,1,6,5,2,4]=>8
[3,1,6,5,4,2]=>7
[3,2,1,4,5,6]=>2
[3,2,1,4,6,5]=>3
[3,2,1,5,4,6]=>3
[3,2,1,5,6,4]=>4
[3,2,1,6,4,5]=>5
[3,2,1,6,5,4]=>4
[3,2,4,1,5,6]=>3
[3,2,4,1,6,5]=>4
[3,2,4,5,1,6]=>4
[3,2,4,5,6,1]=>5
[3,2,4,6,1,5]=>6
[3,2,4,6,5,1]=>5
[3,2,5,1,4,6]=>5
[3,2,5,1,6,4]=>6
[3,2,5,4,1,6]=>4
[3,2,5,4,6,1]=>5
[3,2,5,6,1,4]=>6
[3,2,5,6,4,1]=>7
[3,2,6,1,4,5]=>8
[3,2,6,1,5,4]=>6
[3,2,6,4,1,5]=>7
[3,2,6,4,5,1]=>5
[3,2,6,5,1,4]=>7
[3,2,6,5,4,1]=>6
[3,4,1,2,5,6]=>4
[3,4,1,2,6,5]=>5
[3,4,1,5,2,6]=>5
[3,4,1,5,6,2]=>6
[3,4,1,6,2,5]=>7
[3,4,1,6,5,2]=>6
[3,4,2,1,5,6]=>5
[3,4,2,1,6,5]=>6
[3,4,2,5,1,6]=>6
[3,4,2,5,6,1]=>7
[3,4,2,6,1,5]=>8
[3,4,2,6,5,1]=>7
[3,4,5,1,2,6]=>7
[3,4,5,1,6,2]=>8
[3,4,5,2,1,6]=>6
[3,4,5,2,6,1]=>7
[3,4,5,6,1,2]=>8
[3,4,5,6,2,1]=>9
[3,4,6,1,2,5]=>10
[3,4,6,1,5,2]=>8
[3,4,6,2,1,5]=>9
[3,4,6,2,5,1]=>7
[3,4,6,5,1,2]=>9
[3,4,6,5,2,1]=>8
[3,5,1,2,4,6]=>7
[3,5,1,2,6,4]=>8
[3,5,1,4,2,6]=>5
[3,5,1,4,6,2]=>6
[3,5,1,6,2,4]=>7
[3,5,1,6,4,2]=>9
[3,5,2,1,4,6]=>8
[3,5,2,1,6,4]=>9
[3,5,2,4,1,6]=>6
[3,5,2,4,6,1]=>7
[3,5,2,6,1,4]=>8
[3,5,2,6,4,1]=>10
[3,5,4,1,2,6]=>6
[3,5,4,1,6,2]=>7
[3,5,4,2,1,6]=>7
[3,5,4,2,6,1]=>8
[3,5,4,6,1,2]=>9
[3,5,4,6,2,1]=>8
[3,5,6,1,2,4]=>9
[3,5,6,1,4,2]=>11
[3,5,6,2,1,4]=>10
[3,5,6,2,4,1]=>10
[3,5,6,4,1,2]=>9
[3,5,6,4,2,1]=>8
[3,6,1,2,4,5]=>11
[3,6,1,2,5,4]=>8
[3,6,1,4,2,5]=>9
[3,6,1,4,5,2]=>6
[3,6,1,5,2,4]=>9
[3,6,1,5,4,2]=>7
[3,6,2,1,4,5]=>12
[3,6,2,1,5,4]=>9
[3,6,2,4,1,5]=>10
[3,6,2,4,5,1]=>7
[3,6,2,5,1,4]=>10
[3,6,2,5,4,1]=>8
[3,6,4,1,2,5]=>10
[3,6,4,1,5,2]=>7
[3,6,4,2,1,5]=>11
[3,6,4,2,5,1]=>8
[3,6,4,5,1,2]=>8
[3,6,4,5,2,1]=>9
[3,6,5,1,2,4]=>11
[3,6,5,1,4,2]=>9
[3,6,5,2,1,4]=>10
[3,6,5,2,4,1]=>10
[3,6,5,4,1,2]=>8
[3,6,5,4,2,1]=>9
[4,1,2,3,5,6]=>6
[4,1,2,3,6,5]=>7
[4,1,2,5,3,6]=>7
[4,1,2,5,6,3]=>8
[4,1,2,6,3,5]=>9
[4,1,2,6,5,3]=>8
[4,1,3,2,5,6]=>4
[4,1,3,2,6,5]=>5
[4,1,3,5,2,6]=>5
[4,1,3,5,6,2]=>6
[4,1,3,6,2,5]=>7
[4,1,3,6,5,2]=>6
[4,1,5,2,3,6]=>6
[4,1,5,2,6,3]=>7
