Identifier
Identifier
  • St000342: Permutations ⟶ ℤ (values match St001168The vector space dimension of the tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$.)
Values
[1] => 1
[1,2] => 5
[2,1] => 4
[1,2,3] => 14
[1,3,2] => 13
[2,1,3] => 13
[2,3,1] => 11
[3,1,2] => 11
[3,2,1] => 10
[1,2,3,4] => 30
[1,2,4,3] => 29
[1,3,2,4] => 29
[1,3,4,2] => 27
[1,4,2,3] => 27
[1,4,3,2] => 26
[2,1,3,4] => 29
[2,1,4,3] => 28
[2,3,1,4] => 27
[2,3,4,1] => 24
[2,4,1,3] => 25
[2,4,3,1] => 23
[3,1,2,4] => 27
[3,1,4,2] => 25
[3,2,1,4] => 26
[3,2,4,1] => 23
[3,4,1,2] => 22
[3,4,2,1] => 21
[4,1,2,3] => 24
[4,1,3,2] => 23
[4,2,1,3] => 23
[4,2,3,1] => 21
[4,3,1,2] => 21
[4,3,2,1] => 20
[1,2,3,4,5] => 55
[1,2,3,5,4] => 54
[1,2,4,3,5] => 54
[1,2,4,5,3] => 52
[1,2,5,3,4] => 52
[1,2,5,4,3] => 51
[1,3,2,4,5] => 54
[1,3,2,5,4] => 53
[1,3,4,2,5] => 52
[1,3,4,5,2] => 49
[1,3,5,2,4] => 50
[1,3,5,4,2] => 48
[1,4,2,3,5] => 52
[1,4,2,5,3] => 50
[1,4,3,2,5] => 51
[1,4,3,5,2] => 48
[1,4,5,2,3] => 47
[1,4,5,3,2] => 46
[1,5,2,3,4] => 49
[1,5,2,4,3] => 48
[1,5,3,2,4] => 48
[1,5,3,4,2] => 46
[1,5,4,2,3] => 46
[1,5,4,3,2] => 45
[2,1,3,4,5] => 54
[2,1,3,5,4] => 53
[2,1,4,3,5] => 53
[2,1,4,5,3] => 51
[2,1,5,3,4] => 51
[2,1,5,4,3] => 50
[2,3,1,4,5] => 52
[2,3,1,5,4] => 51
[2,3,4,1,5] => 49
[2,3,4,5,1] => 45
[2,3,5,1,4] => 47
[2,3,5,4,1] => 44
[2,4,1,3,5] => 50
[2,4,1,5,3] => 48
[2,4,3,1,5] => 48
[2,4,3,5,1] => 44
[2,4,5,1,3] => 44
[2,4,5,3,1] => 42
[2,5,1,3,4] => 47
[2,5,1,4,3] => 46
[2,5,3,1,4] => 45
[2,5,3,4,1] => 42
[2,5,4,1,3] => 43
[2,5,4,3,1] => 41
[3,1,2,4,5] => 52
[3,1,2,5,4] => 51
[3,1,4,2,5] => 50
[3,1,4,5,2] => 47
[3,1,5,2,4] => 48
[3,1,5,4,2] => 46
[3,2,1,4,5] => 51
[3,2,1,5,4] => 50
[3,2,4,1,5] => 48
[3,2,4,5,1] => 44
[3,2,5,1,4] => 46
[3,2,5,4,1] => 43
[3,4,1,2,5] => 47
[3,4,1,5,2] => 44
[3,4,2,1,5] => 46
[3,4,2,5,1] => 42
[3,4,5,1,2] => 40
[3,4,5,2,1] => 39
[3,5,1,2,4] => 44
[3,5,1,4,2] => 42
[3,5,2,1,4] => 43
[3,5,2,4,1] => 40
[3,5,4,1,2] => 39
[3,5,4,2,1] => 38
[4,1,2,3,5] => 49
[4,1,2,5,3] => 47
[4,1,3,2,5] => 48
[4,1,3,5,2] => 45
[4,1,5,2,3] => 44
[4,1,5,3,2] => 43
[4,2,1,3,5] => 48
[4,2,1,5,3] => 46
[4,2,3,1,5] => 46
[4,2,3,5,1] => 42
[4,2,5,1,3] => 42
[4,2,5,3,1] => 40
[4,3,1,2,5] => 46
[4,3,1,5,2] => 43
[4,3,2,1,5] => 45
[4,3,2,5,1] => 41
[4,3,5,1,2] => 39
[4,3,5,2,1] => 38
[4,5,1,2,3] => 40
[4,5,1,3,2] => 39
[4,5,2,1,3] => 39
[4,5,2,3,1] => 37
[4,5,3,1,2] => 37
[4,5,3,2,1] => 36
[5,1,2,3,4] => 45
[5,1,2,4,3] => 44
[5,1,3,2,4] => 44
[5,1,3,4,2] => 42
[5,1,4,2,3] => 42
[5,1,4,3,2] => 41
[5,2,1,3,4] => 44
[5,2,1,4,3] => 43
[5,2,3,1,4] => 42
[5,2,3,4,1] => 39
[5,2,4,1,3] => 40
[5,2,4,3,1] => 38
[5,3,1,2,4] => 42
[5,3,1,4,2] => 40
[5,3,2,1,4] => 41
[5,3,2,4,1] => 38
[5,3,4,1,2] => 37
[5,3,4,2,1] => 36
[5,4,1,2,3] => 39
[5,4,1,3,2] => 38
[5,4,2,1,3] => 38
[5,4,2,3,1] => 36
[5,4,3,1,2] => 36
[5,4,3,2,1] => 35
[1,2,3,4,5,6] => 91
[1,2,3,4,6,5] => 90
[1,2,3,5,4,6] => 90
[1,2,3,5,6,4] => 88
[1,2,3,6,4,5] => 88
[1,2,3,6,5,4] => 87
[1,2,4,3,5,6] => 90
[1,2,4,3,6,5] => 89
[1,2,4,5,3,6] => 88
[1,2,4,5,6,3] => 85
[1,2,4,6,3,5] => 86
[1,2,4,6,5,3] => 84
[1,2,5,3,4,6] => 88
[1,2,5,3,6,4] => 86
[1,2,5,4,3,6] => 87
[1,2,5,4,6,3] => 84
[1,2,5,6,3,4] => 83
[1,2,5,6,4,3] => 82
[1,2,6,3,4,5] => 85
