Identifier
- St000030: 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]=>2
[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]=>2
[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]=>3
[2,4,3,1]=>3
[3,1,2,4]=>2
[3,1,4,2]=>4
[3,2,1,4]=>2
[3,2,4,1]=>4
[3,4,1,2]=>3
[3,4,2,1]=>3
[4,1,2,3]=>3
[4,1,3,2]=>4
[4,2,1,3]=>3
[4,2,3,1]=>4
[4,3,1,2]=>3
[4,3,2,1]=>3
[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]=>2
[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]=>3
[1,3,5,4,2]=>3
[1,4,2,3,5]=>2
[1,4,2,5,3]=>4
[1,4,3,2,5]=>2
[1,4,3,5,2]=>4
[1,4,5,2,3]=>3
[1,4,5,3,2]=>3
[1,5,2,3,4]=>3
[1,5,2,4,3]=>4
[1,5,3,2,4]=>3
[1,5,3,4,2]=>4
[1,5,4,2,3]=>3
[1,5,4,3,2]=>3
[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]=>3
[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]=>4
[2,3,5,4,1]=>4
[2,4,1,3,5]=>3
[2,4,1,5,3]=>5
[2,4,3,1,5]=>3
[2,4,3,5,1]=>5
[2,4,5,1,3]=>4
[2,4,5,3,1]=>4
[2,5,1,3,4]=>4
[2,5,1,4,3]=>5
[2,5,3,1,4]=>4
[2,5,3,4,1]=>5
[2,5,4,1,3]=>4
[2,5,4,3,1]=>4
[3,1,2,4,5]=>2
[3,1,2,5,4]=>3
[3,1,4,2,5]=>4
[3,1,4,5,2]=>5
[3,1,5,2,4]=>5
[3,1,5,4,2]=>5
[3,2,1,4,5]=>2
[3,2,1,5,4]=>3
[3,2,4,1,5]=>4
[3,2,4,5,1]=>5
[3,2,5,1,4]=>5
[3,2,5,4,1]=>5
[3,4,1,2,5]=>3
[3,4,1,5,2]=>6
[3,4,2,1,5]=>3
[3,4,2,5,1]=>6
[3,4,5,1,2]=>4
[3,4,5,2,1]=>4
[3,5,1,2,4]=>4
[3,5,1,4,2]=>6
[3,5,2,1,4]=>4
[3,5,2,4,1]=>6
[3,5,4,1,2]=>4
[3,5,4,2,1]=>4
[4,1,2,3,5]=>3
[4,1,2,5,3]=>5
[4,1,3,2,5]=>4
[4,1,3,5,2]=>6
[4,1,5,2,3]=>6
[4,1,5,3,2]=>6
[4,2,1,3,5]=>3
[4,2,1,5,3]=>5
[4,2,3,1,5]=>4
[4,2,3,5,1]=>6
[4,2,5,1,3]=>6
[4,2,5,3,1]=>6
[4,3,1,2,5]=>3
[4,3,1,5,2]=>6
[4,3,2,1,5]=>3
[4,3,2,5,1]=>6
[4,3,5,1,2]=>5
[4,3,5,2,1]=>5
[4,5,1,2,3]=>4
[4,5,1,3,2]=>5
[4,5,2,1,3]=>4
[4,5,2,3,1]=>5
[4,5,3,1,2]=>4
[4,5,3,2,1]=>4
[5,1,2,3,4]=>4
[5,1,2,4,3]=>5
[5,1,3,2,4]=>5
[5,1,3,4,2]=>6
[5,1,4,2,3]=>6
[5,1,4,3,2]=>6
[5,2,1,3,4]=>4
[5,2,1,4,3]=>5
[5,2,3,1,4]=>5
[5,2,3,4,1]=>6
[5,2,4,1,3]=>6
[5,2,4,3,1]=>6
[5,3,1,2,4]=>4
[5,3,1,4,2]=>6
[5,3,2,1,4]=>4
[5,3,2,4,1]=>6
[5,3,4,1,2]=>5
