edit this statistic or download as text // json
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
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
click to show known generating functions       
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