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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].
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