[1,2,6,3,5,4] => 84
[1,2,6,4,3,5] => 84
[1,2,6,4,5,3] => 82
[1,2,6,5,3,4] => 82
[1,2,6,5,4,3] => 81
[1,3,2,4,5,6] => 90
[1,3,2,4,6,5] => 89
[1,3,2,5,4,6] => 89
[1,3,2,5,6,4] => 87
[1,3,2,6,4,5] => 87
[1,3,2,6,5,4] => 86
[1,3,4,2,5,6] => 88
[1,3,4,2,6,5] => 87
[1,3,4,5,2,6] => 85
[1,3,4,5,6,2] => 81
[1,3,4,6,2,5] => 83
[1,3,4,6,5,2] => 80
[1,3,5,2,4,6] => 86
[1,3,5,2,6,4] => 84
[1,3,5,4,2,6] => 84
[1,3,5,4,6,2] => 80
[1,3,5,6,2,4] => 80
[1,3,5,6,4,2] => 78
[1,3,6,2,4,5] => 83
[1,3,6,2,5,4] => 82
[1,3,6,4,2,5] => 81
[1,3,6,4,5,2] => 78
[1,3,6,5,2,4] => 79
[1,3,6,5,4,2] => 77
[1,4,2,3,5,6] => 88
[1,4,2,3,6,5] => 87
[1,4,2,5,3,6] => 86
[1,4,2,5,6,3] => 83
[1,4,2,6,3,5] => 84
[1,4,2,6,5,3] => 82
[1,4,3,2,5,6] => 87
[1,4,3,2,6,5] => 86
[1,4,3,5,2,6] => 84
[1,4,3,5,6,2] => 80
[1,4,3,6,2,5] => 82
[1,4,3,6,5,2] => 79
[1,4,5,2,3,6] => 83
[1,4,5,2,6,3] => 80
[1,4,5,3,2,6] => 82
[1,4,5,3,6,2] => 78
[1,4,5,6,2,3] => 76
[1,4,5,6,3,2] => 75
[1,4,6,2,3,5] => 80
[1,4,6,2,5,3] => 78
[1,4,6,3,2,5] => 79
[1,4,6,3,5,2] => 76
[1,4,6,5,2,3] => 75
[1,4,6,5,3,2] => 74
[1,5,2,3,4,6] => 85
[1,5,2,3,6,4] => 83
[1,5,2,4,3,6] => 84
[1,5,2,4,6,3] => 81
[1,5,2,6,3,4] => 80
[1,5,2,6,4,3] => 79
[1,5,3,2,4,6] => 84
[1,5,3,2,6,4] => 82
[1,5,3,4,2,6] => 82
[1,5,3,4,6,2] => 78
[1,5,3,6,2,4] => 78
[1,5,3,6,4,2] => 76
[1,5,4,2,3,6] => 82
[1,5,4,2,6,3] => 79
[1,5,4,3,2,6] => 81
[1,5,4,3,6,2] => 77
[1,5,4,6,2,3] => 75
[1,5,4,6,3,2] => 74
[1,5,6,2,3,4] => 76
[1,5,6,2,4,3] => 75
[1,5,6,3,2,4] => 75
[1,5,6,3,4,2] => 73
[1,5,6,4,2,3] => 73
[1,5,6,4,3,2] => 72
[1,6,2,3,4,5] => 81
[1,6,2,3,5,4] => 80
[1,6,2,4,3,5] => 80
[1,6,2,4,5,3] => 78
[1,6,2,5,3,4] => 78
[1,6,2,5,4,3] => 77
[1,6,3,2,4,5] => 80
[1,6,3,2,5,4] => 79
[1,6,3,4,2,5] => 78
[1,6,3,4,5,2] => 75
[1,6,3,5,2,4] => 76
[1,6,3,5,4,2] => 74
[1,6,4,2,3,5] => 78
[1,6,4,2,5,3] => 76
[1,6,4,3,2,5] => 77
[1,6,4,3,5,2] => 74
[1,6,4,5,2,3] => 73
[1,6,4,5,3,2] => 72
[1,6,5,2,3,4] => 75
[1,6,5,2,4,3] => 74
[1,6,5,3,2,4] => 74
[1,6,5,3,4,2] => 72
[1,6,5,4,2,3] => 72
[1,6,5,4,3,2] => 71
[2,1,3,4,5,6] => 90
[2,1,3,4,6,5] => 89
[2,1,3,5,4,6] => 89
[2,1,3,5,6,4] => 87
[2,1,3,6,4,5] => 87
[2,1,3,6,5,4] => 86
[2,1,4,3,5,6] => 89
[2,1,4,3,6,5] => 88
[2,1,4,5,3,6] => 87
[2,1,4,5,6,3] => 84
[2,1,4,6,3,5] => 85
[2,1,4,6,5,3] => 83
[2,1,5,3,4,6] => 87
[2,1,5,3,6,4] => 85
[2,1,5,4,3,6] => 86
[2,1,5,4,6,3] => 83
[2,1,5,6,3,4] => 82
[2,1,5,6,4,3] => 81
[2,1,6,3,4,5] => 84
[2,1,6,3,5,4] => 83
[2,1,6,4,3,5] => 83
[2,1,6,4,5,3] => 81
[2,1,6,5,3,4] => 81
[2,1,6,5,4,3] => 80
[2,3,1,4,5,6] => 88
[2,3,1,4,6,5] => 87
[2,3,1,5,4,6] => 87
[2,3,1,5,6,4] => 85
[2,3,1,6,4,5] => 85
[2,3,1,6,5,4] => 84
[2,3,4,1,5,6] => 85
[2,3,4,1,6,5] => 84
[2,3,4,5,1,6] => 81
[2,3,4,5,6,1] => 76
[2,3,4,6,1,5] => 79
[2,3,4,6,5,1] => 75
[2,3,5,1,4,6] => 83
[2,3,5,1,6,4] => 81
[2,3,5,4,1,6] => 80
[2,3,5,4,6,1] => 75
[2,3,5,6,1,4] => 76
[2,3,5,6,4,1] => 73
[2,3,6,1,4,5] => 80
[2,3,6,1,5,4] => 79
[2,3,6,4,1,5] => 77
[2,3,6,4,5,1] => 73
[2,3,6,5,1,4] => 75
[2,3,6,5,4,1] => 72
[2,4,1,3,5,6] => 86
[2,4,1,3,6,5] => 85
[2,4,1,5,3,6] => 84
[2,4,1,5,6,3] => 81
[2,4,1,6,3,5] => 82
[2,4,1,6,5,3] => 80
[2,4,3,1,5,6] => 84
[2,4,3,1,6,5] => 83
[2,4,3,5,1,6] => 80
[2,4,3,5,6,1] => 75
[2,4,3,6,1,5] => 78