[5,3,4,2,1]=>5
[5,4,1,2,3]=>4
[5,4,1,3,2]=>5
[5,4,2,1,3]=>4
[5,4,2,3,1]=>5
[5,4,3,1,2]=>4
[5,4,3,2,1]=>4
[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]=>2
[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]=>3
[1,2,4,6,5,3]=>3
[1,2,5,3,4,6]=>2
[1,2,5,3,6,4]=>4
[1,2,5,4,3,6]=>2
[1,2,5,4,6,3]=>4
[1,2,5,6,3,4]=>3
[1,2,5,6,4,3]=>3
[1,2,6,3,4,5]=>3
[1,2,6,3,5,4]=>4
[1,2,6,4,3,5]=>3
[1,2,6,4,5,3]=>4
[1,2,6,5,3,4]=>3
[1,2,6,5,4,3]=>3
[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]=>3
[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]=>4
[1,3,4,6,5,2]=>4
[1,3,5,2,4,6]=>3
[1,3,5,2,6,4]=>5
[1,3,5,4,2,6]=>3
[1,3,5,4,6,2]=>5
[1,3,5,6,2,4]=>4
[1,3,5,6,4,2]=>4
[1,3,6,2,4,5]=>4
[1,3,6,2,5,4]=>5
[1,3,6,4,2,5]=>4
[1,3,6,4,5,2]=>5
[1,3,6,5,2,4]=>4
[1,3,6,5,4,2]=>4
[1,4,2,3,5,6]=>2
[1,4,2,3,6,5]=>3
[1,4,2,5,3,6]=>4
[1,4,2,5,6,3]=>5
[1,4,2,6,3,5]=>5
[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]=>4
[1,4,3,5,6,2]=>5
[1,4,3,6,2,5]=>5
[1,4,3,6,5,2]=>5
[1,4,5,2,3,6]=>3
[1,4,5,2,6,3]=>6
[1,4,5,3,2,6]=>3
[1,4,5,3,6,2]=>6
[1,4,5,6,2,3]=>4
[1,4,5,6,3,2]=>4
[1,4,6,2,3,5]=>4
[1,4,6,2,5,3]=>6
[1,4,6,3,2,5]=>4
[1,4,6,3,5,2]=>6
[1,4,6,5,2,3]=>4
[1,4,6,5,3,2]=>4
[1,5,2,3,4,6]=>3
[1,5,2,3,6,4]=>5
[1,5,2,4,3,6]=>4
[1,5,2,4,6,3]=>6
[1,5,2,6,3,4]=>6
[1,5,2,6,4,3]=>6
[1,5,3,2,4,6]=>3
[1,5,3,2,6,4]=>5
[1,5,3,4,2,6]=>4
[1,5,3,4,6,2]=>6
[1,5,3,6,2,4]=>6
[1,5,3,6,4,2]=>6
[1,5,4,2,3,6]=>3
[1,5,4,2,6,3]=>6
[1,5,4,3,2,6]=>3
[1,5,4,3,6,2]=>6
[1,5,4,6,2,3]=>5
[1,5,4,6,3,2]=>5
[1,5,6,2,3,4]=>4
[1,5,6,2,4,3]=>5
[1,5,6,3,2,4]=>4
[1,5,6,3,4,2]=>5
[1,5,6,4,2,3]=>4
[1,5,6,4,3,2]=>4
[1,6,2,3,4,5]=>4
[1,6,2,3,5,4]=>5
[1,6,2,4,3,5]=>5
[1,6,2,4,5,3]=>6
[1,6,2,5,3,4]=>6
[1,6,2,5,4,3]=>6
[1,6,3,2,4,5]=>4
[1,6,3,2,5,4]=>5
[1,6,3,4,2,5]=>5
[1,6,3,4,5,2]=>6
[1,6,3,5,2,4]=>6
[1,6,3,5,4,2]=>6
[1,6,4,2,3,5]=>4
[1,6,4,2,5,3]=>6
[1,6,4,3,2,5]=>4
[1,6,4,3,5,2]=>6
[1,6,4,5,2,3]=>5
[1,6,4,5,3,2]=>5
[1,6,5,2,3,4]=>4
[1,6,5,2,4,3]=>5
[1,6,5,3,2,4]=>4
[1,6,5,3,4,2]=>5
[1,6,5,4,2,3]=>4