[4,1,5,3,2,6]=>8
[4,1,5,3,6,2]=>9
[4,1,5,6,2,3]=>10
[4,1,5,6,3,2]=>8
[4,1,6,2,3,5]=>9
[4,1,6,2,5,3]=>7
[4,1,6,3,2,5]=>11
[4,1,6,3,5,2]=>9
[4,1,6,5,2,3]=>8
[4,1,6,5,3,2]=>10
[4,2,1,3,5,6]=>5
[4,2,1,3,6,5]=>6
[4,2,1,5,3,6]=>6
[4,2,1,5,6,3]=>7
[4,2,1,6,3,5]=>8
[4,2,1,6,5,3]=>7
[4,2,3,1,5,6]=>3
[4,2,3,1,6,5]=>4
[4,2,3,5,1,6]=>4
[4,2,3,5,6,1]=>5
[4,2,3,6,1,5]=>6
[4,2,3,6,5,1]=>5
[4,2,5,1,3,6]=>5
[4,2,5,1,6,3]=>6
[4,2,5,3,1,6]=>7
[4,2,5,3,6,1]=>8
[4,2,5,6,1,3]=>9
[4,2,5,6,3,1]=>7
[4,2,6,1,3,5]=>8
[4,2,6,1,5,3]=>6
[4,2,6,3,1,5]=>10
[4,2,6,3,5,1]=>8
[4,2,6,5,1,3]=>7
[4,2,6,5,3,1]=>9
[4,3,1,2,5,6]=>5
[4,3,1,2,6,5]=>6
[4,3,1,5,2,6]=>6
[4,3,1,5,6,2]=>7
[4,3,1,6,2,5]=>8
[4,3,1,6,5,2]=>7
[4,3,2,1,5,6]=>4
[4,3,2,1,6,5]=>5
[4,3,2,5,1,6]=>5
[4,3,2,5,6,1]=>6
[4,3,2,6,1,5]=>7
[4,3,2,6,5,1]=>6
[4,3,5,1,2,6]=>6
[4,3,5,1,6,2]=>7
[4,3,5,2,1,6]=>7
[4,3,5,2,6,1]=>8
[4,3,5,6,1,2]=>9
[4,3,5,6,2,1]=>8
[4,3,6,1,2,5]=>9
[4,3,6,1,5,2]=>7
[4,3,6,2,1,5]=>10
[4,3,6,2,5,1]=>8
[4,3,6,5,1,2]=>8
[4,3,6,5,2,1]=>9
[4,5,1,2,3,6]=>8
[4,5,1,2,6,3]=>9
[4,5,1,3,2,6]=>8
[4,5,1,3,6,2]=>9
[4,5,1,6,2,3]=>10
[4,5,1,6,3,2]=>10
[4,5,2,1,3,6]=>7
[4,5,2,1,6,3]=>8
[4,5,2,3,1,6]=>9
[4,5,2,3,6,1]=>10
[4,5,2,6,1,3]=>11
[4,5,2,6,3,1]=>9
[4,5,3,1,2,6]=>6
[4,5,3,1,6,2]=>7
[4,5,3,2,1,6]=>7
[4,5,3,2,6,1]=>8
[4,5,3,6,1,2]=>9
[4,5,3,6,2,1]=>8
[4,5,6,1,2,3]=>9
[4,5,6,1,3,2]=>10
[4,5,6,2,1,3]=>10
[4,5,6,2,3,1]=>11
[4,5,6,3,1,2]=>12
[4,5,6,3,2,1]=>11
[4,6,1,2,3,5]=>12
[4,6,1,2,5,3]=>9
[4,6,1,3,2,5]=>12
[4,6,1,3,5,2]=>9
[4,6,1,5,2,3]=>10
[4,6,1,5,3,2]=>10
[4,6,2,1,3,5]=>11
[4,6,2,1,5,3]=>8
[4,6,2,3,1,5]=>13
[4,6,2,3,5,1]=>10
[4,6,2,5,1,3]=>9
[4,6,2,5,3,1]=>11
[4,6,3,1,2,5]=>10
[4,6,3,1,5,2]=>7
[4,6,3,2,1,5]=>11
[4,6,3,2,5,1]=>8
[4,6,3,5,1,2]=>8
[4,6,3,5,2,1]=>9
[4,6,5,1,2,3]=>10
[4,6,5,1,3,2]=>9
[4,6,5,2,1,3]=>11
[4,6,5,2,3,1]=>10
[4,6,5,3,1,2]=>11
[4,6,5,3,2,1]=>12
[5,1,2,3,4,6]=>10
[5,1,2,3,6,4]=>11
[5,1,2,4,3,6]=>7
[5,1,2,4,6,3]=>8
[5,1,2,6,3,4]=>9
[5,1,2,6,4,3]=>12
