Identifier
Identifier
St000018:
Permutations ⟶ ℤ
Values
[]
=>
0
[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]
=>
3
[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]
=>
3
[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]
=>
4
[3,1,2,4]
=>
2
[3,1,4,2]
=>
3
[3,2,1,4]
=>
3
[3,2,4,1]
=>
4
[3,4,1,2]
=>
4
[3,4,2,1]
=>
5
[4,1,2,3]
=>
3
[4,1,3,2]
=>
4
[4,2,1,3]
=>
4
[4,2,3,1]
=>
5
[4,3,1,2]
=>
5
[4,3,2,1]
=>
6
[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]
=>
3
[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]
=>
4
[1,4,2,3,5]
=>
2
[1,4,2,5,3]
=>
3
[1,4,3,2,5]
=>
3
[1,4,3,5,2]
=>
4
[1,4,5,2,3]
=>
4
[1,4,5,3,2]
=>
5
[1,5,2,3,4]
=>
3
[1,5,2,4,3]
=>
4
[1,5,3,2,4]
=>
4
[1,5,3,4,2]
=>
5
[1,5,4,2,3]
=>
5
[1,5,4,3,2]
=>
6
[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]
=>
4
[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]
=>
5
[2,4,1,3,5]
=>
3
[2,4,1,5,3]
=>
4
[2,4,3,1,5]
=>
4
[2,4,3,5,1]
=>
5
[2,4,5,1,3]
=>
5
[2,4,5,3,1]
=>
6
[2,5,1,3,4]
=>
4
[2,5,1,4,3]
=>
5
[2,5,3,1,4]
=>
5
[2,5,3,4,1]
=>
6
[2,5,4,1,3]
=>
6
[2,5,4,3,1]
=>
7
[3,1,2,4,5]
=>
2
[3,1,2,5,4]
=>
3
[3,1,4,2,5]
=>
3
[3,1,4,5,2]
=>
4
[3,1,5,2,4]
=>
4
[3,1,5,4,2]
=>
5
[3,2,1,4,5]
=>
3
[3,2,1,5,4]
=>
4
[3,2,4,1,5]
=>
4
[3,2,4,5,1]
=>
5
[3,2,5,1,4]
=>
5
[3,2,5,4,1]
=>
6
[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]
=>
6
[3,4,5,2,1]
=>
7
[3,5,1,2,4]
=>
5
[3,5,1,4,2]
=>
6
[3,5,2,1,4]
=>
6
[3,5,2,4,1]
=>
7
[3,5,4,1,2]
=>
7
[3,5,4,2,1]
=>
8
[4,1,2,3,5]
=>
3
[4,1,2,5,3]
=>
4
[4,1,3,2,5]
=>
4
[4,1,3,5,2]
=>
5
[4,1,5,2,3]
=>
5
[4,1,5,3,2]
=>
6
[4,2,1,3,5]
=>
4
[4,2,1,5,3]
=>
5
[4,2,3,1,5]
=>
5
[4,2,3,5,1]
=>
6
[4,2,5,1,3]
=>
6
[4,2,5,3,1]
=>
7
[4,3,1,2,5]
=>
5
[4,3,1,5,2]
=>
6
[4,3,2,1,5]
=>
6
[4,3,2,5,1]
=>
7
[4,3,5,1,2]
=>
7
[4,3,5,2,1]
=>
8
[4,5,1,2,3]
=>
6
[4,5,1,3,2]
=>
7
[4,5,2,1,3]
=>
7
[4,5,2,3,1]
=>
8
[4,5,3,1,2]
=>
8
[4,5,3,2,1]
=>
9
[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]
=>
7
[5,2,1,3,4]
=>
5
[5,2,1,4,3]
=>
6
[5,2,3,1,4]
=>
6
[5,2,3,4,1]
=>