[1,6,5,4,3,2]=>4
[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]=>3
[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]=>4
[2,1,4,6,5,3]=>4
[2,1,5,3,4,6]=>3
[2,1,5,3,6,4]=>5
[2,1,5,4,3,6]=>3
[2,1,5,4,6,3]=>5
[2,1,5,6,3,4]=>4
[2,1,5,6,4,3]=>4
[2,1,6,3,4,5]=>4
[2,1,6,3,5,4]=>5
[2,1,6,4,3,5]=>4
[2,1,6,4,5,3]=>5
[2,1,6,5,3,4]=>4
[2,1,6,5,4,3]=>4
[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]=>4
[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]=>5
[2,3,4,6,5,1]=>5
[2,3,5,1,4,6]=>4
[2,3,5,1,6,4]=>6
[2,3,5,4,1,6]=>4
[2,3,5,4,6,1]=>6
[2,3,5,6,1,4]=>5
[2,3,5,6,4,1]=>5
[2,3,6,1,4,5]=>5
[2,3,6,1,5,4]=>6
[2,3,6,4,1,5]=>5
[2,3,6,4,5,1]=>6
[2,3,6,5,1,4]=>5
[2,3,6,5,4,1]=>5
[2,4,1,3,5,6]=>3
[2,4,1,3,6,5]=>4
[2,4,1,5,3,6]=>5
[2,4,1,5,6,3]=>6
[2,4,1,6,3,5]=>6
[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]=>5
[2,4,3,5,6,1]=>6
[2,4,3,6,1,5]=>6
[2,4,3,6,5,1]=>6
[2,4,5,1,3,6]=>4
[2,4,5,1,6,3]=>7
[2,4,5,3,1,6]=>4
[2,4,5,3,6,1]=>7
[2,4,5,6,1,3]=>5
[2,4,5,6,3,1]=>5
[2,4,6,1,3,5]=>5
[2,4,6,1,5,3]=>7
[2,4,6,3,1,5]=>5
[2,4,6,3,5,1]=>7
[2,4,6,5,1,3]=>5
[2,4,6,5,3,1]=>5
[2,5,1,3,4,6]=>4
[2,5,1,3,6,4]=>6
[2,5,1,4,3,6]=>5
[2,5,1,4,6,3]=>7
[2,5,1,6,3,4]=>7
[2,5,1,6,4,3]=>7
[2,5,3,1,4,6]=>4
[2,5,3,1,6,4]=>6
[2,5,3,4,1,6]=>5
[2,5,3,4,6,1]=>7
[2,5,3,6,1,4]=>7
[2,5,3,6,4,1]=>7
[2,5,4,1,3,6]=>4
[2,5,4,1,6,3]=>7
[2,5,4,3,1,6]=>4
[2,5,4,3,6,1]=>7
[2,5,4,6,1,3]=>6
[2,5,4,6,3,1]=>6
[2,5,6,1,3,4]=>5
[2,5,6,1,4,3]=>6
[2,5,6,3,1,4]=>5
[2,5,6,3,4,1]=>6
[2,5,6,4,1,3]=>5
[2,5,6,4,3,1]=>5
[2,6,1,3,4,5]=>5
[2,6,1,3,5,4]=>6
[2,6,1,4,3,5]=>6
[2,6,1,4,5,3]=>7
[2,6,1,5,3,4]=>7
[2,6,1,5,4,3]=>7
[2,6,3,1,4,5]=>5
[2,6,3,1,5,4]=>6
[2,6,3,4,1,5]=>6
[2,6,3,4,5,1]=>7
[2,6,3,5,1,4]=>7
[2,6,3,5,4,1]=>7
[2,6,4,1,3,5]=>5
[2,6,4,1,5,3]=>7
[2,6,4,3,1,5]=>5
[2,6,4,3,5,1]=>7
[2,6,4,5,1,3]=>6
[2,6,4,5,3,1]=>6
[2,6,5,1,3,4]=>5
[2,6,5,1,4,3]=>6
[2,6,5,3,1,4]=>5
[2,6,5,3,4,1]=>6
[2,6,5,4,1,3]=>5
[2,6,5,4,3,1]=>5
[3,1,2,4,5,6]=>2
[3,1,2,4,6,5]=>3
[3,1,2,5,4,6]=>3
[3,1,2,5,6,4]=>4