[5,1,3,2,4,6]=>8
[5,1,3,2,6,4]=>9
[5,1,3,4,2,6]=>5
[5,1,3,4,6,2]=>6
[5,1,3,6,2,4]=>7
[5,1,3,6,4,2]=>10
[5,1,4,2,3,6]=>8
[5,1,4,2,6,3]=>9
[5,1,4,3,2,6]=>6
[5,1,4,3,6,2]=>7
[5,1,4,6,2,3]=>8
[5,1,4,6,3,2]=>10
[5,1,6,2,3,4]=>11
[5,1,6,2,4,3]=>11
[5,1,6,3,2,4]=>9
[5,1,6,3,4,2]=>13
[5,1,6,4,2,3]=>8
[5,1,6,4,3,2]=>10
[5,2,1,3,4,6]=>9
[5,2,1,3,6,4]=>10
[5,2,1,4,3,6]=>6
[5,2,1,4,6,3]=>7
[5,2,1,6,3,4]=>8
[5,2,1,6,4,3]=>11
[5,2,3,1,4,6]=>7
[5,2,3,1,6,4]=>8
[5,2,3,4,1,6]=>4
[5,2,3,4,6,1]=>5
[5,2,3,6,1,4]=>6
[5,2,3,6,4,1]=>9
[5,2,4,1,3,6]=>7
[5,2,4,1,6,3]=>8
[5,2,4,3,1,6]=>5
[5,2,4,3,6,1]=>6
[5,2,4,6,1,3]=>7
[5,2,4,6,3,1]=>9
[5,2,6,1,3,4]=>10
[5,2,6,1,4,3]=>10
[5,2,6,3,1,4]=>8
[5,2,6,3,4,1]=>12
[5,2,6,4,1,3]=>7
[5,2,6,4,3,1]=>9
[5,3,1,2,4,6]=>9
[5,3,1,2,6,4]=>10
[5,3,1,4,2,6]=>6
[5,3,1,4,6,2]=>7
[5,3,1,6,2,4]=>8
[5,3,1,6,4,2]=>11
[5,3,2,1,4,6]=>8
[5,3,2,1,6,4]=>9
[5,3,2,4,1,6]=>5
[5,3,2,4,6,1]=>6
[5,3,2,6,1,4]=>7
[5,3,2,6,4,1]=>10
[5,3,4,1,2,6]=>7
[5,3,4,1,6,2]=>8
[5,3,4,2,1,6]=>6
[5,3,4,2,6,1]=>7
[5,3,4,6,1,2]=>8
[5,3,4,6,2,1]=>9
[5,3,6,1,2,4]=>10
[5,3,6,1,4,2]=>11
[5,3,6,2,1,4]=>9
[5,3,6,2,4,1]=>12
[5,3,6,4,1,2]=>8
[5,3,6,4,2,1]=>9
[5,4,1,2,3,6]=>8
[5,4,1,2,6,3]=>9
[5,4,1,3,2,6]=>8
[5,4,1,3,6,2]=>9
[5,4,1,6,2,3]=>10
[5,4,1,6,3,2]=>10
[5,4,2,1,3,6]=>9
[5,4,2,1,6,3]=>10
[5,4,2,3,1,6]=>7
[5,4,2,3,6,1]=>8
[5,4,2,6,1,3]=>9
[5,4,2,6,3,1]=>11
[5,4,3,1,2,6]=>7
[5,4,3,1,6,2]=>8
[5,4,3,2,1,6]=>6
[5,4,3,2,6,1]=>7
[5,4,3,6,1,2]=>8
[5,4,3,6,2,1]=>9
[5,4,6,1,2,3]=>10
[5,4,6,1,3,2]=>12
[5,4,6,2,1,3]=>9
[5,4,6,2,3,1]=>11
[5,4,6,3,1,2]=>10
[5,4,6,3,2,1]=>11
[5,6,1,2,3,4]=>12
[5,6,1,2,4,3]=>13
[5,6,1,3,2,4]=>12
[5,6,1,3,4,2]=>13
[5,6,1,4,2,3]=>10
[5,6,1,4,3,2]=>10
[5,6,2,1,3,4]=>13
[5,6,2,1,4,3]=>12
[5,6,2,3,1,4]=>11
[5,6,2,3,4,1]=>14
[5,6,2,4,1,3]=>9
[5,6,2,4,3,1]=>11
[5,6,3,1,2,4]=>11
[5,6,3,1,4,2]=>11
[5,6,3,2,1,4]=>10
[5,6,3,2,4,1]=>12
[5,6,3,4,1,2]=>8
[5,6,3,4,2,1]=>9
[5,6,4,1,2,3]=>11
[5,6,4,1,3,2]=>11