7
[5,2,4,1,3]
=>
7
[5,2,4,3,1]
=>
8
[5,3,1,2,4]
=>
6
[5,3,1,4,2]
=>
7
[5,3,2,1,4]
=>
7
[5,3,2,4,1]
=>
8
[5,3,4,1,2]
=>
8
[5,3,4,2,1]
=>
9
[5,4,1,2,3]
=>
7
[5,4,1,3,2]
=>
8
[5,4,2,1,3]
=>
8
[5,4,2,3,1]
=>
9
[5,4,3,1,2]
=>
9
[5,4,3,2,1]
=>
10
[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]
=>
3
[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]
=>
4
[1,2,5,3,4,6]
=>
2
[1,2,5,3,6,4]
=>
3
[1,2,5,4,3,6]
=>
3
[1,2,5,4,6,3]
=>
4
[1,2,5,6,3,4]
=>
4
[1,2,5,6,4,3]
=>
5
[1,2,6,3,4,5]
=>
3
[1,2,6,3,5,4]
=>
4
[1,2,6,4,3,5]
=>
4
[1,2,6,4,5,3]
=>
5
[1,2,6,5,3,4]
=>
5
[1,2,6,5,4,3]
=>
6
[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]
=>
4
[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]
=>
5
[1,3,5,2,4,6]
=>
3
[1,3,5,2,6,4]
=>
4
[1,3,5,4,2,6]
=>
4
[1,3,5,4,6,2]
=>
5
[1,3,5,6,2,4]
=>
5
[1,3,5,6,4,2]
=>
6
[1,3,6,2,4,5]
=>
4
[1,3,6,2,5,4]
=>
5
[1,3,6,4,2,5]
=>
5
[1,3,6,4,5,2]
=>
6
[1,3,6,5,2,4]
=>
6
[1,3,6,5,4,2]
=>
7
[1,4,2,3,5,6]
=>
2
[1,4,2,3,6,5]
=>
3
[1,4,2,5,3,6]
=>
3
[1,4,2,5,6,3]
=>
4
[1,4,2,6,3,5]
=>
4
[1,4,2,6,5,3]
=>
5
[1,4,3,2,5,6]
=>
3
[1,4,3,2,6,5]
=>
4
[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]
=>
6
[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]
=>
6
[1,4,5,6,3,2]
=>
7
[1,4,6,2,3,5]
=>
5
[1,4,6,2,5,3]
=>
6
[1,4,6,3,2,5]
=>
6
[1,4,6,3,5,2]
=>
7
[1,4,6,5,2,3]
=>
7
[1,4,6,5,3,2]
=>
8
[1,5,2,3,4,6]
=>
3
[1,5,2,3,6,4]
=>
4
[1,5,2,4,3,6]
=>
4
[1,5,2,4,6,3]
=>
5
[1,5,2,6,3,4]
=>
5
[1,5,2,6,4,3]
=>
6
[1,5,3,2,4,6]
=>
4
[1,5,3,2,6,4]
=>
5
[1,5,3,4,2,6]
=>
5
[1,5,3,4,6,2]
=>
6
[1,5,3,6,2,4]
=>
6
[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]
=>
6
[1,5,4,3,6,2]
=>
7
[1,5,4,6,2,3]
=>
7
[1,5,4,6,3,2]
=>
8
[1,5,6,2,3,4]
=>
6
[1,5,6,2,4,3]
=>
7
[1,5,6,3,2,4]
=>
7
[1,5,6,3,4,2]
=>
8
[1,5,6,4,2,3]
=>
8
[1,5,6,4,3,2]
=>
9
[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]
=>
7
[1,6,3,2,4,5]
=>
5
[1,6,3,2,5,4]
=>
6
[1,6,3,4,2,5]
=>
6
[1,6,3,4,5,2]
=>
7
[1,6,3,5,2,4]
=>
7
[1,6,3,5,4,2]
=>
8
[1,6,4,2,3,5]
=>
6
[1,6,4,2,5,3]
