Identifier
Identifier
Values
[1] => 0
[1,2] => 0
[2,1] => 2
[1,2,3] => 0
[1,3,2] => 3
[2,1,3] => 2
[2,3,1] => 5
[3,1,2] => 6
[3,2,1] => 8
[1,2,3,4] => 0
[1,2,4,3] => 4
[1,3,2,4] => 3
[1,3,4,2] => 7
[1,4,2,3] => 8
[1,4,3,2] => 11
[2,1,3,4] => 2
[2,1,4,3] => 6
[2,3,1,4] => 5
[2,3,4,1] => 9
[2,4,1,3] => 10
[2,4,3,1] => 13
[3,1,2,4] => 6
[3,1,4,2] => 10
[3,2,1,4] => 8
[3,2,4,1] => 12
[3,4,1,2] => 14
[3,4,2,1] => 16
[4,1,2,3] => 12
[4,1,3,2] => 15
[4,2,1,3] => 14
[4,2,3,1] => 17
[4,3,1,2] => 18
[4,3,2,1] => 20
[1,2,3,4,5] => 0
[1,2,3,5,4] => 5
[1,2,4,3,5] => 4
[1,2,4,5,3] => 9
[1,2,5,3,4] => 10
[1,2,5,4,3] => 14
[1,3,2,4,5] => 3
[1,3,2,5,4] => 8
[1,3,4,2,5] => 7
[1,3,4,5,2] => 12
[1,3,5,2,4] => 13
[1,3,5,4,2] => 17
[1,4,2,3,5] => 8
[1,4,2,5,3] => 13
[1,4,3,2,5] => 11
[1,4,3,5,2] => 16
[1,4,5,2,3] => 18
[1,4,5,3,2] => 21
[1,5,2,3,4] => 15
[1,5,2,4,3] => 19
[1,5,3,2,4] => 18
[1,5,3,4,2] => 22
[1,5,4,2,3] => 23
[1,5,4,3,2] => 26
[2,1,3,4,5] => 2
[2,1,3,5,4] => 7
[2,1,4,3,5] => 6
[2,1,4,5,3] => 11
[2,1,5,3,4] => 12
[2,1,5,4,3] => 16
[2,3,1,4,5] => 5
[2,3,1,5,4] => 10
[2,3,4,1,5] => 9
[2,3,4,5,1] => 14
[2,3,5,1,4] => 15
[2,3,5,4,1] => 19
[2,4,1,3,5] => 10
[2,4,1,5,3] => 15
[2,4,3,1,5] => 13
[2,4,3,5,1] => 18
[2,4,5,1,3] => 20
[2,4,5,3,1] => 23
[2,5,1,3,4] => 17
[2,5,1,4,3] => 21
[2,5,3,1,4] => 20
[2,5,3,4,1] => 24
[2,5,4,1,3] => 25
[2,5,4,3,1] => 28
[3,1,2,4,5] => 6
[3,1,2,5,4] => 11
[3,1,4,2,5] => 10
[3,1,4,5,2] => 15
[3,1,5,2,4] => 16
[3,1,5,4,2] => 20
[3,2,1,4,5] => 8
[3,2,1,5,4] => 13
[3,2,4,1,5] => 12
[3,2,4,5,1] => 17
[3,2,5,1,4] => 18
[3,2,5,4,1] => 22
[3,4,1,2,5] => 14
[3,4,1,5,2] => 19
[3,4,2,1,5] => 16
[3,4,2,5,1] => 21
[3,4,5,1,2] => 24
[3,4,5,2,1] => 26
[3,5,1,2,4] => 21
[3,5,1,4,2] => 25
[3,5,2,1,4] => 23
[3,5,2,4,1] => 27
[3,5,4,1,2] => 29
[3,5,4,2,1] => 31
[4,1,2,3,5] => 12
[4,1,2,5,3] => 17
[4,1,3,2,5] => 15
[4,1,3,5,2] => 20
[4,1,5,2,3] => 22
[4,1,5,3,2] => 25
[4,2,1,3,5] => 14
[4,2,1,5,3] => 19
[4,2,3,1,5] => 17
[4,2,3,5,1] => 22
[4,2,5,1,3] => 24
[4,2,5,3,1] => 27
[4,3,1,2,5] => 18
[4,3,1,5,2] => 23
[4,3,2,1,5] => 20
[4,3,2,5,1] => 25
[4,3,5,1,2] => 28
[4,3,5,2,1] => 30
[4,5,1,2,3] => 27
[4,5,1,3,2] => 30
[4,5,2,1,3] => 29
[4,5,2,3,1] => 32
[4,5,3,1,2] => 33
[4,5,3,2,1] => 35
[5,1,2,3,4] => 20