[2,4,3,6,5,1] => 74
[2,4,5,1,3,6] => 80
[2,4,5,1,6,3] => 77
[2,4,5,3,1,6] => 78
[2,4,5,3,6,1] => 73
[2,4,5,6,1,3] => 72
[2,4,5,6,3,1] => 70
[2,4,6,1,3,5] => 77
[2,4,6,1,5,3] => 75
[2,4,6,3,1,5] => 75
[2,4,6,3,5,1] => 71
[2,4,6,5,1,3] => 71
[2,4,6,5,3,1] => 69
[2,5,1,3,4,6] => 83
[2,5,1,3,6,4] => 81
[2,5,1,4,3,6] => 82
[2,5,1,4,6,3] => 79
[2,5,1,6,3,4] => 78
[2,5,1,6,4,3] => 77
[2,5,3,1,4,6] => 81
[2,5,3,1,6,4] => 79
[2,5,3,4,1,6] => 78
[2,5,3,4,6,1] => 73
[2,5,3,6,1,4] => 74
[2,5,3,6,4,1] => 71
[2,5,4,1,3,6] => 79
[2,5,4,1,6,3] => 76
[2,5,4,3,1,6] => 77
[2,5,4,3,6,1] => 72
[2,5,4,6,1,3] => 71
[2,5,4,6,3,1] => 69
[2,5,6,1,3,4] => 73
[2,5,6,1,4,3] => 72
[2,5,6,3,1,4] => 71
[2,5,6,3,4,1] => 68
[2,5,6,4,1,3] => 69
[2,5,6,4,3,1] => 67
[2,6,1,3,4,5] => 79
[2,6,1,3,5,4] => 78
[2,6,1,4,3,5] => 78
[2,6,1,4,5,3] => 76
[2,6,1,5,3,4] => 76
[2,6,1,5,4,3] => 75
[2,6,3,1,4,5] => 77
[2,6,3,1,5,4] => 76
[2,6,3,4,1,5] => 74
[2,6,3,4,5,1] => 70
[2,6,3,5,1,4] => 72
[2,6,3,5,4,1] => 69
[2,6,4,1,3,5] => 75
[2,6,4,1,5,3] => 73
[2,6,4,3,1,5] => 73
[2,6,4,3,5,1] => 69
[2,6,4,5,1,3] => 69
[2,6,4,5,3,1] => 67
[2,6,5,1,3,4] => 72
[2,6,5,1,4,3] => 71
[2,6,5,3,1,4] => 70
[2,6,5,3,4,1] => 67
[2,6,5,4,1,3] => 68
[2,6,5,4,3,1] => 66
[3,1,2,4,5,6] => 88
[3,1,2,4,6,5] => 87
[3,1,2,5,4,6] => 87
[3,1,2,5,6,4] => 85
[3,1,2,6,4,5] => 85
[3,1,2,6,5,4] => 84
[3,1,4,2,5,6] => 86
[3,1,4,2,6,5] => 85
[3,1,4,5,2,6] => 83
[3,1,4,5,6,2] => 79
[3,1,4,6,2,5] => 81
[3,1,4,6,5,2] => 78
[3,1,5,2,4,6] => 84
[3,1,5,2,6,4] => 82
[3,1,5,4,2,6] => 82
[3,1,5,4,6,2] => 78
[3,1,5,6,2,4] => 78
[3,1,5,6,4,2] => 76
[3,1,6,2,4,5] => 81
[3,1,6,2,5,4] => 80
[3,1,6,4,2,5] => 79
[3,1,6,4,5,2] => 76
[3,1,6,5,2,4] => 77
[3,1,6,5,4,2] => 75
[3,2,1,4,5,6] => 87
[3,2,1,4,6,5] => 86
[3,2,1,5,4,6] => 86
[3,2,1,5,6,4] => 84
[3,2,1,6,4,5] => 84
[3,2,1,6,5,4] => 83
[3,2,4,1,5,6] => 84
[3,2,4,1,6,5] => 83
[3,2,4,5,1,6] => 80
[3,2,4,5,6,1] => 75
[3,2,4,6,1,5] => 78
[3,2,4,6,5,1] => 74
[3,2,5,1,4,6] => 82
[3,2,5,1,6,4] => 80
[3,2,5,4,1,6] => 79
[3,2,5,4,6,1] => 74
[3,2,5,6,1,4] => 75
[3,2,5,6,4,1] => 72
[3,2,6,1,4,5] => 79
[3,2,6,1,5,4] => 78
[3,2,6,4,1,5] => 76
[3,2,6,4,5,1] => 72
[3,2,6,5,1,4] => 74
[3,2,6,5,4,1] => 71
[3,4,1,2,5,6] => 83
[3,4,1,2,6,5] => 82
[3,4,1,5,2,6] => 80
[3,4,1,5,6,2] => 76
[3,4,1,6,2,5] => 78
[3,4,1,6,5,2] => 75
[3,4,2,1,5,6] => 82
[3,4,2,1,6,5] => 81
[3,4,2,5,1,6] => 78
[3,4,2,5,6,1] => 73
[3,4,2,6,1,5] => 76
[3,4,2,6,5,1] => 72
[3,4,5,1,2,6] => 76
[3,4,5,1,6,2] => 72
[3,4,5,2,1,6] => 75
[3,4,5,2,6,1] => 70
[3,4,5,6,1,2] => 67
[3,4,5,6,2,1] => 66
[3,4,6,1,2,5] => 73
[3,4,6,1,5,2] => 70
[3,4,6,2,1,5] => 72
[3,4,6,2,5,1] => 68
[3,4,6,5,1,2] => 66
[3,4,6,5,2,1] => 65
[3,5,1,2,4,6] => 80
[3,5,1,2,6,4] => 78
[3,5,1,4,2,6] => 78
[3,5,1,4,6,2] => 74
[3,5,1,6,2,4] => 74
[3,5,1,6,4,2] => 72
[3,5,2,1,4,6] => 79
[3,5,2,1,6,4] => 77
[3,5,2,4,1,6] => 76
[3,5,2,4,6,1] => 71
[3,5,2,6,1,4] => 72
[3,5,2,6,4,1] => 69
[3,5,4,1,2,6] => 75
[3,5,4,1,6,2] => 71
[3,5,4,2,1,6] => 74
[3,5,4,2,6,1] => 69
[3,5,4,6,1,2] => 66
[3,5,4,6,2,1] => 65
[3,5,6,1,2,4] => 69
[3,5,6,1,4,2] => 67
[3,5,6,2,1,4] => 68
[3,5,6,2,4,1] => 65
[3,5,6,4,1,2] => 64
[3,5,6,4,2,1] => 63
[3,6,1,2,4,5] => 76
[3,6,1,2,5,4] => 75
[3,6,1,4,2,5] => 74