=>
7
[1,6,4,3,2,5]
=>
7
[1,6,4,3,5,2]
=>
8
[1,6,4,5,2,3]
=>
8
[1,6,4,5,3,2]
=>
9
[1,6,5,2,3,4]
=>
7
[1,6,5,2,4,3]
=>
8
[1,6,5,3,2,4]
=>
8
[1,6,5,3,4,2]
=>
9
[1,6,5,4,2,3]
=>
9
[1,6,5,4,3,2]
=>
10
[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]
=>
4
[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]
=>
5
[2,1,5,3,4,6]
=>
3
[2,1,5,3,6,4]
=>
4
[2,1,5,4,3,6]
=>
4
[2,1,5,4,6,3]
=>
5
[2,1,5,6,3,4]
=>
5
[2,1,5,6,4,3]
=>
6
[2,1,6,3,4,5]
=>
4
[2,1,6,3,5,4]
=>
5
[2,1,6,4,3,5]
=>
5
[2,1,6,4,5,3]
=>
6
[2,1,6,5,3,4]
=>
6
[2,1,6,5,4,3]
=>
7
[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]
=>
5
[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]
=>
6
[2,3,5,1,4,6]
=>
4
[2,3,5,1,6,4]
=>
5
[2,3,5,4,1,6]
=>
5
[2,3,5,4,6,1]
=>
6
[2,3,5,6,1,4]
=>
6
[2,3,5,6,4,1]
=>
7
[2,3,6,1,4,5]
=>
5
[2,3,6,1,5,4]
=>
6
[2,3,6,4,1,5]
=>
6
[2,3,6,4,5,1]
=>
7
[2,3,6,5,1,4]
=>
7
[2,3,6,5,4,1]
=>
8
[2,4,1,3,5,6]
=>
3
[2,4,1,3,6,5]
=>
4
[2,4,1,5,3,6]
=>
4
[2,4,1,5,6,3]
=>
5
[2,4,1,6,3,5]
=>
5
[2,4,1,6,5,3]
=>
6
[2,4,3,1,5,6]
=>
4
[2,4,3,1,6,5]
=>
5
[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]
=>
7
[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]
=>
7
[2,4,5,6,3,1]
=>
8
[2,4,6,1,3,5]
=>
6
[2,4,6,1,5,3]
=>
7
[2,4,6,3,1,5]
=>
7
[2,4,6,3,5,1]
=>
8
[2,4,6,5,1,3]
=>
8
[2,4,6,5,3,1]
=>
9
[2,5,1,3,4,6]
=>
4
[2,5,1,3,6,4]
=>
5
[2,5,1,4,3,6]
=>
5
[2,5,1,4,6,3]
=>
6
[2,5,1,6,3,4]
=>
6
[2,5,1,6,4,3]
=>
7
[2,5,3,1,4,6]
=>
5
[2,5,3,1,6,4]
=>
6
[2,5,3,4,1,6]
=>
6
[2,5,3,4,6,1]
=>
7
[2,5,3,6,1,4]
=>
7
[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]
=>
7
[2,5,4,3,6,1]
=>
8
[2,5,4,6,1,3]
=>
8
[2,5,4,6,3,1]
=>
9
[2,5,6,1,3,4]
=>
7
[2,5,6,1,4,3]
=>
8
[2,5,6,3,1,4]
=>
8
[2,5,6,3,4,1]
=>
9
[2,5,6,4,1,3]
=>
9
[2,5,6,4,3,1]
=>
10
[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]
=>
8
[2,6,3,1,4,5]
=>
6
[2,6,3,1,5,4]
=>
7
[2,6,3,4,1,5]
=>
7
[2,6,3,4,5,1]
=>
8
[2,6,3,5,1,4]
=>
8
[2,6,3,5,4,1]
=>
9
[2,6,4,1,3,5]
=>
7
[2,6,4,1,5,3]
=>
8
[2,6,4,3,1,5]
=>
8
[2,6,4,3,5,1]
=>
9