[5,1,2,4,3] => 24
[5,1,3,2,4] => 23
[5,1,3,4,2] => 27
[5,1,4,2,3] => 28
[5,1,4,3,2] => 31
[5,2,1,3,4] => 22
[5,2,1,4,3] => 26
[5,2,3,1,4] => 25
[5,2,3,4,1] => 29
[5,2,4,1,3] => 30
[5,2,4,3,1] => 33
[5,3,1,2,4] => 26
[5,3,1,4,2] => 30
[5,3,2,1,4] => 28
[5,3,2,4,1] => 32
[5,3,4,1,2] => 34
[5,3,4,2,1] => 36
[5,4,1,2,3] => 32
[5,4,1,3,2] => 35
[5,4,2,1,3] => 34
[5,4,2,3,1] => 37
[5,4,3,1,2] => 38
[5,4,3,2,1] => 40
[1,2,3,4,5,6] => 0
[1,2,3,4,6,5] => 6
[1,2,3,5,4,6] => 5
[1,2,3,5,6,4] => 11
[1,2,3,6,4,5] => 12
[1,2,3,6,5,4] => 17
[1,2,4,3,5,6] => 4
[1,2,4,3,6,5] => 10
[1,2,4,5,3,6] => 9
[1,2,4,5,6,3] => 15
[1,2,4,6,3,5] => 16
[1,2,4,6,5,3] => 21
[1,2,5,3,4,6] => 10
[1,2,5,3,6,4] => 16
[1,2,5,4,3,6] => 14
[1,2,5,4,6,3] => 20
[1,2,5,6,3,4] => 22
[1,2,5,6,4,3] => 26
[1,2,6,3,4,5] => 18
[1,2,6,3,5,4] => 23
[1,2,6,4,3,5] => 22
[1,2,6,4,5,3] => 27
[1,2,6,5,3,4] => 28
[1,2,6,5,4,3] => 32
[1,3,2,4,5,6] => 3
[1,3,2,4,6,5] => 9
[1,3,2,5,4,6] => 8
[1,3,2,5,6,4] => 14
[1,3,2,6,4,5] => 15
[1,3,2,6,5,4] => 20
[1,3,4,2,5,6] => 7
[1,3,4,2,6,5] => 13
[1,3,4,5,2,6] => 12
[1,3,4,5,6,2] => 18
[1,3,4,6,2,5] => 19
[1,3,4,6,5,2] => 24
[1,3,5,2,4,6] => 13
[1,3,5,2,6,4] => 19
[1,3,5,4,2,6] => 17
[1,3,5,4,6,2] => 23
[1,3,5,6,2,4] => 25
[1,3,5,6,4,2] => 29
[1,3,6,2,4,5] => 21
[1,3,6,2,5,4] => 26
[1,3,6,4,2,5] => 25
[1,3,6,4,5,2] => 30
[1,3,6,5,2,4] => 31
[1,3,6,5,4,2] => 35
[1,4,2,3,5,6] => 8
[1,4,2,3,6,5] => 14
[1,4,2,5,3,6] => 13
[1,4,2,5,6,3] => 19
[1,4,2,6,3,5] => 20
[1,4,2,6,5,3] => 25
[1,4,3,2,5,6] => 11
[1,4,3,2,6,5] => 17
[1,4,3,5,2,6] => 16
[1,4,3,5,6,2] => 22
[1,4,3,6,2,5] => 23
[1,4,3,6,5,2] => 28
[1,4,5,2,3,6] => 18
[1,4,5,2,6,3] => 24
[1,4,5,3,2,6] => 21
[1,4,5,3,6,2] => 27
[1,4,5,6,2,3] => 30
[1,4,5,6,3,2] => 33
[1,4,6,2,3,5] => 26
[1,4,6,2,5,3] => 31
[1,4,6,3,2,5] => 29
[1,4,6,3,5,2] => 34
[1,4,6,5,2,3] => 36
[1,4,6,5,3,2] => 39
[1,5,2,3,4,6] => 15
[1,5,2,3,6,4] => 21
[1,5,2,4,3,6] => 19
[1,5,2,4,6,3] => 25
[1,5,2,6,3,4] => 27
[1,5,2,6,4,3] => 31
[1,5,3,2,4,6] => 18
[1,5,3,2,6,4] => 24
[1,5,3,4,2,6] => 22
[1,5,3,4,6,2] => 28
[1,5,3,6,2,4] => 30
[1,5,3,6,4,2] => 34
[1,5,4,2,3,6] => 23
[1,5,4,2,6,3] => 29
[1,5,4,3,2,6] => 26
[1,5,4,3,6,2] => 32
[1,5,4,6,2,3] => 35
[1,5,4,6,3,2] => 38
[1,5,6,2,3,4] => 33
[1,5,6,2,4,3] => 37