[5,6,4,2,1,3]=>10
[5,6,4,2,3,1]=>12
[5,6,4,3,1,2]=>9
[5,6,4,3,2,1]=>10
[6,1,2,3,4,5]=>15
[6,1,2,3,5,4]=>11
[6,1,2,4,3,5]=>12
[6,1,2,4,5,3]=>8
[6,1,2,5,3,4]=>12
[6,1,2,5,4,3]=>9
[6,1,3,2,4,5]=>13
[6,1,3,2,5,4]=>9
[6,1,3,4,2,5]=>10
[6,1,3,4,5,2]=>6
[6,1,3,5,2,4]=>10
[6,1,3,5,4,2]=>7
[6,1,4,2,3,5]=>13
[6,1,4,2,5,3]=>9
[6,1,4,3,2,5]=>11
[6,1,4,3,5,2]=>7
[6,1,4,5,2,3]=>10
[6,1,4,5,3,2]=>8
[6,1,5,2,3,4]=>11
[6,1,5,2,4,3]=>11
[6,1,5,3,2,4]=>13
[6,1,5,3,4,2]=>9
[6,1,5,4,2,3]=>10
[6,1,5,4,3,2]=>8
[6,2,1,3,4,5]=>14
[6,2,1,3,5,4]=>10
[6,2,1,4,3,5]=>11
[6,2,1,4,5,3]=>7
[6,2,1,5,3,4]=>11
[6,2,1,5,4,3]=>8
[6,2,3,1,4,5]=>12
[6,2,3,1,5,4]=>8
[6,2,3,4,1,5]=>9
[6,2,3,4,5,1]=>5
[6,2,3,5,1,4]=>9
[6,2,3,5,4,1]=>6
[6,2,4,1,3,5]=>12
[6,2,4,1,5,3]=>8
[6,2,4,3,1,5]=>10
[6,2,4,3,5,1]=>6
[6,2,4,5,1,3]=>9
[6,2,4,5,3,1]=>7
[6,2,5,1,3,4]=>10
[6,2,5,1,4,3]=>10
[6,2,5,3,1,4]=>12
[6,2,5,3,4,1]=>8
[6,2,5,4,1,3]=>9
[6,2,5,4,3,1]=>7
[6,3,1,2,4,5]=>14
[6,3,1,2,5,4]=>10
[6,3,1,4,2,5]=>11
[6,3,1,4,5,2]=>7
[6,3,1,5,2,4]=>11
[6,3,1,5,4,2]=>8
[6,3,2,1,4,5]=>13
[6,3,2,1,5,4]=>9
[6,3,2,4,1,5]=>10
[6,3,2,4,5,1]=>6
[6,3,2,5,1,4]=>10
[6,3,2,5,4,1]=>7
[6,3,4,1,2,5]=>12
[6,3,4,1,5,2]=>8
[6,3,4,2,1,5]=>11
[6,3,4,2,5,1]=>7
[6,3,4,5,1,2]=>9
[6,3,4,5,2,1]=>8
[6,3,5,1,2,4]=>11
[6,3,5,1,4,2]=>10
[6,3,5,2,1,4]=>12
[6,3,5,2,4,1]=>9
[6,3,5,4,1,2]=>9
[6,3,5,4,2,1]=>8
[6,4,1,2,3,5]=>13
[6,4,1,2,5,3]=>9
[6,4,1,3,2,5]=>13
[6,4,1,3,5,2]=>9
[6,4,1,5,2,3]=>10
[6,4,1,5,3,2]=>10
[6,4,2,1,3,5]=>14
[6,4,2,1,5,3]=>10
[6,4,2,3,1,5]=>12
[6,4,2,3,5,1]=>8
[6,4,2,5,1,3]=>11
[6,4,2,5,3,1]=>9
[6,4,3,1,2,5]=>12
[6,4,3,1,5,2]=>8
[6,4,3,2,1,5]=>11
[6,4,3,2,5,1]=>7
[6,4,3,5,1,2]=>9
[6,4,3,5,2,1]=>8
[6,4,5,1,2,3]=>12
[6,4,5,1,3,2]=>10
[6,4,5,2,1,3]=>11
[6,4,5,2,3,1]=>9
[6,4,5,3,1,2]=>11
[6,4,5,3,2,1]=>10
[6,5,1,2,3,4]=>13
[6,5,1,2,4,3]=>12
[6,5,1,3,2,4]=>13
[6,5,1,3,4,2]=>12
[6,5,1,4,2,3]=>10
[6,5,1,4,3,2]=>10
[6,5,2,1,3,4]=>12
[6,5,2,1,4,3]=>13
[6,5,2,3,1,4]=>14