[2,6,4,5,1,3]
=>
9
[2,6,4,5,3,1]
=>
10
[2,6,5,1,3,4]
=>
8
[2,6,5,1,4,3]
=>
9
[2,6,5,3,1,4]
=>
9
[2,6,5,3,4,1]
=>
10
[2,6,5,4,1,3]
=>
10
[2,6,5,4,3,1]
=>
11
[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]
=>
5
[3,1,4,2,5,6]
=>
3
[3,1,4,2,6,5]
=>
4
[3,1,4,5,2,6]
=>
4
[3,1,4,5,6,2]
=>
5
[3,1,4,6,2,5]
=>
5
[3,1,4,6,5,2]
=>
6
[3,1,5,2,4,6]
=>
4
[3,1,5,2,6,4]
=>
5
[3,1,5,4,2,6]
=>
5
[3,1,5,4,6,2]
=>
6
[3,1,5,6,2,4]
=>
6
[3,1,5,6,4,2]
=>
7
[3,1,6,2,4,5]
=>
5
[3,1,6,2,5,4]
=>
6
[3,1,6,4,2,5]
=>
6
[3,1,6,4,5,2]
=>
7
[3,1,6,5,2,4]
=>
7
[3,1,6,5,4,2]
=>
8
[3,2,1,4,5,6]
=>
3
[3,2,1,4,6,5]
=>
4
[3,2,1,5,4,6]
=>
4
[3,2,1,5,6,4]
=>
5
[3,2,1,6,4,5]
=>
5
[3,2,1,6,5,4]
=>
6
[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]
=>
7
[3,2,5,1,4,6]
=>
5
[3,2,5,1,6,4]
=>
6
[3,2,5,4,1,6]
=>
6
[3,2,5,4,6,1]
=>
7
[3,2,5,6,1,4]
=>
7
[3,2,5,6,4,1]
=>
8
[3,2,6,1,4,5]
=>
6
[3,2,6,1,5,4]
=>
7
[3,2,6,4,1,5]
=>
7
[3,2,6,4,5,1]
=>
8
[3,2,6,5,1,4]
=>
8
[3,2,6,5,4,1]
=>
9
[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]
=>
6
[3,4,1,6,5,2]
=>
7
[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]
=>
7
[3,4,2,6,5,1]
=>
8
[3,4,5,1,2,6]
=>
6
[3,4,5,1,6,2]
=>
7
[3,4,5,2,1,6]
=>
7
[3,4,5,2,6,1]
=>
8
[3,4,5,6,1,2]
=>
8
[3,4,5,6,2,1]
=>
9
[3,4,6,1,2,5]
=>
7
[3,4,6,1,5,2]
=>
8
[3,4,6,2,1,5]
=>
8
[3,4,6,2,5,1]
=>
9
[3,4,6,5,1,2]
=>
9
[3,4,6,5,2,1]
=>
10
[3,5,1,2,4,6]
=>
5
[3,5,1,2,6,4]
=>
6
[3,5,1,4,2,6]
=>
6
[3,5,1,4,6,2]
=>
7
[3,5,1,6,2,4]
=>
7
[3,5,1,6,4,2]
=>
8
[3,5,2,1,4,6]
=>
6
[3,5,2,1,6,4]
=>
7
[3,5,2,4,1,6]
=>
7
[3,5,2,4,6,1]
=>
8
[3,5,2,6,1,4]
=>
8
[3,5,2,6,4,1]
=>
9
[3,5,4,1,2,6]
=>
7
[3,5,4,1,6,2]
=>
8
[3,5,4,2,1,6]
=>
8
[3,5,4,2,6,1]
=>
9
[3,5,4,6,1,2]
=>
9
[3,5,4,6,2,1]
=>
10
[3,5,6,1,2,4]
=>
8
[3,5,6,1,4,2]
=>
9
[3,5,6,2,1,4]
=>
9
[3,5,6,2,4,1]
=>
10
[3,5,6,4,1,2]
=>
10
[3,5,6,4,2,1]
=>
11
[3,6,1,2,4,5]
=>
6
[3,6,1,2,5,4]
=>
7
[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]
=>
9
[3,6,2,1,4,5]
=>
7
[3,6,2,1,5,4]
=>
8
[3,6,2,4,1,5]
=>
8
[3,6,2,4,5,1]
=>
9
[3,6,2,5,1,4]
