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
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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].
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., Úlfarsson, 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
[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
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