[3,1,2,6,4,5]=>4
[3,1,2,6,5,4]=>4
[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]=>6
[3,1,4,6,5,2]=>6
[3,1,5,2,4,6]=>5
[3,1,5,2,6,4]=>7
[3,1,5,4,2,6]=>5
[3,1,5,4,6,2]=>7
[3,1,5,6,2,4]=>6
[3,1,5,6,4,2]=>6
[3,1,6,2,4,5]=>6
[3,1,6,2,5,4]=>7
[3,1,6,4,2,5]=>6
[3,1,6,4,5,2]=>7
[3,1,6,5,2,4]=>6
[3,1,6,5,4,2]=>6
[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]=>4
[3,2,1,6,5,4]=>4
[3,2,4,1,5,6]=>4
[3,2,4,1,6,5]=>5
[3,2,4,5,1,6]=>5
[3,2,4,5,6,1]=>6
[3,2,4,6,1,5]=>6
[3,2,4,6,5,1]=>6
[3,2,5,1,4,6]=>5
[3,2,5,1,6,4]=>7
[3,2,5,4,1,6]=>5
[3,2,5,4,6,1]=>7
[3,2,5,6,1,4]=>6
[3,2,5,6,4,1]=>6
[3,2,6,1,4,5]=>6
[3,2,6,1,5,4]=>7
[3,2,6,4,1,5]=>6
[3,2,6,4,5,1]=>7
[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]=>4
[3,4,1,5,2,6]=>6
[3,4,1,5,6,2]=>7
[3,4,1,6,2,5]=>7
[3,4,1,6,5,2]=>7
[3,4,2,1,5,6]=>3
[3,4,2,1,6,5]=>4
[3,4,2,5,1,6]=>6
[3,4,2,5,6,1]=>7
[3,4,2,6,1,5]=>7
[3,4,2,6,5,1]=>7
[3,4,5,1,2,6]=>4
[3,4,5,1,6,2]=>8
[3,4,5,2,1,6]=>4
[3,4,5,2,6,1]=>8
[3,4,5,6,1,2]=>5
[3,4,5,6,2,1]=>5
[3,4,6,1,2,5]=>5
[3,4,6,1,5,2]=>8
[3,4,6,2,1,5]=>5
[3,4,6,2,5,1]=>8
[3,4,6,5,1,2]=>5
[3,4,6,5,2,1]=>5
[3,5,1,2,4,6]=>4
[3,5,1,2,6,4]=>6
[3,5,1,4,2,6]=>6
[3,5,1,4,6,2]=>8
[3,5,1,6,2,4]=>8
[3,5,1,6,4,2]=>8
[3,5,2,1,4,6]=>4
[3,5,2,1,6,4]=>6
[3,5,2,4,1,6]=>6
[3,5,2,4,6,1]=>8
[3,5,2,6,1,4]=>8
[3,5,2,6,4,1]=>8
[3,5,4,1,2,6]=>4
[3,5,4,1,6,2]=>8
[3,5,4,2,1,6]=>4
[3,5,4,2,6,1]=>8
[3,5,4,6,1,2]=>6
[3,5,4,6,2,1]=>6
[3,5,6,1,2,4]=>5
[3,5,6,1,4,2]=>7
[3,5,6,2,1,4]=>5
[3,5,6,2,4,1]=>7
[3,5,6,4,1,2]=>5
[3,5,6,4,2,1]=>5
[3,6,1,2,4,5]=>5
[3,6,1,2,5,4]=>6
[3,6,1,4,2,5]=>7
[3,6,1,4,5,2]=>8
[3,6,1,5,2,4]=>8
[3,6,1,5,4,2]=>8
[3,6,2,1,4,5]=>5
[3,6,2,1,5,4]=>6
[3,6,2,4,1,5]=>7
[3,6,2,4,5,1]=>8
[3,6,2,5,1,4]=>8
[3,6,2,5,4,1]=>8
[3,6,4,1,2,5]=>5
[3,6,4,1,5,2]=>8
[3,6,4,2,1,5]=>5
[3,6,4,2,5,1]=>8
[3,6,4,5,1,2]=>6
[3,6,4,5,2,1]=>6
[3,6,5,1,2,4]=>5
[3,6,5,1,4,2]=>7
[3,6,5,2,1,4]=>5
[3,6,5,2,4,1]=>7
[3,6,5,4,1,2]=>5
[3,6,5,4,2,1]=>5
[4,1,2,3,5,6]=>3
[4,1,2,3,6,5]=>4
[4,1,2,5,3,6]=>5
[4,1,2,5,6,3]=>6