=>
9
[3,6,2,5,4,1]
=>
10
[3,6,4,1,2,5]
=>
8
[3,6,4,1,5,2]
=>
9
[3,6,4,2,1,5]
=>
9
[3,6,4,2,5,1]
=>
10
[3,6,4,5,1,2]
=>
10
[3,6,4,5,2,1]
=>
11
[3,6,5,1,2,4]
=>
9
[3,6,5,1,4,2]
=>
10
[3,6,5,2,1,4]
=>
10
[3,6,5,2,4,1]
=>
11
[3,6,5,4,1,2]
=>
11
[3,6,5,4,2,1]
=>
12
[4,1,2,3,5,6]
=>
3
[4,1,2,3,6,5]
=>
4
[4,1,2,5,3,6]
=>
4
[4,1,2,5,6,3]
=>
5
[4,1,2,6,3,5]
=>
5
[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]
=>
5
[4,1,3,5,6,2]
=>
6
[4,1,3,6,2,5]
=>
6
[4,1,3,6,5,2]
=>
7
[4,1,5,2,3,6]
=>
5
[4,1,5,2,6,3]
=>
6
[4,1,5,3,2,6]
=>
6
[4,1,5,3,6,2]
=>
7
[4,1,5,6,2,3]
=>
7
[4,1,5,6,3,2]
=>
8
[4,1,6,2,3,5]
=>
6
[4,1,6,2,5,3]
=>
7
[4,1,6,3,2,5]
=>
7
[4,1,6,3,5,2]
=>
8
[4,1,6,5,2,3]
=>
8
[4,1,6,5,3,2]
=>
9
[4,2,1,3,5,6]
=>
4
[4,2,1,3,6,5]
=>
5
[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]
=>
7
[4,2,3,1,5,6]
=>
5
[4,2,3,1,6,5]
=>
6
[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]
=>
8
[4,2,5,1,3,6]
=>
6
[4,2,5,1,6,3]
=>
7
[4,2,5,3,1,6]
=>
7
[4,2,5,3,6,1]
=>
8
[4,2,5,6,1,3]
=>
8
[4,2,5,6,3,1]
=>
9
[4,2,6,1,3,5]
=>
7
[4,2,6,1,5,3]
=>
8
[4,2,6,3,1,5]
=>
8
[4,2,6,3,5,1]
=>
9
[4,2,6,5,1,3]
=>
9
[4,2,6,5,3,1]
=>
10
[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]
=>
7
[4,3,1,6,5,2]
=>
8
[4,3,2,1,5,6]
=>
6
[4,3,2,1,6,5]
=>
7
[4,3,2,5,1,6]
=>
7
[4,3,2,5,6,1]
=>
8
[4,3,2,6,1,5]
=>
8
[4,3,2,6,5,1]
=>
9
[4,3,5,1,2,6]
=>
7
[4,3,5,1,6,2]
=>
8
[4,3,5,2,1,6]
=>
8
[4,3,5,2,6,1]
=>
9
[4,3,5,6,1,2]
=>
9
[4,3,5,6,2,1]
=>
10
[4,3,6,1,2,5]
=>
8
[4,3,6,1,5,2]
=>
9
[4,3,6,2,1,5]
=>
9
[4,3,6,2,5,1]
=>
10
[4,3,6,5,1,2]
=>
10
[4,3,6,5,2,1]
=>
11
[4,5,1,2,3,6]
=>
6
[4,5,1,2,6,3]
=>
7
[4,5,1,3,2,6]
=>
7
[4,5,1,3,6,2]
=>
8
[4,5,1,6,2,3]
=>
8
[4,5,1,6,3,2]
=>
9
[4,5,2,1,3,6]
=>
7
[4,5,2,1,6,3]
=>
8
[4,5,2,3,1,6]
=>
8
[4,5,2,3,6,1]
=>
9
[4,5,2,6,1,3]
=>
9
[4,5,2,6,3,1]
=>
10
[4,5,3,1,2,6]
=>
8
[4,5,3,1,6,2]
=>
9
[4,5,3,2,1,6]
=>
9
[4,5,3,2,6,1]
=>
10
[4,5,3,6,1,2]
=>
10
[4,5,3,6,2,1]
=>
11
[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]
=>
11
[4,5,6,3,2,1]
=>
12
[4,6,1,2,3,5]