[1,5,6,3,2,4] => 36
[1,5,6,3,4,2] => 40
[1,5,6,4,2,3] => 41
[1,5,6,4,3,2] => 44
[1,6,2,3,4,5] => 24
[1,6,2,3,5,4] => 29
[1,6,2,4,3,5] => 28
[1,6,2,4,5,3] => 33
[1,6,2,5,3,4] => 34
[1,6,2,5,4,3] => 38
[1,6,3,2,4,5] => 27
[1,6,3,2,5,4] => 32
[1,6,3,4,2,5] => 31
[1,6,3,4,5,2] => 36
[1,6,3,5,2,4] => 37
[1,6,3,5,4,2] => 41
[1,6,4,2,3,5] => 32
[1,6,4,2,5,3] => 37
[1,6,4,3,2,5] => 35
[1,6,4,3,5,2] => 40
[1,6,4,5,2,3] => 42
[1,6,4,5,3,2] => 45
[1,6,5,2,3,4] => 39
[1,6,5,2,4,3] => 43
[1,6,5,3,2,4] => 42
[1,6,5,3,4,2] => 46
[1,6,5,4,2,3] => 47
[1,6,5,4,3,2] => 50
[2,1,3,4,5,6] => 2
[2,1,3,4,6,5] => 8
[2,1,3,5,4,6] => 7
[2,1,3,5,6,4] => 13
[2,1,3,6,4,5] => 14
[2,1,3,6,5,4] => 19
[2,1,4,3,5,6] => 6
[2,1,4,3,6,5] => 12
[2,1,4,5,3,6] => 11
[2,1,4,5,6,3] => 17
[2,1,4,6,3,5] => 18
[2,1,4,6,5,3] => 23
[2,1,5,3,4,6] => 12
[2,1,5,3,6,4] => 18
[2,1,5,4,3,6] => 16
[2,1,5,4,6,3] => 22
[2,1,5,6,3,4] => 24
[2,1,5,6,4,3] => 28
[2,1,6,3,4,5] => 20
[2,1,6,3,5,4] => 25
[2,1,6,4,3,5] => 24
[2,1,6,4,5,3] => 29
[2,1,6,5,3,4] => 30
[2,1,6,5,4,3] => 34
[2,3,1,4,5,6] => 5
[2,3,1,4,6,5] => 11
[2,3,1,5,4,6] => 10
[2,3,1,5,6,4] => 16
[2,3,1,6,4,5] => 17
[2,3,1,6,5,4] => 22
[2,3,4,1,5,6] => 9
[2,3,4,1,6,5] => 15
[2,3,4,5,1,6] => 14
[2,3,4,5,6,1] => 20
[2,3,4,6,1,5] => 21
[2,3,4,6,5,1] => 26
[2,3,5,1,4,6] => 15
[2,3,5,1,6,4] => 21
[2,3,5,4,1,6] => 19
[2,3,5,4,6,1] => 25
[2,3,5,6,1,4] => 27
[2,3,5,6,4,1] => 31
[2,3,6,1,4,5] => 23
[2,3,6,1,5,4] => 28
[2,3,6,4,1,5] => 27
[2,3,6,4,5,1] => 32
[2,3,6,5,1,4] => 33
[2,3,6,5,4,1] => 37
[2,4,1,3,5,6] => 10
[2,4,1,3,6,5] => 16
[2,4,1,5,3,6] => 15
[2,4,1,5,6,3] => 21
[2,4,1,6,3,5] => 22
[2,4,1,6,5,3] => 27
[2,4,3,1,5,6] => 13
[2,4,3,1,6,5] => 19
[2,4,3,5,1,6] => 18
[2,4,3,5,6,1] => 24
[2,4,3,6,1,5] => 25
[2,4,3,6,5,1] => 30
[2,4,5,1,3,6] => 20
[2,4,5,1,6,3] => 26
[2,4,5,3,1,6] => 23
[2,4,5,3,6,1] => 29
[2,4,5,6,1,3] => 32
[2,4,5,6,3,1] => 35
[2,4,6,1,3,5] => 28
[2,4,6,1,5,3] => 33
[2,4,6,3,1,5] => 31
[2,4,6,3,5,1] => 36
[2,4,6,5,1,3] => 38
[2,4,6,5,3,1] => 41
[2,5,1,3,4,6] => 17
[2,5,1,3,6,4] => 23
[2,5,1,4,3,6] => 21
[2,5,1,4,6,3] => 27
[2,5,1,6,3,4] => 29
[2,5,1,6,4,3] => 33
[2,5,3,1,4,6] => 20
[2,5,3,1,6,4] => 26
[2,5,3,4,1,6] => 24
[2,5,3,4,6,1] => 30
[2,5,3,6,1,4] => 32
[2,5,3,6,4,1] => 36