[4,1,2,6,3,5]=>6
[4,1,2,6,5,3]=>6
[4,1,3,2,5,6]=>4
[4,1,3,2,6,5]=>5
[4,1,3,5,2,6]=>6
[4,1,3,5,6,2]=>7
[4,1,3,6,2,5]=>7
[4,1,3,6,5,2]=>7
[4,1,5,2,3,6]=>6
[4,1,5,2,6,3]=>9
[4,1,5,3,2,6]=>6
[4,1,5,3,6,2]=>9
[4,1,5,6,2,3]=>7
[4,1,5,6,3,2]=>7
[4,1,6,2,3,5]=>7
[4,1,6,2,5,3]=>9
[4,1,6,3,2,5]=>7
[4,1,6,3,5,2]=>9
[4,1,6,5,2,3]=>7
[4,1,6,5,3,2]=>7
[4,2,1,3,5,6]=>3
[4,2,1,3,6,5]=>4
[4,2,1,5,3,6]=>5
[4,2,1,5,6,3]=>6
[4,2,1,6,3,5]=>6
[4,2,1,6,5,3]=>6
[4,2,3,1,5,6]=>4
[4,2,3,1,6,5]=>5
[4,2,3,5,1,6]=>6
[4,2,3,5,6,1]=>7
[4,2,3,6,1,5]=>7
[4,2,3,6,5,1]=>7
[4,2,5,1,3,6]=>6
[4,2,5,1,6,3]=>9
[4,2,5,3,1,6]=>6
[4,2,5,3,6,1]=>9
[4,2,5,6,1,3]=>7
[4,2,5,6,3,1]=>7
[4,2,6,1,3,5]=>7
[4,2,6,1,5,3]=>9
[4,2,6,3,1,5]=>7
[4,2,6,3,5,1]=>9
[4,2,6,5,1,3]=>7
[4,2,6,5,3,1]=>7
[4,3,1,2,5,6]=>3
[4,3,1,2,6,5]=>4
[4,3,1,5,2,6]=>6
[4,3,1,5,6,2]=>7
[4,3,1,6,2,5]=>7
[4,3,1,6,5,2]=>7
[4,3,2,1,5,6]=>3
[4,3,2,1,6,5]=>4
[4,3,2,5,1,6]=>6
[4,3,2,5,6,1]=>7
[4,3,2,6,1,5]=>7
[4,3,2,6,5,1]=>7
[4,3,5,1,2,6]=>5
[4,3,5,1,6,2]=>9
[4,3,5,2,1,6]=>5
[4,3,5,2,6,1]=>9
[4,3,5,6,1,2]=>6
[4,3,5,6,2,1]=>6
[4,3,6,1,2,5]=>6
[4,3,6,1,5,2]=>9
[4,3,6,2,1,5]=>6
[4,3,6,2,5,1]=>9
[4,3,6,5,1,2]=>6
[4,3,6,5,2,1]=>6
[4,5,1,2,3,6]=>4
[4,5,1,2,6,3]=>7
[4,5,1,3,2,6]=>5
[4,5,1,3,6,2]=>8
[4,5,1,6,2,3]=>8
[4,5,1,6,3,2]=>8
[4,5,2,1,3,6]=>4
[4,5,2,1,6,3]=>7
[4,5,2,3,1,6]=>5
[4,5,2,3,6,1]=>8
[4,5,2,6,1,3]=>8
[4,5,2,6,3,1]=>8
[4,5,3,1,2,6]=>4
[4,5,3,1,6,2]=>8
[4,5,3,2,1,6]=>4
[4,5,3,2,6,1]=>8
[4,5,3,6,1,2]=>7
[4,5,3,6,2,1]=>7
[4,5,6,1,2,3]=>5
[4,5,6,1,3,2]=>6
[4,5,6,2,1,3]=>5
[4,5,6,2,3,1]=>6
[4,5,6,3,1,2]=>5
[4,5,6,3,2,1]=>5
[4,6,1,2,3,5]=>5
[4,6,1,2,5,3]=>7
[4,6,1,3,2,5]=>6
[4,6,1,3,5,2]=>8
[4,6,1,5,2,3]=>8
[4,6,1,5,3,2]=>8
[4,6,2,1,3,5]=>5
[4,6,2,1,5,3]=>7
[4,6,2,3,1,5]=>6
[4,6,2,3,5,1]=>8
[4,6,2,5,1,3]=>8
[4,6,2,5,3,1]=>8
[4,6,3,1,2,5]=>5
[4,6,3,1,5,2]=>8
[4,6,3,2,1,5]=>5
[4,6,3,2,5,1]=>8
[4,6,3,5,1,2]=>7
[4,6,3,5,2,1]=>7
[4,6,5,1,2,3]=>5
[4,6,5,1,3,2]=>6
[4,6,5,2,1,3]=>5
[4,6,5,2,3,1]=>6
[4,6,5,3,1,2]=>5
[4,6,5,3,2,1]=>5