=>
7
[4,6,1,2,5,3]
=>
8
[4,6,1,3,2,5]
=>
8
[4,6,1,3,5,2]
=>
9
[4,6,1,5,2,3]
=>
9
[4,6,1,5,3,2]
=>
10
[4,6,2,1,3,5]
=>
8
[4,6,2,1,5,3]
=>
9
[4,6,2,3,1,5]
=>
9
[4,6,2,3,5,1]
=>
10
[4,6,2,5,1,3]
=>
10
[4,6,2,5,3,1]
=>
11
[4,6,3,1,2,5]
=>
9
[4,6,3,1,5,2]
=>
10
[4,6,3,2,1,5]
=>
10
[4,6,3,2,5,1]
=>
11
[4,6,3,5,1,2]
=>
11
[4,6,3,5,2,1]
=>
12
[4,6,5,1,2,3]
=>
10
[4,6,5,1,3,2]
=>
11
[4,6,5,2,1,3]
=>
11
[4,6,5,2,3,1]
=>
12
[4,6,5,3,1,2]
=>
12
[4,6,5,3,2,1]
=>
13
[5,1,2,3,4,6]
=>
4
[5,1,2,3,6,4]
=>
5
[5,1,2,4,3,6]
=>
5
[5,1,2,4,6,3]
=>
6
[5,1,2,6,3,4]
=>
6
[5,1,2,6,4,3]
=>
7
[5,1,3,2,4,6]
=>
5
[5,1,3,2,6,4]
=>
6
[5,1,3,4,2,6]
=>
6
[5,1,3,4,6,2]
=>
7
[5,1,3,6,2,4]
=>
7
[5,1,3,6,4,2]
=>
8
[5,1,4,2,3,6]
=>
6
[5,1,4,2,6,3]
=>
7
[5,1,4,3,2,6]
=>
7
[5,1,4,3,6,2]
=>
8
[5,1,4,6,2,3]
=>
8
[5,1,4,6,3,2]
=>
9
[5,1,6,2,3,4]
=>
7
[5,1,6,2,4,3]
=>
8
[5,1,6,3,2,4]
=>
8
[5,1,6,3,4,2]
=>
9
[5,1,6,4,2,3]
=>
9
[5,1,6,4,3,2]
=>
10
[5,2,1,3,4,6]
=>
5
[5,2,1,3,6,4]
=>
6
[5,2,1,4,3,6]
=>
6
[5,2,1,4,6,3]
=>
7
[5,2,1,6,3,4]
=>
7
[5,2,1,6,4,3]
=>
8
[5,2,3,1,4,6]
=>
6
[5,2,3,1,6,4]
=>
7
[5,2,3,4,1,6]
=>
7
[5,2,3,4,6,1]
=>
8
[5,2,3,6,1,4]
=>
8
[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]
=>
8
[5,2,4,3,6,1]
=>
9
[5,2,4,6,1,3]
=>
9
[5,2,4,6,3,1]
=>
10
[5,2,6,1,3,4]
=>
8
[5,2,6,1,4,3]
=>
9
[5,2,6,3,1,4]
=>
9
[5,2,6,3,4,1]
=>
10
[5,2,6,4,1,3]
=>
10
[5,2,6,4,3,1]
=>
11
[5,3,1,2,4,6]
=>
6
[5,3,1,2,6,4]
=>
7
[5,3,1,4,2,6]
=>
7
[5,3,1,4,6,2]
=>
8
[5,3,1,6,2,4]
=>
8
[5,3,1,6,4,2]
=>
9
[5,3,2,1,4,6]
=>
7
[5,3,2,1,6,4]
=>
8
[5,3,2,4,1,6]
=>
8
[5,3,2,4,6,1]
=>
9
[5,3,2,6,1,4]
=>
9
[5,3,2,6,4,1]
=>
10
[5,3,4,1,2,6]
=>
8
[5,3,4,1,6,2]
=>
9
[5,3,4,2,1,6]
=>
9
[5,3,4,2,6,1]
=>
10
[5,3,4,6,1,2]
=>
10
[5,3,4,6,2,1]
=>
11
[5,3,6,1,2,4]
=>
9
[5,3,6,1,4,2]
=>
10
[5,3,6,2,1,4]
=>
10
[5,3,6,2,4,1]
=>
11
[5,3,6,4,1,2]
=>
11
[5,3,6,4,2,1]
=>
12
[5,4,1,2,3,6]
=>
7
[5,4,1,2,6,3]
=>
8
[5,4,1,3,2,6]
=>
8
[5,4,1,3,6,2]
=>
9
[5,4,1,6,2,3]
=>
9
[5,4,1,6,3,2]
=>
10
[5,4,2,1,3,6]
=>
8
[5,4,2,1,6,3]
=>
9
[5,4,2,3,1,6]