[2,5,4,1,3,6] => 25
[2,5,4,1,6,3] => 31
[2,5,4,3,1,6] => 28
[2,5,4,3,6,1] => 34
[2,5,4,6,1,3] => 37
[2,5,4,6,3,1] => 40
[2,5,6,1,3,4] => 35
[2,5,6,1,4,3] => 39
[2,5,6,3,1,4] => 38
[2,5,6,3,4,1] => 42
[2,5,6,4,1,3] => 43
[2,5,6,4,3,1] => 46
[2,6,1,3,4,5] => 26
[2,6,1,3,5,4] => 31
[2,6,1,4,3,5] => 30
[2,6,1,4,5,3] => 35
[2,6,1,5,3,4] => 36
[2,6,1,5,4,3] => 40
[2,6,3,1,4,5] => 29
[2,6,3,1,5,4] => 34
[2,6,3,4,1,5] => 33
[2,6,3,4,5,1] => 38
[2,6,3,5,1,4] => 39
[2,6,3,5,4,1] => 43
[2,6,4,1,3,5] => 34
[2,6,4,1,5,3] => 39
[2,6,4,3,1,5] => 37
[2,6,4,3,5,1] => 42
[2,6,4,5,1,3] => 44
[2,6,4,5,3,1] => 47
[2,6,5,1,3,4] => 41
[2,6,5,1,4,3] => 45
[2,6,5,3,1,4] => 44
[2,6,5,3,4,1] => 48
[2,6,5,4,1,3] => 49
[2,6,5,4,3,1] => 52
[3,1,2,4,5,6] => 6
[3,1,2,4,6,5] => 12
[3,1,2,5,4,6] => 11
[3,1,2,5,6,4] => 17
[3,1,2,6,4,5] => 18
[3,1,2,6,5,4] => 23
[3,1,4,2,5,6] => 10
[3,1,4,2,6,5] => 16
[3,1,4,5,2,6] => 15
[3,1,4,5,6,2] => 21
[3,1,4,6,2,5] => 22
[3,1,4,6,5,2] => 27
[3,1,5,2,4,6] => 16
[3,1,5,2,6,4] => 22
[3,1,5,4,2,6] => 20
[3,1,5,4,6,2] => 26
[3,1,5,6,2,4] => 28
[3,1,5,6,4,2] => 32
[3,1,6,2,4,5] => 24
[3,1,6,2,5,4] => 29
[3,1,6,4,2,5] => 28
[3,1,6,4,5,2] => 33
[3,1,6,5,2,4] => 34
[3,1,6,5,4,2] => 38
[3,2,1,4,5,6] => 8
[3,2,1,4,6,5] => 14
[3,2,1,5,4,6] => 13
[3,2,1,5,6,4] => 19
[3,2,1,6,4,5] => 20
[3,2,1,6,5,4] => 25
[3,2,4,1,5,6] => 12
[3,2,4,1,6,5] => 18
[3,2,4,5,1,6] => 17
[3,2,4,5,6,1] => 23
[3,2,4,6,1,5] => 24
[3,2,4,6,5,1] => 29
[3,2,5,1,4,6] => 18
[3,2,5,1,6,4] => 24
[3,2,5,4,1,6] => 22
[3,2,5,4,6,1] => 28
[3,2,5,6,1,4] => 30
[3,2,5,6,4,1] => 34
[3,2,6,1,4,5] => 26
[3,2,6,1,5,4] => 31
[3,2,6,4,1,5] => 30
[3,2,6,4,5,1] => 35
[3,2,6,5,1,4] => 36
[3,2,6,5,4,1] => 40
[3,4,1,2,5,6] => 14
[3,4,1,2,6,5] => 20
[3,4,1,5,2,6] => 19
[3,4,1,5,6,2] => 25
[3,4,1,6,2,5] => 26
[3,4,1,6,5,2] => 31
[3,4,2,1,5,6] => 16
[3,4,2,1,6,5] => 22
[3,4,2,5,1,6] => 21
[3,4,2,5,6,1] => 27
[3,4,2,6,1,5] => 28
[3,4,2,6,5,1] => 33
[3,4,5,1,2,6] => 24
[3,4,5,1,6,2] => 30
[3,4,5,2,1,6] => 26
[3,4,5,2,6,1] => 32
[3,4,5,6,1,2] => 36
[3,4,5,6,2,1] => 38
[3,4,6,1,2,5] => 32
[3,4,6,1,5,2] => 37
[3,4,6,2,1,5] => 34
[3,4,6,2,5,1] => 39
[3,4,6,5,1,2] => 42
[3,4,6,5,2,1] => 44
[3,5,1,2,4,6] => 21
[3,5,1,2,6,4] => 27
[3,5,1,4,2,6] => 25
[3,5,1,4,6,2] => 31
[3,5,1,6,2,4] => 33