[5,1,2,3,4,6]=>4
[5,1,2,3,6,4]=>6
[5,1,2,4,3,6]=>5
[5,1,2,4,6,3]=>7
[5,1,2,6,3,4]=>7
[5,1,2,6,4,3]=>7
[5,1,3,2,4,6]=>5
[5,1,3,2,6,4]=>7
[5,1,3,4,2,6]=>6
[5,1,3,4,6,2]=>8
[5,1,3,6,2,4]=>8
[5,1,3,6,4,2]=>8
[5,1,4,2,3,6]=>6
[5,1,4,2,6,3]=>9
[5,1,4,3,2,6]=>6
[5,1,4,3,6,2]=>9
[5,1,4,6,2,3]=>8
[5,1,4,6,3,2]=>8
[5,1,6,2,3,4]=>8
[5,1,6,2,4,3]=>9
[5,1,6,3,2,4]=>8
[5,1,6,3,4,2]=>9
[5,1,6,4,2,3]=>8
[5,1,6,4,3,2]=>8
[5,2,1,3,4,6]=>4
[5,2,1,3,6,4]=>6
[5,2,1,4,3,6]=>5
[5,2,1,4,6,3]=>7
[5,2,1,6,3,4]=>7
[5,2,1,6,4,3]=>7
[5,2,3,1,4,6]=>5
[5,2,3,1,6,4]=>7
[5,2,3,4,1,6]=>6
[5,2,3,4,6,1]=>8
[5,2,3,6,1,4]=>8
[5,2,3,6,4,1]=>8
[5,2,4,1,3,6]=>6
[5,2,4,1,6,3]=>9
[5,2,4,3,1,6]=>6
[5,2,4,3,6,1]=>9
[5,2,4,6,1,3]=>8
[5,2,4,6,3,1]=>8
[5,2,6,1,3,4]=>8
[5,2,6,1,4,3]=>9
[5,2,6,3,1,4]=>8
[5,2,6,3,4,1]=>9
[5,2,6,4,1,3]=>8
[5,2,6,4,3,1]=>8
[5,3,1,2,4,6]=>4
[5,3,1,2,6,4]=>6
[5,3,1,4,2,6]=>6
[5,3,1,4,6,2]=>8
[5,3,1,6,2,4]=>8
[5,3,1,6,4,2]=>8
[5,3,2,1,4,6]=>4
[5,3,2,1,6,4]=>6
[5,3,2,4,1,6]=>6
[5,3,2,4,6,1]=>8
[5,3,2,6,1,4]=>8
[5,3,2,6,4,1]=>8
[5,3,4,1,2,6]=>5
[5,3,4,1,6,2]=>9
[5,3,4,2,1,6]=>5
[5,3,4,2,6,1]=>9
[5,3,4,6,1,2]=>7
[5,3,4,6,2,1]=>7
[5,3,6,1,2,4]=>7
[5,3,6,1,4,2]=>9
[5,3,6,2,1,4]=>7
[5,3,6,2,4,1]=>9
[5,3,6,4,1,2]=>7
[5,3,6,4,2,1]=>7
[5,4,1,2,3,6]=>4
[5,4,1,2,6,3]=>7
[5,4,1,3,2,6]=>5
[5,4,1,3,6,2]=>8
[5,4,1,6,2,3]=>8
[5,4,1,6,3,2]=>8
[5,4,2,1,3,6]=>4
[5,4,2,1,6,3]=>7
[5,4,2,3,1,6]=>5
[5,4,2,3,6,1]=>8
[5,4,2,6,1,3]=>8
[5,4,2,6,3,1]=>8
[5,4,3,1,2,6]=>4
[5,4,3,1,6,2]=>8
[5,4,3,2,1,6]=>4
[5,4,3,2,6,1]=>8
[5,4,3,6,1,2]=>7
[5,4,3,6,2,1]=>7
[5,4,6,1,2,3]=>6
[5,4,6,1,3,2]=>7
[5,4,6,2,1,3]=>6
[5,4,6,2,3,1]=>7
[5,4,6,3,1,2]=>6
[5,4,6,3,2,1]=>6
[5,6,1,2,3,4]=>5
[5,6,1,2,4,3]=>6
[5,6,1,3,2,4]=>6
[5,6,1,3,4,2]=>7
[5,6,1,4,2,3]=>7
[5,6,1,4,3,2]=>7
[5,6,2,1,3,4]=>5
[5,6,2,1,4,3]=>6
[5,6,2,3,1,4]=>6
[5,6,2,3,4,1]=>7
[5,6,2,4,1,3]=>7
[5,6,2,4,3,1]=>7
[5,6,3,1,2,4]=>5
[5,6,3,1,4,2]=>7
[5,6,3,2,1,4]=>5
[5,6,3,2,4,1]=>7
[5,6,3,4,1,2]=>6
[5,6,3,4,2,1]=>6
[5,6,4,1,2,3]=>5
[5,6,4,1,3,2]=>6