[3,6,1,4,5,2] => 71
[3,6,1,5,2,4] => 72
[3,6,1,5,4,2] => 70
[3,6,2,1,4,5] => 75
[3,6,2,1,5,4] => 74
[3,6,2,4,1,5] => 72
[3,6,2,4,5,1] => 68
[3,6,2,5,1,4] => 70
[3,6,2,5,4,1] => 67
[3,6,4,1,2,5] => 71
[3,6,4,1,5,2] => 68
[3,6,4,2,1,5] => 70
[3,6,4,2,5,1] => 66
[3,6,4,5,1,2] => 64
[3,6,4,5,2,1] => 63
[3,6,5,1,2,4] => 68
[3,6,5,1,4,2] => 66
[3,6,5,2,1,4] => 67
[3,6,5,2,4,1] => 64
[3,6,5,4,1,2] => 63
[3,6,5,4,2,1] => 62
[4,1,2,3,5,6] => 85
[4,1,2,3,6,5] => 84
[4,1,2,5,3,6] => 83
[4,1,2,5,6,3] => 80
[4,1,2,6,3,5] => 81
[4,1,2,6,5,3] => 79
[4,1,3,2,5,6] => 84
[4,1,3,2,6,5] => 83
[4,1,3,5,2,6] => 81
[4,1,3,5,6,2] => 77
[4,1,3,6,2,5] => 79
[4,1,3,6,5,2] => 76
[4,1,5,2,3,6] => 80
[4,1,5,2,6,3] => 77
[4,1,5,3,2,6] => 79
[4,1,5,3,6,2] => 75
[4,1,5,6,2,3] => 73
[4,1,5,6,3,2] => 72
[4,1,6,2,3,5] => 77
[4,1,6,2,5,3] => 75
[4,1,6,3,2,5] => 76
[4,1,6,3,5,2] => 73
[4,1,6,5,2,3] => 72
[4,1,6,5,3,2] => 71
[4,2,1,3,5,6] => 84
[4,2,1,3,6,5] => 83
[4,2,1,5,3,6] => 82
[4,2,1,5,6,3] => 79
[4,2,1,6,3,5] => 80
[4,2,1,6,5,3] => 78
[4,2,3,1,5,6] => 82
[4,2,3,1,6,5] => 81
[4,2,3,5,1,6] => 78
[4,2,3,5,6,1] => 73
[4,2,3,6,1,5] => 76
[4,2,3,6,5,1] => 72
[4,2,5,1,3,6] => 78
[4,2,5,1,6,3] => 75
[4,2,5,3,1,6] => 76
[4,2,5,3,6,1] => 71
[4,2,5,6,1,3] => 70
[4,2,5,6,3,1] => 68
[4,2,6,1,3,5] => 75
[4,2,6,1,5,3] => 73
[4,2,6,3,1,5] => 73
[4,2,6,3,5,1] => 69
[4,2,6,5,1,3] => 69
[4,2,6,5,3,1] => 67
[4,3,1,2,5,6] => 82
[4,3,1,2,6,5] => 81
[4,3,1,5,2,6] => 79
[4,3,1,5,6,2] => 75
[4,3,1,6,2,5] => 77
[4,3,1,6,5,2] => 74
[4,3,2,1,5,6] => 81
[4,3,2,1,6,5] => 80
[4,3,2,5,1,6] => 77
[4,3,2,5,6,1] => 72
[4,3,2,6,1,5] => 75
[4,3,2,6,5,1] => 71
[4,3,5,1,2,6] => 75
[4,3,5,1,6,2] => 71
[4,3,5,2,1,6] => 74
[4,3,5,2,6,1] => 69
[4,3,5,6,1,2] => 66
[4,3,5,6,2,1] => 65
[4,3,6,1,2,5] => 72
[4,3,6,1,5,2] => 69
[4,3,6,2,1,5] => 71
[4,3,6,2,5,1] => 67
[4,3,6,5,1,2] => 65
[4,3,6,5,2,1] => 64
[4,5,1,2,3,6] => 76
[4,5,1,2,6,3] => 73
[4,5,1,3,2,6] => 75
[4,5,1,3,6,2] => 71
[4,5,1,6,2,3] => 69
[4,5,1,6,3,2] => 68
[4,5,2,1,3,6] => 75
[4,5,2,1,6,3] => 72
[4,5,2,3,1,6] => 73
[4,5,2,3,6,1] => 68
[4,5,2,6,1,3] => 67
[4,5,2,6,3,1] => 65
[4,5,3,1,2,6] => 73
[4,5,3,1,6,2] => 69
[4,5,3,2,1,6] => 72
[4,5,3,2,6,1] => 67
[4,5,3,6,1,2] => 64
[4,5,3,6,2,1] => 63
[4,5,6,1,2,3] => 64
[4,5,6,1,3,2] => 63
[4,5,6,2,1,3] => 63
[4,5,6,2,3,1] => 61
[4,5,6,3,1,2] => 61
[4,5,6,3,2,1] => 60
[4,6,1,2,3,5] => 72
[4,6,1,2,5,3] => 70
[4,6,1,3,2,5] => 71
[4,6,1,3,5,2] => 68
[4,6,1,5,2,3] => 67
[4,6,1,5,3,2] => 66
[4,6,2,1,3,5] => 71
[4,6,2,1,5,3] => 69
[4,6,2,3,1,5] => 69
[4,6,2,3,5,1] => 65
[4,6,2,5,1,3] => 65
[4,6,2,5,3,1] => 63
[4,6,3,1,2,5] => 69
[4,6,3,1,5,2] => 66
[4,6,3,2,1,5] => 68
[4,6,3,2,5,1] => 64
[4,6,3,5,1,2] => 62
[4,6,3,5,2,1] => 61
[4,6,5,1,2,3] => 63
[4,6,5,1,3,2] => 62
[4,6,5,2,1,3] => 62
[4,6,5,2,3,1] => 60
[4,6,5,3,1,2] => 60
[4,6,5,3,2,1] => 59
[5,1,2,3,4,6] => 81
[5,1,2,3,6,4] => 79
[5,1,2,4,3,6] => 80
[5,1,2,4,6,3] => 77
[5,1,2,6,3,4] => 76
[5,1,2,6,4,3] => 75
[5,1,3,2,4,6] => 80
[5,1,3,2,6,4] => 78
[5,1,3,4,2,6] => 78
[5,1,3,4,6,2] => 74
[5,1,3,6,2,4] => 74
[5,1,3,6,4,2] => 72
[5,1,4,2,3,6] => 78
[5,1,4,2,6,3] => 75
[5,1,4,3,2,6] => 77
[5,1,4,3,6,2] => 73
[5,1,4,6,2,3] => 71
[5,1,4,6,3,2] => 70
[5,1,6,2,3,4] => 72