=>
9
[5,4,2,3,6,1]
=>
10
[5,4,2,6,1,3]
=>
10
[5,4,2,6,3,1]
=>
11
[5,4,3,1,2,6]
=>
9
[5,4,3,1,6,2]
=>
10
[5,4,3,2,1,6]
=>
10
[5,4,3,2,6,1]
=>
11
[5,4,3,6,1,2]
=>
11
[5,4,3,6,2,1]
=>
12
[5,4,6,1,2,3]
=>
10
[5,4,6,1,3,2]
=>
11
[5,4,6,2,1,3]
=>
11
[5,4,6,2,3,1]
=>
12
[5,4,6,3,1,2]
=>
12
[5,4,6,3,2,1]
=>
13
[5,6,1,2,3,4]
=>
8
[5,6,1,2,4,3]
=>
9
[5,6,1,3,2,4]
=>
9
[5,6,1,3,4,2]
=>
10
[5,6,1,4,2,3]
=>
10
[5,6,1,4,3,2]
=>
11
[5,6,2,1,3,4]
=>
9
[5,6,2,1,4,3]
=>
10
[5,6,2,3,1,4]
=>
10
[5,6,2,3,4,1]
=>
11
[5,6,2,4,1,3]
=>
11
[5,6,2,4,3,1]
=>
12
[5,6,3,1,2,4]
=>
10
[5,6,3,1,4,2]
=>
11
[5,6,3,2,1,4]
=>
11
[5,6,3,2,4,1]
=>
12
[5,6,3,4,1,2]
=>
12
[5,6,3,4,2,1]
=>
13
[5,6,4,1,2,3]
=>
11
[5,6,4,1,3,2]
=>
12
[5,6,4,2,1,3]
=>
12
[5,6,4,2,3,1]
=>
13
[5,6,4,3,1,2]
=>
13
[5,6,4,3,2,1]
=>
14
[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]
=>
8
[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]
=>
9
[6,1,4,2,3,5]
=>
7
[6,1,4,2,5,3]
=>
8
[6,1,4,3,2,5]
=>
8
[6,1,4,3,5,2]
=>
9
[6,1,4,5,2,3]
=>
9
[6,1,4,5,3,2]
=>
10
[6,1,5,2,3,4]
=>
8
[6,1,5,2,4,3]
=>
9
[6,1,5,3,2,4]
=>
9
[6,1,5,3,4,2]
=>
10
[6,1,5,4,2,3]
=>
10
[6,1,5,4,3,2]
=>
11
[6,2,1,3,4,5]
=>
6
[6,2,1,3,5,4]
=>
7
[6,2,1,4,3,5]
=>
7
[6,2,1,4,5,3]
=>
8
[6,2,1,5,3,4]
=>
8
[6,2,1,5,4,3]
=>
9
[6,2,3,1,4,5]
=>
7
[6,2,3,1,5,4]
=>
8
[6,2,3,4,1,5]
=>
8
[6,2,3,4,5,1]
=>
9
[6,2,3,5,1,4]
=>
9
[6,2,3,5,4,1]
=>
10
[6,2,4,1,3,5]
=>
8
[6,2,4,1,5,3]
=>
9
[6,2,4,3,1,5]
=>
9
[6,2,4,3,5,1]
=>
10
[6,2,4,5,1,3]
=>
10
[6,2,4,5,3,1]
=>
11
[6,2,5,1,3,4]
=>
9
[6,2,5,1,4,3]
=>
10
[6,2,5,3,1,4]
=>
10
[6,2,5,3,4,1]
=>
11
[6,2,5,4,1,3]
=>
11
[6,2,5,4,3,1]
=>
12
[6,3,1,2,4,5]
=>
7
[6,3,1,2,5,4]
=>
8
[6,3,1,4,2,5]
=>
8
[6,3,1,4,5,2]
=>
9
[6,3,1,5,2,4]
=>
9
[6,3,1,5,4,2]
=>
10
[6,3,2,1,4,5]
=>
8
[6,3,2,1,5,4]
=>
9
[6,3,2,4,1,5]
=>
9
[6,3,2,4,5,1]
=>
10
[6,3,2,5,1,4]
=>
10
[6,3,2,5,4,1]
=>
11
[6,3,4,1,2,5]
=>
9
[6,3,4,1,5,2]
=>
10
[6,3,4,2,1,5]
=>
10
[6,3,4,2,5,1]
=>
11
[6,3,4,5,1,2]
=>
11
[6,3,4,5,2,1]
=>
12
[6,3,5,1,2,4]
=>
10
[6,3,5,1,4,2]
=>
11
[6,3,5,2,1,4]