[3,5,1,6,4,2] => 37
[3,5,2,1,4,6] => 23
[3,5,2,1,6,4] => 29
[3,5,2,4,1,6] => 27
[3,5,2,4,6,1] => 33
[3,5,2,6,1,4] => 35
[3,5,2,6,4,1] => 39
[3,5,4,1,2,6] => 29
[3,5,4,1,6,2] => 35
[3,5,4,2,1,6] => 31
[3,5,4,2,6,1] => 37
[3,5,4,6,1,2] => 41
[3,5,4,6,2,1] => 43
[3,5,6,1,2,4] => 39
[3,5,6,1,4,2] => 43
[3,5,6,2,1,4] => 41
[3,5,6,2,4,1] => 45
[3,5,6,4,1,2] => 47
[3,5,6,4,2,1] => 49
[3,6,1,2,4,5] => 30
[3,6,1,2,5,4] => 35
[3,6,1,4,2,5] => 34
[3,6,1,4,5,2] => 39
[3,6,1,5,2,4] => 40
[3,6,1,5,4,2] => 44
[3,6,2,1,4,5] => 32
[3,6,2,1,5,4] => 37
[3,6,2,4,1,5] => 36
[3,6,2,4,5,1] => 41
[3,6,2,5,1,4] => 42
[3,6,2,5,4,1] => 46
[3,6,4,1,2,5] => 38
[3,6,4,1,5,2] => 43
[3,6,4,2,1,5] => 40
[3,6,4,2,5,1] => 45
[3,6,4,5,1,2] => 48
[3,6,4,5,2,1] => 50
[3,6,5,1,2,4] => 45
[3,6,5,1,4,2] => 49
[3,6,5,2,1,4] => 47
[3,6,5,2,4,1] => 51
[3,6,5,4,1,2] => 53
[3,6,5,4,2,1] => 55
[4,1,2,3,5,6] => 12
[4,1,2,3,6,5] => 18
[4,1,2,5,3,6] => 17
[4,1,2,5,6,3] => 23
[4,1,2,6,3,5] => 24
[4,1,2,6,5,3] => 29
[4,1,3,2,5,6] => 15
[4,1,3,2,6,5] => 21
[4,1,3,5,2,6] => 20
[4,1,3,5,6,2] => 26
[4,1,3,6,2,5] => 27
[4,1,3,6,5,2] => 32
[4,1,5,2,3,6] => 22
[4,1,5,2,6,3] => 28
[4,1,5,3,2,6] => 25
[4,1,5,3,6,2] => 31
[4,1,5,6,2,3] => 34
[4,1,5,6,3,2] => 37
[4,1,6,2,3,5] => 30
[4,1,6,2,5,3] => 35
[4,1,6,3,2,5] => 33
[4,1,6,3,5,2] => 38
[4,1,6,5,2,3] => 40
[4,1,6,5,3,2] => 43
[4,2,1,3,5,6] => 14
[4,2,1,3,6,5] => 20
[4,2,1,5,3,6] => 19
[4,2,1,5,6,3] => 25
[4,2,1,6,3,5] => 26
[4,2,1,6,5,3] => 31
[4,2,3,1,5,6] => 17
[4,2,3,1,6,5] => 23
[4,2,3,5,1,6] => 22
[4,2,3,5,6,1] => 28
[4,2,3,6,1,5] => 29
[4,2,3,6,5,1] => 34
[4,2,5,1,3,6] => 24
[4,2,5,1,6,3] => 30
[4,2,5,3,1,6] => 27
[4,2,5,3,6,1] => 33
[4,2,5,6,1,3] => 36
[4,2,5,6,3,1] => 39
[4,2,6,1,3,5] => 32
[4,2,6,1,5,3] => 37
[4,2,6,3,1,5] => 35
[4,2,6,3,5,1] => 40
[4,2,6,5,1,3] => 42
[4,2,6,5,3,1] => 45
[4,3,1,2,5,6] => 18
[4,3,1,2,6,5] => 24
[4,3,1,5,2,6] => 23
[4,3,1,5,6,2] => 29
[4,3,1,6,2,5] => 30
[4,3,1,6,5,2] => 35
[4,3,2,1,5,6] => 20
[4,3,2,1,6,5] => 26
[4,3,2,5,1,6] => 25
[4,3,2,5,6,1] => 31
[4,3,2,6,1,5] => 32
[4,3,2,6,5,1] => 37
[4,3,5,1,2,6] => 28
[4,3,5,1,6,2] => 34
[4,3,5,2,1,6] => 30
[4,3,5,2,6,1] => 36
[4,3,5,6,1,2] => 40
[4,3,5,6,2,1] => 42
[4,3,6,1,2,5] => 36
[4,3,6,1,5,2] => 41
[4,3,6,2,1,5] => 38