[5,1,6,2,4,3] => 71
[5,1,6,3,2,4] => 71
[5,1,6,3,4,2] => 69
[5,1,6,4,2,3] => 69
[5,1,6,4,3,2] => 68
[5,2,1,3,4,6] => 80
[5,2,1,3,6,4] => 78
[5,2,1,4,3,6] => 79
[5,2,1,4,6,3] => 76
[5,2,1,6,3,4] => 75
[5,2,1,6,4,3] => 74
[5,2,3,1,4,6] => 78
[5,2,3,1,6,4] => 76
[5,2,3,4,1,6] => 75
[5,2,3,4,6,1] => 70
[5,2,3,6,1,4] => 71
[5,2,3,6,4,1] => 68
[5,2,4,1,3,6] => 76
[5,2,4,1,6,3] => 73
[5,2,4,3,1,6] => 74
[5,2,4,3,6,1] => 69
[5,2,4,6,1,3] => 68
[5,2,4,6,3,1] => 66
[5,2,6,1,3,4] => 70
[5,2,6,1,4,3] => 69
[5,2,6,3,1,4] => 68
[5,2,6,3,4,1] => 65
[5,2,6,4,1,3] => 66
[5,2,6,4,3,1] => 64
[5,3,1,2,4,6] => 78
[5,3,1,2,6,4] => 76
[5,3,1,4,2,6] => 76
[5,3,1,4,6,2] => 72
[5,3,1,6,2,4] => 72
[5,3,1,6,4,2] => 70
[5,3,2,1,4,6] => 77
[5,3,2,1,6,4] => 75
[5,3,2,4,1,6] => 74
[5,3,2,4,6,1] => 69
[5,3,2,6,1,4] => 70
[5,3,2,6,4,1] => 67
[5,3,4,1,2,6] => 73
[5,3,4,1,6,2] => 69
[5,3,4,2,1,6] => 72
[5,3,4,2,6,1] => 67
[5,3,4,6,1,2] => 64
[5,3,4,6,2,1] => 63
[5,3,6,1,2,4] => 67
[5,3,6,1,4,2] => 65
[5,3,6,2,1,4] => 66
[5,3,6,2,4,1] => 63
[5,3,6,4,1,2] => 62
[5,3,6,4,2,1] => 61
[5,4,1,2,3,6] => 75
[5,4,1,2,6,3] => 72
[5,4,1,3,2,6] => 74
[5,4,1,3,6,2] => 70
[5,4,1,6,2,3] => 68
[5,4,1,6,3,2] => 67
[5,4,2,1,3,6] => 74
[5,4,2,1,6,3] => 71
[5,4,2,3,1,6] => 72
[5,4,2,3,6,1] => 67
[5,4,2,6,1,3] => 66
[5,4,2,6,3,1] => 64
[5,4,3,1,2,6] => 72
[5,4,3,1,6,2] => 68
[5,4,3,2,1,6] => 71
[5,4,3,2,6,1] => 66
[5,4,3,6,1,2] => 63
[5,4,3,6,2,1] => 62
[5,4,6,1,2,3] => 63
[5,4,6,1,3,2] => 62
[5,4,6,2,1,3] => 62
[5,4,6,2,3,1] => 60
[5,4,6,3,1,2] => 60
[5,4,6,3,2,1] => 59
[5,6,1,2,3,4] => 67
[5,6,1,2,4,3] => 66
[5,6,1,3,2,4] => 66
[5,6,1,3,4,2] => 64
[5,6,1,4,2,3] => 64
[5,6,1,4,3,2] => 63
[5,6,2,1,3,4] => 66
[5,6,2,1,4,3] => 65
[5,6,2,3,1,4] => 64
[5,6,2,3,4,1] => 61
[5,6,2,4,1,3] => 62
[5,6,2,4,3,1] => 60
[5,6,3,1,2,4] => 64
[5,6,3,1,4,2] => 62
[5,6,3,2,1,4] => 63
[5,6,3,2,4,1] => 60
[5,6,3,4,1,2] => 59
[5,6,3,4,2,1] => 58
[5,6,4,1,2,3] => 61
[5,6,4,1,3,2] => 60
[5,6,4,2,1,3] => 60
[5,6,4,2,3,1] => 58
[5,6,4,3,1,2] => 58
[5,6,4,3,2,1] => 57
[6,1,2,3,4,5] => 76
[6,1,2,3,5,4] => 75
[6,1,2,4,3,5] => 75
[6,1,2,4,5,3] => 73
[6,1,2,5,3,4] => 73
[6,1,2,5,4,3] => 72
[6,1,3,2,4,5] => 75
[6,1,3,2,5,4] => 74
[6,1,3,4,2,5] => 73
[6,1,3,4,5,2] => 70
[6,1,3,5,2,4] => 71
[6,1,3,5,4,2] => 69
[6,1,4,2,3,5] => 73
[6,1,4,2,5,3] => 71
[6,1,4,3,2,5] => 72
[6,1,4,3,5,2] => 69
[6,1,4,5,2,3] => 68
[6,1,4,5,3,2] => 67
[6,1,5,2,3,4] => 70
[6,1,5,2,4,3] => 69
[6,1,5,3,2,4] => 69
[6,1,5,3,4,2] => 67
[6,1,5,4,2,3] => 67
[6,1,5,4,3,2] => 66
[6,2,1,3,4,5] => 75
[6,2,1,3,5,4] => 74
[6,2,1,4,3,5] => 74
[6,2,1,4,5,3] => 72
[6,2,1,5,3,4] => 72
[6,2,1,5,4,3] => 71
[6,2,3,1,4,5] => 73
[6,2,3,1,5,4] => 72
[6,2,3,4,1,5] => 70
[6,2,3,4,5,1] => 66
[6,2,3,5,1,4] => 68
[6,2,3,5,4,1] => 65
[6,2,4,1,3,5] => 71
[6,2,4,1,5,3] => 69
[6,2,4,3,1,5] => 69
[6,2,4,3,5,1] => 65
[6,2,4,5,1,3] => 65
[6,2,4,5,3,1] => 63
[6,2,5,1,3,4] => 68
[6,2,5,1,4,3] => 67
[6,2,5,3,1,4] => 66
[6,2,5,3,4,1] => 63
[6,2,5,4,1,3] => 64
[6,2,5,4,3,1] => 62
[6,3,1,2,4,5] => 73
[6,3,1,2,5,4] => 72
[6,3,1,4,2,5] => 71
[6,3,1,4,5,2] => 68
[6,3,1,5,2,4] => 69
[6,3,1,5,4,2] => 67
[6,3,2,1,4,5] => 72
[6,3,2,1,5,4] => 71
[6,3,2,4,1,5] => 69
[6,3,2,4,5,1] => 65
[6,3,2,5,1,4] => 67
[6,3,2,5,4,1] => 64