[6,5,2,3,4,1]=>11
[6,5,2,4,1,3]=>11
[6,5,2,4,3,1]=>9
[6,5,3,1,2,4]=>11
[6,5,3,1,4,2]=>11
[6,5,3,2,1,4]=>12
[6,5,3,2,4,1]=>10
[6,5,3,4,1,2]=>9
[6,5,3,4,2,1]=>8
[6,5,4,1,2,3]=>11
[6,5,4,1,3,2]=>11
[6,5,4,2,1,3]=>12
[6,5,4,2,3,1]=>10
[6,5,4,3,1,2]=>10
[6,5,4,3,2,1]=>9
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Description
The sorting index of a permutation.
The sorting index counts the total distance that symbols move during a selection sort of a permutation. This sorting algorithm swaps symbol n into index n and then recursively sorts the first n-1 symbols.
Compare this to St000018The number of inversions of a permutation., the number of inversions of a permutation, which is also the total distance that elements move during a bubble sort.
The sorting index counts the total distance that symbols move during a selection sort of a permutation. This sorting algorithm swaps symbol n into index n and then recursively sorts the first n-1 symbols.
Compare this to St000018The number of inversions of a permutation., the number of inversions of a permutation, which is also the total distance that elements move during a bubble sort.
References
[1] Triangle of Mahonian numbers T(n,k): coefficients in expansion of Product_i=0..n-1 (1 + x + ... + x^i), where k ranges from 0 to A000217(n-1). OEIS:A008302
[2] Wilson, M. C. An interesting new Mahonian permutation statistic MathSciNet:2745700
[3] Petersen, T. K. The sorting index MathSciNet:2822205
[2] Wilson, M. C. An interesting new Mahonian permutation statistic MathSciNet:2745700
[3] Petersen, T. K. The sorting index MathSciNet:2822205
Code
def statistic(pi):
n = len(pi)
if n == 0:
return 0
else:
x = pi.index(n) + 1
if x == n:
return statistic(pi[:n-1])
else:
return (n-x) + statistic(Permutation([(n, x)])*pi)
Created
Sep 30, 2014 at 09:17 by Martin Rubey
Updated
Jun 24, 2020 at 21:07 by Mark Wilson
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