[4,3,6,2,5,1] => 43
[4,3,6,5,1,2] => 46
[4,3,6,5,2,1] => 48
[4,5,1,2,3,6] => 27
[4,5,1,2,6,3] => 33
[4,5,1,3,2,6] => 30
[4,5,1,3,6,2] => 36
[4,5,1,6,2,3] => 39
[4,5,1,6,3,2] => 42
[4,5,2,1,3,6] => 29
[4,5,2,1,6,3] => 35
[4,5,2,3,1,6] => 32
[4,5,2,3,6,1] => 38
[4,5,2,6,1,3] => 41
[4,5,2,6,3,1] => 44
[4,5,3,1,2,6] => 33
[4,5,3,1,6,2] => 39
[4,5,3,2,1,6] => 35
[4,5,3,2,6,1] => 41
[4,5,3,6,1,2] => 45
[4,5,3,6,2,1] => 47
[4,5,6,1,2,3] => 45
[4,5,6,1,3,2] => 48
[4,5,6,2,1,3] => 47
[4,5,6,2,3,1] => 50
[4,5,6,3,1,2] => 51
[4,5,6,3,2,1] => 53
[4,6,1,2,3,5] => 36
[4,6,1,2,5,3] => 41
[4,6,1,3,2,5] => 39
[4,6,1,3,5,2] => 44
[4,6,1,5,2,3] => 46
[4,6,1,5,3,2] => 49
[4,6,2,1,3,5] => 38
[4,6,2,1,5,3] => 43
[4,6,2,3,1,5] => 41
[4,6,2,3,5,1] => 46
[4,6,2,5,1,3] => 48
[4,6,2,5,3,1] => 51
[4,6,3,1,2,5] => 42
[4,6,3,1,5,2] => 47
[4,6,3,2,1,5] => 44
[4,6,3,2,5,1] => 49
[4,6,3,5,1,2] => 52
[4,6,3,5,2,1] => 54
[4,6,5,1,2,3] => 51
[4,6,5,1,3,2] => 54
[4,6,5,2,1,3] => 53
[4,6,5,2,3,1] => 56
[4,6,5,3,1,2] => 57
[4,6,5,3,2,1] => 59
[5,1,2,3,4,6] => 20
[5,1,2,3,6,4] => 26
[5,1,2,4,3,6] => 24
[5,1,2,4,6,3] => 30
[5,1,2,6,3,4] => 32
[5,1,2,6,4,3] => 36
[5,1,3,2,4,6] => 23
[5,1,3,2,6,4] => 29
[5,1,3,4,2,6] => 27
[5,1,3,4,6,2] => 33
[5,1,3,6,2,4] => 35
[5,1,3,6,4,2] => 39
[5,1,4,2,3,6] => 28
[5,1,4,2,6,3] => 34
[5,1,4,3,2,6] => 31
[5,1,4,3,6,2] => 37
[5,1,4,6,2,3] => 40
[5,1,4,6,3,2] => 43
[5,1,6,2,3,4] => 38
[5,1,6,2,4,3] => 42
[5,1,6,3,2,4] => 41
[5,1,6,3,4,2] => 45
[5,1,6,4,2,3] => 46
[5,1,6,4,3,2] => 49
[5,2,1,3,4,6] => 22
[5,2,1,3,6,4] => 28
[5,2,1,4,3,6] => 26
[5,2,1,4,6,3] => 32
[5,2,1,6,3,4] => 34
[5,2,1,6,4,3] => 38
[5,2,3,1,4,6] => 25
[5,2,3,1,6,4] => 31
[5,2,3,4,1,6] => 29
[5,2,3,4,6,1] => 35
[5,2,3,6,1,4] => 37
[5,2,3,6,4,1] => 41
[5,2,4,1,3,6] => 30
[5,2,4,1,6,3] => 36
[5,2,4,3,1,6] => 33
[5,2,4,3,6,1] => 39
[5,2,4,6,1,3] => 42
[5,2,4,6,3,1] => 45
[5,2,6,1,3,4] => 40
[5,2,6,1,4,3] => 44
[5,2,6,3,1,4] => 43
[5,2,6,3,4,1] => 47
[5,2,6,4,1,3] => 48
[5,2,6,4,3,1] => 51
[5,3,1,2,4,6] => 26
[5,3,1,2,6,4] => 32
[5,3,1,4,2,6] => 30
[5,3,1,4,6,2] => 36
[5,3,1,6,2,4] => 38
[5,3,1,6,4,2] => 42
[5,3,2,1,4,6] => 28
[5,3,2,1,6,4] => 34
[5,3,2,4,1,6] => 32
[5,3,2,4,6,1] => 38
[5,3,2,6,1,4] => 40
[5,3,2,6,4,1] => 44
[5,3,4,1,2,6] => 34