[6,3,4,1,2,5] => 68
[6,3,4,1,5,2] => 65
[6,3,4,2,1,5] => 67
[6,3,4,2,5,1] => 63
[6,3,4,5,1,2] => 61
[6,3,4,5,2,1] => 60
[6,3,5,1,2,4] => 65
[6,3,5,1,4,2] => 63
[6,3,5,2,1,4] => 64
[6,3,5,2,4,1] => 61
[6,3,5,4,1,2] => 60
[6,3,5,4,2,1] => 59
[6,4,1,2,3,5] => 70
[6,4,1,2,5,3] => 68
[6,4,1,3,2,5] => 69
[6,4,1,3,5,2] => 66
[6,4,1,5,2,3] => 65
[6,4,1,5,3,2] => 64
[6,4,2,1,3,5] => 69
[6,4,2,1,5,3] => 67
[6,4,2,3,1,5] => 67
[6,4,2,3,5,1] => 63
[6,4,2,5,1,3] => 63
[6,4,2,5,3,1] => 61
[6,4,3,1,2,5] => 67
[6,4,3,1,5,2] => 64
[6,4,3,2,1,5] => 66
[6,4,3,2,5,1] => 62
[6,4,3,5,1,2] => 60
[6,4,3,5,2,1] => 59
[6,4,5,1,2,3] => 61
[6,4,5,1,3,2] => 60
[6,4,5,2,1,3] => 60
[6,4,5,2,3,1] => 58
[6,4,5,3,1,2] => 58
[6,4,5,3,2,1] => 57
[6,5,1,2,3,4] => 66
[6,5,1,2,4,3] => 65
[6,5,1,3,2,4] => 65
[6,5,1,3,4,2] => 63
[6,5,1,4,2,3] => 63
[6,5,1,4,3,2] => 62
[6,5,2,1,3,4] => 65
[6,5,2,1,4,3] => 64
[6,5,2,3,1,4] => 63
[6,5,2,3,4,1] => 60
[6,5,2,4,1,3] => 61
[6,5,2,4,3,1] => 59
[6,5,3,1,2,4] => 63
[6,5,3,1,4,2] => 61
[6,5,3,2,1,4] => 62
[6,5,3,2,4,1] => 59
[6,5,3,4,1,2] => 58
[6,5,3,4,2,1] => 57
[6,5,4,1,2,3] => 60
[6,5,4,1,3,2] => 59
[6,5,4,2,1,3] => 59
[6,5,4,2,3,1] => 57
[6,5,4,3,1,2] => 57
[6,5,4,3,2,1] => 56
[1,2,3,4,5,6,7] => 140
[1,2,3,4,5,7,6] => 139
[1,2,3,4,6,5,7] => 139
[1,2,3,4,6,7,5] => 137
[1,2,3,4,7,5,6] => 137
[1,2,3,4,7,6,5] => 136
[1,2,3,5,4,6,7] => 139
[1,2,3,5,4,7,6] => 138
[1,2,3,5,6,4,7] => 137
[1,2,3,5,6,7,4] => 134
[1,2,3,5,7,4,6] => 135
[1,2,3,5,7,6,4] => 133
[1,2,3,6,4,5,7] => 137
[1,2,3,6,4,7,5] => 135
[1,2,3,6,5,4,7] => 136
[1,2,3,6,5,7,4] => 133
[1,2,3,6,7,4,5] => 132
[1,2,3,6,7,5,4] => 131
[1,2,3,7,4,5,6] => 134
[1,2,3,7,4,6,5] => 133
[1,2,3,7,5,4,6] => 133
[1,2,3,7,5,6,4] => 131
[1,2,3,7,6,4,5] => 131
[1,2,3,7,6,5,4] => 130
[1,2,4,3,5,6,7] => 139
[1,2,4,3,5,7,6] => 138
[1,2,4,3,6,5,7] => 138
[1,2,4,3,6,7,5] => 136
[1,2,4,3,7,5,6] => 136
[1,2,4,3,7,6,5] => 135
[1,2,4,5,3,6,7] => 137
[1,2,4,5,3,7,6] => 136
[1,2,4,5,6,3,7] => 134
[1,2,4,5,6,7,3] => 130
[1,2,4,5,7,3,6] => 132
[1,2,4,5,7,6,3] => 129
[1,2,4,6,3,5,7] => 135
[1,2,4,6,3,7,5] => 133
[1,2,4,6,5,3,7] => 133
[1,2,4,6,5,7,3] => 129
[1,2,4,6,7,3,5] => 129
[1,2,4,6,7,5,3] => 127
[1,2,4,7,3,5,6] => 132
[1,2,4,7,3,6,5] => 131
[1,2,4,7,5,3,6] => 130
[1,2,4,7,5,6,3] => 127
[1,2,4,7,6,3,5] => 128
[1,2,4,7,6,5,3] => 126
[1,2,5,3,4,6,7] => 137
[1,2,5,3,4,7,6] => 136
[1,2,5,3,6,4,7] => 135
[1,2,5,3,6,7,4] => 132
[1,2,5,3,7,4,6] => 133
[1,2,5,3,7,6,4] => 131
[1,2,5,4,3,6,7] => 136
[1,2,5,4,3,7,6] => 135
[1,2,5,4,6,3,7] => 133
[1,2,5,4,6,7,3] => 129
[1,2,5,4,7,3,6] => 131
[1,2,5,4,7,6,3] => 128
[1,2,5,6,3,4,7] => 132
[1,2,5,6,3,7,4] => 129
[1,2,5,6,4,3,7] => 131
[1,2,5,6,4,7,3] => 127
[1,2,5,6,7,3,4] => 125
[1,2,5,6,7,4,3] => 124
[1,2,5,7,3,4,6] => 129
[1,2,5,7,3,6,4] => 127
[1,2,5,7,4,3,6] => 128
[1,2,5,7,4,6,3] => 125
[1,2,5,7,6,3,4] => 124
[1,2,5,7,6,4,3] => 123
[1,2,6,3,4,5,7] => 134
[1,2,6,3,4,7,5] => 132
[1,2,6,3,5,4,7] => 133
[1,2,6,3,5,7,4] => 130
[1,2,6,3,7,4,5] => 129
[1,2,6,3,7,5,4] => 128
[1,2,6,4,3,5,7] => 133
[1,2,6,4,3,7,5] => 131
[1,2,6,4,5,3,7] => 131
[1,2,6,4,5,7,3] => 127
[1,2,6,4,7,3,5] => 127
[1,2,6,4,7,5,3] => 125
[1,2,6,5,3,4,7] => 131
[1,2,6,5,3,7,4] => 128
[1,2,6,5,4,3,7] => 130