[5,6,4,2,1,3]=>5
[5,6,4,2,3,1]=>6
[5,6,4,3,1,2]=>5
[5,6,4,3,2,1]=>5
[6,1,2,3,4,5]=>5
[6,1,2,3,5,4]=>6
[6,1,2,4,3,5]=>6
[6,1,2,4,5,3]=>7
[6,1,2,5,3,4]=>7
[6,1,2,5,4,3]=>7
[6,1,3,2,4,5]=>6
[6,1,3,2,5,4]=>7
[6,1,3,4,2,5]=>7
[6,1,3,4,5,2]=>8
[6,1,3,5,2,4]=>8
[6,1,3,5,4,2]=>8
[6,1,4,2,3,5]=>7
[6,1,4,2,5,3]=>9
[6,1,4,3,2,5]=>7
[6,1,4,3,5,2]=>9
[6,1,4,5,2,3]=>8
[6,1,4,5,3,2]=>8
[6,1,5,2,3,4]=>8
[6,1,5,2,4,3]=>9
[6,1,5,3,2,4]=>8
[6,1,5,3,4,2]=>9
[6,1,5,4,2,3]=>8
[6,1,5,4,3,2]=>8
[6,2,1,3,4,5]=>5
[6,2,1,3,5,4]=>6
[6,2,1,4,3,5]=>6
[6,2,1,4,5,3]=>7
[6,2,1,5,3,4]=>7
[6,2,1,5,4,3]=>7
[6,2,3,1,4,5]=>6
[6,2,3,1,5,4]=>7
[6,2,3,4,1,5]=>7
[6,2,3,4,5,1]=>8
[6,2,3,5,1,4]=>8
[6,2,3,5,4,1]=>8
[6,2,4,1,3,5]=>7
[6,2,4,1,5,3]=>9
[6,2,4,3,1,5]=>7
[6,2,4,3,5,1]=>9
[6,2,4,5,1,3]=>8
[6,2,4,5,3,1]=>8
[6,2,5,1,3,4]=>8
[6,2,5,1,4,3]=>9
[6,2,5,3,1,4]=>8
[6,2,5,3,4,1]=>9
[6,2,5,4,1,3]=>8
[6,2,5,4,3,1]=>8
[6,3,1,2,4,5]=>5
[6,3,1,2,5,4]=>6
[6,3,1,4,2,5]=>7
[6,3,1,4,5,2]=>8
[6,3,1,5,2,4]=>8
[6,3,1,5,4,2]=>8
[6,3,2,1,4,5]=>5
[6,3,2,1,5,4]=>6
[6,3,2,4,1,5]=>7
[6,3,2,4,5,1]=>8
[6,3,2,5,1,4]=>8
[6,3,2,5,4,1]=>8
[6,3,4,1,2,5]=>6
[6,3,4,1,5,2]=>9
[6,3,4,2,1,5]=>6
[6,3,4,2,5,1]=>9
[6,3,4,5,1,2]=>7
[6,3,4,5,2,1]=>7
[6,3,5,1,2,4]=>7
[6,3,5,1,4,2]=>9
[6,3,5,2,1,4]=>7
[6,3,5,2,4,1]=>9
[6,3,5,4,1,2]=>7
[6,3,5,4,2,1]=>7
[6,4,1,2,3,5]=>5
[6,4,1,2,5,3]=>7
[6,4,1,3,2,5]=>6
[6,4,1,3,5,2]=>8
[6,4,1,5,2,3]=>8
[6,4,1,5,3,2]=>8
[6,4,2,1,3,5]=>5
[6,4,2,1,5,3]=>7
[6,4,2,3,1,5]=>6
[6,4,2,3,5,1]=>8
[6,4,2,5,1,3]=>8
[6,4,2,5,3,1]=>8
[6,4,3,1,2,5]=>5
[6,4,3,1,5,2]=>8
[6,4,3,2,1,5]=>5
[6,4,3,2,5,1]=>8
[6,4,3,5,1,2]=>7
[6,4,3,5,2,1]=>7
[6,4,5,1,2,3]=>6
[6,4,5,1,3,2]=>7
[6,4,5,2,1,3]=>6
[6,4,5,2,3,1]=>7
[6,4,5,3,1,2]=>6
[6,4,5,3,2,1]=>6
[6,5,1,2,3,4]=>5
[6,5,1,2,4,3]=>6
[6,5,1,3,2,4]=>6
[6,5,1,3,4,2]=>7
[6,5,1,4,2,3]=>7
[6,5,1,4,3,2]=>7
[6,5,2,1,3,4]=>5
[6,5,2,1,4,3]=>6
[6,5,2,3,1,4]=>6
[6,5,2,3,4,1]=>7
[6,5,2,4,1,3]=>7
[6,5,2,4,3,1]=>7
[6,5,3,1,2,4]=>5
[6,5,3,1,4,2]=>7
[6,5,3,2,1,4]=>5
[6,5,3,2,4,1]=>7