=>
11
[6,3,5,2,4,1]
=>
12
[6,3,5,4,1,2]
=>
12
[6,3,5,4,2,1]
=>
13
[6,4,1,2,3,5]
=>
8
[6,4,1,2,5,3]
=>
9
[6,4,1,3,2,5]
=>
9
[6,4,1,3,5,2]
=>
10
[6,4,1,5,2,3]
=>
10
[6,4,1,5,3,2]
=>
11
[6,4,2,1,3,5]
=>
9
[6,4,2,1,5,3]
=>
10
[6,4,2,3,1,5]
=>
10
[6,4,2,3,5,1]
=>
11
[6,4,2,5,1,3]
=>
11
[6,4,2,5,3,1]
=>
12
[6,4,3,1,2,5]
=>
10
[6,4,3,1,5,2]
=>
11
[6,4,3,2,1,5]
=>
11
[6,4,3,2,5,1]
=>
12
[6,4,3,5,1,2]
=>
12
[6,4,3,5,2,1]
=>
13
[6,4,5,1,2,3]
=>
11
[6,4,5,1,3,2]
=>
12
[6,4,5,2,1,3]
=>
12
[6,4,5,2,3,1]
=>
13
[6,4,5,3,1,2]
=>
13
[6,4,5,3,2,1]
=>
14
[6,5,1,2,3,4]
=>
9
[6,5,1,2,4,3]
=>
10
[6,5,1,3,2,4]
=>
10
[6,5,1,3,4,2]
=>
11
[6,5,1,4,2,3]
=>
11
[6,5,1,4,3,2]
=>
12
[6,5,2,1,3,4]
=>
10
[6,5,2,1,4,3]
=>
11
[6,5,2,3,1,4]
=>
11
[6,5,2,3,4,1]
=>
12
[6,5,2,4,1,3]
=>
12
[6,5,2,4,3,1]
=>
13
[6,5,3,1,2,4]
=>
11
[6,5,3,1,4,2]
=>
12
[6,5,3,2,1,4]
=>
12
[6,5,3,2,4,1]
=>
13
[6,5,3,4,1,2]
=>
13
[6,5,3,4,2,1]
=>
14
[6,5,4,1,2,3]
=>
12
[6,5,4,1,3,2]
=>
13
[6,5,4,2,1,3]
=>
13
[6,5,4,2,3,1]
=>
14
[6,5,4,3,1,2]
=>
14
[6,5,4,3,2,1]
=>
15
Description
The number of inversions of a permutation.
This equals the minimal number of simple transpositions $(i,i+1)$ needed to write $\pi$. Thus, it is also the Coxeter length of $\pi$.
This equals the minimal number of simple transpositions $(i,i+1)$ needed to write $\pi$. Thus, it is also the Coxeter length of $\pi$.
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] List of permutations of 1,2,3,...,n for n=1,2,3,..., in lexicographic order. OEIS:A030298
[3] Array of digit sums of factorial representation of numbers 0,1,...,n!-1 for n>=1. OEIS:A139365
[2] List of permutations of 1,2,3,...,n for n=1,2,3,..., in lexicographic order. OEIS:A030298
[3] Array of digit sums of factorial representation of numbers 0,1,...,n!-1 for n>=1. OEIS:A139365
Code
def statistic(x):
return x.number_of_inversions()
Created
Sep 27, 2011 at 23:29 by Christian Stump
Updated
May 10, 2019 at 17:10 by Henning Ulfarsson
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