[1,2,6,5,4,7,3] => 126
[1,2,6,5,7,3,4] => 124
[1,2,6,5,7,4,3] => 123
[1,2,6,7,3,4,5] => 125
[1,2,6,7,3,5,4] => 124
[1,2,6,7,4,3,5] => 124
[1,2,6,7,4,5,3] => 122
[1,2,6,7,5,3,4] => 122
[1,2,6,7,5,4,3] => 121
[1,2,7,3,4,5,6] => 130
[1,2,7,3,4,6,5] => 129
[1,2,7,3,5,4,6] => 129
[1,2,7,3,5,6,4] => 127
[1,2,7,3,6,4,5] => 127
[1,2,7,3,6,5,4] => 126
[1,2,7,4,3,5,6] => 129
[1,2,7,4,3,6,5] => 128
[1,2,7,4,5,3,6] => 127
[1,2,7,4,5,6,3] => 124
[1,2,7,4,6,3,5] => 125
[1,2,7,4,6,5,3] => 123
[1,2,7,5,3,4,6] => 127
[1,2,7,5,3,6,4] => 125
[1,2,7,5,4,3,6] => 126
[1,2,7,5,4,6,3] => 123
[1,2,7,5,6,3,4] => 122
[1,2,7,5,6,4,3] => 121
[1,2,7,6,3,4,5] => 124
[1,2,7,6,3,5,4] => 123
[1,2,7,6,4,3,5] => 123
[1,2,7,6,4,5,3] => 121
[1,2,7,6,5,3,4] => 121
[1,2,7,6,5,4,3] => 120
[1,3,2,4,5,6,7] => 139
[1,3,2,4,5,7,6] => 138
[1,3,2,4,6,5,7] => 138
[1,3,2,4,6,7,5] => 136
[1,3,2,4,7,5,6] => 136
[1,3,2,4,7,6,5] => 135
[1,3,2,5,4,6,7] => 138
[1,3,2,5,4,7,6] => 137
[1,3,2,5,6,4,7] => 136
[1,3,2,5,6,7,4] => 133
[1,3,2,5,7,4,6] => 134
[1,3,2,5,7,6,4] => 132
[1,3,2,6,4,5,7] => 136
[1,3,2,6,4,7,5] => 134
[1,3,2,6,5,4,7] => 135
[1,3,2,6,5,7,4] => 132
[1,3,2,6,7,4,5] => 131
[1,3,2,6,7,5,4] => 130
[1,3,2,7,4,5,6] => 133
[1,3,2,7,4,6,5] => 132
[1,3,2,7,5,4,6] => 132
[1,3,2,7,5,6,4] => 130
[1,3,2,7,6,4,5] => 130
[1,3,2,7,6,5,4] => 129
[1,3,4,2,5,6,7] => 137
[1,3,4,2,5,7,6] => 136
[1,3,4,2,6,5,7] => 136
[1,3,4,2,6,7,5] => 134
[1,3,4,2,7,5,6] => 134
[1,3,4,2,7,6,5] => 133
[1,3,4,5,2,6,7] => 134
[1,3,4,5,2,7,6] => 133
[1,3,4,5,6,2,7] => 130
[1,3,4,5,6,7,2] => 125
[1,3,4,5,7,2,6] => 128
[1,3,4,5,7,6,2] => 124
[1,3,4,6,2,5,7] => 132
[1,3,4,6,2,7,5] => 130
[1,3,4,6,5,2,7] => 129
[1,3,4,6,5,7,2] => 124
[1,3,4,6,7,2,5] => 125
[1,3,4,6,7,5,2] => 122
[1,3,4,7,2,5,6] => 129
[1,3,4,7,2,6,5] => 128
[1,3,4,7,5,2,6] => 126
[1,3,4,7,5,6,2] => 122
[1,3,4,7,6,2,5] => 124
[1,3,4,7,6,5,2] => 121
[1,3,5,2,4,6,7] => 135
[1,3,5,2,4,7,6] => 134
[1,3,5,2,6,4,7] => 133
[1,3,5,2,6,7,4] => 130
[1,3,5,2,7,4,6] => 131
[1,3,5,2,7,6,4] => 129
[1,3,5,4,2,6,7] => 133
[1,3,5,4,2,7,6] => 132
[1,3,5,4,6,2,7] => 129
[1,3,5,4,6,7,2] => 124
[1,3,5,4,7,2,6] => 127
[1,3,5,4,7,6,2] => 123
[1,3,5,6,2,4,7] => 129
[1,3,5,6,2,7,4] => 126
[1,3,5,6,4,2,7] => 127
[1,3,5,6,4,7,2] => 122
[1,3,5,6,7,2,4] => 121
[1,3,5,6,7,4,2] => 119
[1,3,5,7,2,4,6] => 126
[1,3,5,7,2,6,4] => 124
[1,3,5,7,4,2,6] => 124
[1,3,5,7,4,6,2] => 120
[1,3,5,7,6,2,4] => 120
[1,3,5,7,6,4,2] => 118
[1,3,6,2,4,5,7] => 132
[1,3,6,2,4,7,5] => 130
[1,3,6,2,5,4,7] => 131
[1,3,6,2,5,7,4] => 128
[1,3,6,2,7,4,5] => 127
[1,3,6,2,7,5,4] => 126
[1,3,6,4,2,5,7] => 130
[1,3,6,4,2,7,5] => 128
[1,3,6,4,5,2,7] => 127
[1,3,6,4,5,7,2] => 122
[1,3,6,4,7,2,5] => 123
[1,3,6,4,7,5,2] => 120
[1,3,6,5,2,4,7] => 128
[1,3,6,5,2,7,4] => 125
[1,3,6,5,4,2,7] => 126
[1,3,6,5,4,7,2] => 121
[1,3,6,5,7,2,4] => 120
[1,3,6,5,7,4,2] => 118
[1,3,6,7,2,4,5] => 122
[1,3,6,7,2,5,4] => 121
[1,3,6,7,4,2,5] => 120
[1,3,6,7,4,5,2] => 117
[1,3,6,7,5,2,4] => 118
[1,3,6,7,5,4,2] => 116
[1,3,7,2,4,5,6] => 128
[1,3,7,2,4,6,5] => 127
[1,3,7,2,5,4,6] => 127
[1,3,7,2,5,6,4] => 125
[1,3,7,2,6,4,5] => 125
[1,3,7,2,6,5,4] => 124
[1,3,7,4,2,5,6] => 126
[1,3,7,4,2,6,5] => 125
[1,3,7,4,5,2,6] => 123
[1,3,7,4,5,6,2] => 119