[6,5,3,4,1,2]=>6
[6,5,3,4,2,1]=>6
[6,5,4,1,2,3]=>5
[6,5,4,1,3,2]=>6
[6,5,4,2,1,3]=>5
[6,5,4,2,3,1]=>6
[6,5,4,3,1,2]=>5
[6,5,4,3,2,1]=>5
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Description
The sum of the descent differences of a permutations.
This statistic is given by
$$\pi \mapsto \sum_{i\in\operatorname{Des}(\pi)} (\pi_i-\pi_{i+1}).$$
See St000111The sum of the descent tops (or Genocchi descents) of a permutation. and St000154The sum of the descent bottoms of a permutation. for the sum of the descent tops and the descent bottoms, respectively. This statistic was studied in [1] and [2] where is was called the drop of a permutation.
This statistic is given by
$$\pi \mapsto \sum_{i\in\operatorname{Des}(\pi)} (\pi_i-\pi_{i+1}).$$
See St000111The sum of the descent tops (or Genocchi descents) of a permutation. and St000154The sum of the descent bottoms of a permutation. for the sum of the descent tops and the descent bottoms, respectively. This statistic was studied in [1] and [2] where is was called the drop of a permutation.
References
[1] Babson, E., Steingr'ımsson, E. Generalized permutation patterns and a classification of the Mahonian statistics MathSciNet:1758852
[2] Petersen, T. K., Tenner, B. E. The depth of a permutation arXiv:1202.4765
[3] Triangle read by rows: For n >= 1, k >= 0, T(n,k) = the number of permutations pi of n such that the total distance sum_i abs(i-pi(i)) = 2k. Equivalently, k = sum_i max(i-pi(i),0). OEIS:A062869
[2] Petersen, T. K., Tenner, B. E. The depth of a permutation arXiv:1202.4765
[3] Triangle read by rows: For n >= 1, k >= 0, T(n,k) = the number of permutations pi of n such that the total distance sum_i abs(i-pi(i)) = 2k. Equivalently, k = sum_i max(i-pi(i),0). OEIS:A062869
Code
def statistic(x):
return sum(x[i]-x[i+1] for i in range(x.size()-1) if x[i]>x[i+1])
Created
Nov 30, 2012 at 21:30 by Chris Berg
Updated
May 29, 2015 at 16:16 by Martin Rubey
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