[5,3,4,1,6,2] => 40
[5,3,4,2,1,6] => 36
[5,3,4,2,6,1] => 42
[5,3,4,6,1,2] => 46
[5,3,4,6,2,1] => 48
[5,3,6,1,2,4] => 44
[5,3,6,1,4,2] => 48
[5,3,6,2,1,4] => 46
[5,3,6,2,4,1] => 50
[5,3,6,4,1,2] => 52
[5,3,6,4,2,1] => 54
[5,4,1,2,3,6] => 32
[5,4,1,2,6,3] => 38
[5,4,1,3,2,6] => 35
[5,4,1,3,6,2] => 41
[5,4,1,6,2,3] => 44
[5,4,1,6,3,2] => 47
[5,4,2,1,3,6] => 34
[5,4,2,1,6,3] => 40
[5,4,2,3,1,6] => 37
[5,4,2,3,6,1] => 43
[5,4,2,6,1,3] => 46
[5,4,2,6,3,1] => 49
[5,4,3,1,2,6] => 38
[5,4,3,1,6,2] => 44
[5,4,3,2,1,6] => 40
[5,4,3,2,6,1] => 46
[5,4,3,6,1,2] => 50
[5,4,3,6,2,1] => 52
[5,4,6,1,2,3] => 50
[5,4,6,1,3,2] => 53
[5,4,6,2,1,3] => 52
[5,4,6,2,3,1] => 55
[5,4,6,3,1,2] => 56
[5,4,6,3,2,1] => 58
[5,6,1,2,3,4] => 44
[5,6,1,2,4,3] => 48
[5,6,1,3,2,4] => 47
[5,6,1,3,4,2] => 51
[5,6,1,4,2,3] => 52
[5,6,1,4,3,2] => 55
[5,6,2,1,3,4] => 46
[5,6,2,1,4,3] => 50
[5,6,2,3,1,4] => 49
[5,6,2,3,4,1] => 53
[5,6,2,4,1,3] => 54
[5,6,2,4,3,1] => 57
[5,6,3,1,2,4] => 50
[5,6,3,1,4,2] => 54
[5,6,3,2,1,4] => 52
[5,6,3,2,4,1] => 56
[5,6,3,4,1,2] => 58
[5,6,3,4,2,1] => 60
[5,6,4,1,2,3] => 56
[5,6,4,1,3,2] => 59
[5,6,4,2,1,3] => 58
[5,6,4,2,3,1] => 61
[5,6,4,3,1,2] => 62
[5,6,4,3,2,1] => 64
[6,1,2,3,4,5] => 30
[6,1,2,3,5,4] => 35
[6,1,2,4,3,5] => 34
[6,1,2,4,5,3] => 39
[6,1,2,5,3,4] => 40
[6,1,2,5,4,3] => 44
[6,1,3,2,4,5] => 33
[6,1,3,2,5,4] => 38
[6,1,3,4,2,5] => 37
[6,1,3,4,5,2] => 42
[6,1,3,5,2,4] => 43
[6,1,3,5,4,2] => 47
[6,1,4,2,3,5] => 38
[6,1,4,2,5,3] => 43
[6,1,4,3,2,5] => 41
[6,1,4,3,5,2] => 46
[6,1,4,5,2,3] => 48
[6,1,4,5,3,2] => 51
[6,1,5,2,3,4] => 45
[6,1,5,2,4,3] => 49
[6,1,5,3,2,4] => 48
[6,1,5,3,4,2] => 52
[6,1,5,4,2,3] => 53
[6,1,5,4,3,2] => 56
[6,2,1,3,4,5] => 32
[6,2,1,3,5,4] => 37
[6,2,1,4,3,5] => 36
[6,2,1,4,5,3] => 41
[6,2,1,5,3,4] => 42
[6,2,1,5,4,3] => 46
[6,2,3,1,4,5] => 35
[6,2,3,1,5,4] => 40
[6,2,3,4,1,5] => 39
[6,2,3,4,5,1] => 44
[6,2,3,5,1,4] => 45
[6,2,3,5,4,1] => 49
[6,2,4,1,3,5] => 40
[6,2,4,1,5,3] => 45
[6,2,4,3,1,5] => 43
[6,2,4,3,5,1] => 48
[6,2,4,5,1,3] => 50
[6,2,4,5,3,1] => 53
[6,2,5,1,3,4] => 47
[6,2,5,1,4,3] => 51
[6,2,5,3,1,4] => 50
[6,2,5,3,4,1] => 54
[6,2,5,4,1,3] => 55
[6,2,5,4,3,1] => 58
[6,3,1,2,4,5] => 36
[6,3,1,2,5,4] => 41
[6,3,1,4,2,5] => 40
[6,3,1,4,5,2] => 45
[6,3,1,5,2,4] => 46