[1,3,7,4,6,2,5] => 121
[1,3,7,4,6,5,2] => 118
[1,3,7,5,2,4,6] => 124
[1,3,7,5,2,6,4] => 122
[1,3,7,5,4,2,6] => 122
[1,3,7,5,4,6,2] => 118
[1,3,7,5,6,2,4] => 118
[1,3,7,5,6,4,2] => 116
[1,3,7,6,2,4,5] => 121
[1,3,7,6,2,5,4] => 120
[1,3,7,6,4,2,5] => 119
[1,3,7,6,4,5,2] => 116
[1,3,7,6,5,2,4] => 117
[1,3,7,6,5,4,2] => 115
[1,4,2,3,5,6,7] => 137
[1,4,2,3,5,7,6] => 136
[1,4,2,3,6,5,7] => 136
[1,4,2,3,6,7,5] => 134
[1,4,2,3,7,5,6] => 134
[1,4,2,3,7,6,5] => 133
[1,4,2,5,3,6,7] => 135
[1,4,2,5,3,7,6] => 134
[1,4,2,5,6,3,7] => 132
[1,4,2,5,6,7,3] => 128
[1,4,2,5,7,3,6] => 130
[1,4,2,5,7,6,3] => 127
[1,4,2,6,3,5,7] => 133
[1,4,2,6,3,7,5] => 131
[1,4,2,6,5,3,7] => 131
[1,4,2,6,5,7,3] => 127
[1,4,2,6,7,3,5] => 127
[1,4,2,6,7,5,3] => 125
[1,4,2,7,3,5,6] => 130
[1,4,2,7,3,6,5] => 129
[1,4,2,7,5,3,6] => 128
[1,4,2,7,5,6,3] => 125
[1,4,2,7,6,3,5] => 126
[1,4,2,7,6,5,3] => 124
[1,4,3,2,5,6,7] => 136
[1,4,3,2,5,7,6] => 135
[1,4,3,2,6,5,7] => 135
[1,4,3,2,6,7,5] => 133
[1,4,3,2,7,5,6] => 133
[1,4,3,2,7,6,5] => 132
[1,4,3,5,2,6,7] => 133
[1,4,3,5,2,7,6] => 132
[1,4,3,5,6,2,7] => 129
[1,4,3,5,6,7,2] => 124
[1,4,3,5,7,2,6] => 127
[1,4,3,5,7,6,2] => 123
[1,4,3,6,2,5,7] => 131
[1,4,3,6,2,7,5] => 129
[1,4,3,6,5,2,7] => 128
[1,4,3,6,5,7,2] => 123
[1,4,3,6,7,2,5] => 124
[1,4,3,6,7,5,2] => 121
[1,4,3,7,2,5,6] => 128
[1,4,3,7,2,6,5] => 127
[1,4,3,7,5,2,6] => 125
[1,4,3,7,5,6,2] => 121
[1,4,3,7,6,2,5] => 123
[1,4,3,7,6,5,2] => 120
[1,4,5,2,3,6,7] => 132
[1,4,5,2,3,7,6] => 131
[1,4,5,2,6,3,7] => 129
[1,4,5,2,6,7,3] => 125
[1,4,5,2,7,3,6] => 127
[1,4,5,2,7,6,3] => 124
[1,4,5,3,2,6,7] => 131
[1,4,5,3,2,7,6] => 130
[1,4,5,3,6,2,7] => 127
[1,4,5,3,6,7,2] => 122
[1,4,5,3,7,2,6] => 125
[1,4,5,3,7,6,2] => 121
[1,4,5,6,2,3,7] => 125
[1,4,5,6,2,7,3] => 121
[1,4,5,6,3,2,7] => 124
[1,4,5,6,3,7,2] => 119
[1,4,5,6,7,2,3] => 116
[1,4,5,6,7,3,2] => 115
[1,4,5,7,2,3,6] => 122
[1,4,5,7,2,6,3] => 119
[1,4,5,7,3,2,6] => 121
[1,4,5,7,3,6,2] => 117
[1,4,5,7,6,2,3] => 115
[1,4,5,7,6,3,2] => 114
[1,4,6,2,3,5,7] => 129
[1,4,6,2,3,7,5] => 127
[1,4,6,2,5,3,7] => 127
[1,4,6,2,5,7,3] => 123
[1,4,6,2,7,3,5] => 123
[1,4,6,2,7,5,3] => 121
[1,4,6,3,2,5,7] => 128
[1,4,6,3,2,7,5] => 126
[1,4,6,3,5,2,7] => 125
[1,4,6,3,5,7,2] => 120
[1,4,6,3,7,2,5] => 121
[1,4,6,3,7,5,2] => 118
[1,4,6,5,2,3,7] => 124
[1,4,6,5,2,7,3] => 120
[1,4,6,5,3,2,7] => 123
[1,4,6,5,3,7,2] => 118
click to show generating function       
Description
The cosine of a permutation.
For a permutation $\pi = [\pi_1,\ldots,\pi_n]$, this is given by $\sum_{i=1}^n (i\pi_i)$.
The name comes from the observation that this equals $\frac{n(n+1)(2n+1)}{6}\cos(\theta)$ where $\theta$ is the angle between the vector $(\pi_1,\ldots,\pi_n)$ and the vector $(1,\ldots,n)$, see [1].
References
[1] Sack, J., Ăšlfarsson, H. Refined inversion statistics on permutations MathSciNet:2880660 arXiv:1106.1995
[2] a(n) = the total number of permutations (m(1),m(2),m(3)...m(j)) of (1,2,3,...,j) where n = 1*m(1) + 2*m(2) + 3*m(3) + ...+j*m(j), where j is over all positive integers. OEIS:A135298
Code
def statistic(pi):
        return sum( (i+1)*val for i,val in enumerate(pi) )

Created
Dec 23, 2015 at 08:44 by Christian Stump
Updated
May 10, 2019 at 17:24 by Henning Ulfarsson