[6,3,1,5,4,2] => 50
[6,3,2,1,4,5] => 38
[6,3,2,1,5,4] => 43
[6,3,2,4,1,5] => 42
[6,3,2,4,5,1] => 47
[6,3,2,5,1,4] => 48
[6,3,2,5,4,1] => 52
[6,3,4,1,2,5] => 44
[6,3,4,1,5,2] => 49
[6,3,4,2,1,5] => 46
[6,3,4,2,5,1] => 51
[6,3,4,5,1,2] => 54
[6,3,4,5,2,1] => 56
[6,3,5,1,2,4] => 51
[6,3,5,1,4,2] => 55
[6,3,5,2,1,4] => 53
[6,3,5,2,4,1] => 57
[6,3,5,4,1,2] => 59
[6,3,5,4,2,1] => 61
[6,4,1,2,3,5] => 42
[6,4,1,2,5,3] => 47
[6,4,1,3,2,5] => 45
[6,4,1,3,5,2] => 50
[6,4,1,5,2,3] => 52
[6,4,1,5,3,2] => 55
[6,4,2,1,3,5] => 44
[6,4,2,1,5,3] => 49
[6,4,2,3,1,5] => 47
[6,4,2,3,5,1] => 52
[6,4,2,5,1,3] => 54
[6,4,2,5,3,1] => 57
[6,4,3,1,2,5] => 48
[6,4,3,1,5,2] => 53
[6,4,3,2,1,5] => 50
[6,4,3,2,5,1] => 55
[6,4,3,5,1,2] => 58
[6,4,3,5,2,1] => 60
[6,4,5,1,2,3] => 57
[6,4,5,1,3,2] => 60
[6,4,5,2,1,3] => 59
[6,4,5,2,3,1] => 62
[6,4,5,3,1,2] => 63
[6,4,5,3,2,1] => 65
[6,5,1,2,3,4] => 50
[6,5,1,2,4,3] => 54
[6,5,1,3,2,4] => 53
[6,5,1,3,4,2] => 57
[6,5,1,4,2,3] => 58
[6,5,1,4,3,2] => 61
[6,5,2,1,3,4] => 52
[6,5,2,1,4,3] => 56
[6,5,2,3,1,4] => 55
[6,5,2,3,4,1] => 59
[6,5,2,4,1,3] => 60
[6,5,2,4,3,1] => 63
[6,5,3,1,2,4] => 56
[6,5,3,1,4,2] => 60
[6,5,3,2,1,4] => 58
[6,5,3,2,4,1] => 62
[6,5,3,4,1,2] => 64
[6,5,3,4,2,1] => 66
[6,5,4,1,2,3] => 62
[6,5,4,1,3,2] => 65
[6,5,4,2,1,3] => 64
[6,5,4,2,3,1] => 67
[6,5,4,3,1,2] => 68
[6,5,4,3,2,1] => 70
click to show generating function       
Description
The inversion index of a permutation.
The inversion index of a permutation $\sigma=\sigma_1\sigma_2\ldots\sigma_n$ is defined as
$$ \sum_{\mbox{inversion pairs } (\sigma_i,\sigma_j)} \sigma_i $$
where $(\sigma_i,\sigma_j)$ is an inversion pair if i < j and $\sigma_i > \sigma_j$.
This equals the sum of the entries in the corresponding descending plane partition; see [1].
References
[1] Striker, J. A direct bijection between descending plane partitions with no special parts and permutation matrices arXiv:1002.3391
[2] Irregular triangle read by rows: row n gives expansion of g.f. for descending plane partitions of order n with weight equal to sum of the parts. OEIS:A198890
Code
def statistic(p):
    return sum( p[i-1] for i,j in p.inversions() )
Created
Aug 22, 2016 at 17:56 by Jessica Striker
Updated
Dec 30, 2016 at 10:30 by Christian Stump