Identifier
- St000341: Permutations ⟶ ℤ
Values
=>
[1]=>0
[1,2]=>1
[2,1]=>0
[1,2,3]=>4
[1,3,2]=>3
[2,1,3]=>3
[2,3,1]=>1
[3,1,2]=>1
[3,2,1]=>0
[1,2,3,4]=>10
[1,2,4,3]=>9
[1,3,2,4]=>9
[1,3,4,2]=>7
[1,4,2,3]=>7
[1,4,3,2]=>6
[2,1,3,4]=>9
[2,1,4,3]=>8
[2,3,1,4]=>7
[2,3,4,1]=>4
[2,4,1,3]=>5
[2,4,3,1]=>3
[3,1,2,4]=>7
[3,1,4,2]=>5
[3,2,1,4]=>6
[3,2,4,1]=>3
[3,4,1,2]=>2
[3,4,2,1]=>1
[4,1,2,3]=>4
[4,1,3,2]=>3
[4,2,1,3]=>3
[4,2,3,1]=>1
[4,3,1,2]=>1
[4,3,2,1]=>0
[1,2,3,4,5]=>20
[1,2,3,5,4]=>19
[1,2,4,3,5]=>19
[1,2,4,5,3]=>17
[1,2,5,3,4]=>17
[1,2,5,4,3]=>16
[1,3,2,4,5]=>19
[1,3,2,5,4]=>18
[1,3,4,2,5]=>17
[1,3,4,5,2]=>14
[1,3,5,2,4]=>15
[1,3,5,4,2]=>13
[1,4,2,3,5]=>17
[1,4,2,5,3]=>15
[1,4,3,2,5]=>16
[1,4,3,5,2]=>13
[1,4,5,2,3]=>12
[1,4,5,3,2]=>11
[1,5,2,3,4]=>14
[1,5,2,4,3]=>13
[1,5,3,2,4]=>13
[1,5,3,4,2]=>11
[1,5,4,2,3]=>11
[1,5,4,3,2]=>10
[2,1,3,4,5]=>19
[2,1,3,5,4]=>18
[2,1,4,3,5]=>18
[2,1,4,5,3]=>16
[2,1,5,3,4]=>16
[2,1,5,4,3]=>15
[2,3,1,4,5]=>17
[2,3,1,5,4]=>16
[2,3,4,1,5]=>14
[2,3,4,5,1]=>10
[2,3,5,1,4]=>12
[2,3,5,4,1]=>9
[2,4,1,3,5]=>15
[2,4,1,5,3]=>13
[2,4,3,1,5]=>13
[2,4,3,5,1]=>9
[2,4,5,1,3]=>9
[2,4,5,3,1]=>7
[2,5,1,3,4]=>12
[2,5,1,4,3]=>11
[2,5,3,1,4]=>10
[2,5,3,4,1]=>7
[2,5,4,1,3]=>8
[2,5,4,3,1]=>6
[3,1,2,4,5]=>17
[3,1,2,5,4]=>16
[3,1,4,2,5]=>15
[3,1,4,5,2]=>12
[3,1,5,2,4]=>13
[3,1,5,4,2]=>11
[3,2,1,4,5]=>16
[3,2,1,5,4]=>15
[3,2,4,1,5]=>13
[3,2,4,5,1]=>9
[3,2,5,1,4]=>11
[3,2,5,4,1]=>8
[3,4,1,2,5]=>12
[3,4,1,5,2]=>9
[3,4,2,1,5]=>11
[3,4,2,5,1]=>7
[3,4,5,1,2]=>5
[3,4,5,2,1]=>4
[3,5,1,2,4]=>9
[3,5,1,4,2]=>7
[3,5,2,1,4]=>8
[3,5,2,4,1]=>5
[3,5,4,1,2]=>4
[3,5,4,2,1]=>3
[4,1,2,3,5]=>14
[4,1,2,5,3]=>12
[4,1,3,2,5]=>13
[4,1,3,5,2]=>10
[4,1,5,2,3]=>9
[4,1,5,3,2]=>8
[4,2,1,3,5]=>13
[4,2,1,5,3]=>11
[4,2,3,1,5]=>11
[4,2,3,5,1]=>7
[4,2,5,1,3]=>7
[4,2,5,3,1]=>5
[4,3,1,2,5]=>11
[4,3,1,5,2]=>8
[4,3,2,1,5]=>10
[4,3,2,5,1]=>6
[4,3,5,1,2]=>4
[4,3,5,2,1]=>3
[4,5,1,2,3]=>5
[4,5,1,3,2]=>4
[4,5,2,1,3]=>4
[4,5,2,3,1]=>2
[4,5,3,1,2]=>2
[4,5,3,2,1]=>1
[5,1,2,3,4]=>10
[5,1,2,4,3]=>9
[5,1,3,2,4]=>9
[5,1,3,4,2]=>7
[5,1,4,2,3]=>7
[5,1,4,3,2]=>6
[5,2,1,3,4]=>9
[5,2,1,4,3]=>8
[5,2,3,1,4]=>7
[5,2,3,4,1]=>4
[5,2,4,1,3]=>5
[5,2,4,3,1]=>3
[5,3,1,2,4]=>7
[5,3,1,4,2]=>5
[5,3,2,1,4]=>6
[5,3,2,4,1]=>3
[5,3,4,1,2]=>2
[5,3,4,2,1]=>1
[5,4,1,2,3]=>4
[5,4,1,3,2]=>3
[5,4,2,1,3]=>3
[5,4,2,3,1]=>1
[5,4,3,1,2]=>1
[5,4,3,2,1]=>0
[1,2,3,4,5,6]=>35
[1,2,3,4,6,5]=>34
[1,2,3,5,4,6]=>34
[1,2,3,5,6,4]=>32
[1,2,3,6,4,5]=>32
[1,2,3,6,5,4]=>31
[1,2,4,3,5,6]=>34
[1,2,4,3,6,5]=>33
[1,2,4,5,3,6]=>32
[1,2,4,5,6,3]=>29
[1,2,4,6,3,5]=>30
[1,2,4,6,5,3]=>28
[1,2,5,3,4,6]=>32
[1,2,5,3,6,4]=>30
[1,2,5,4,3,6]=>31
[1,2,5,4,6,3]=>28
[1,2,5,6,3,4]=>27
[1,2,5,6,4,3]=>26
[1,2,6,3,4,5]=>29
[1,2,6,3,5,4]=>28
[1,2,6,4,3,5]=>28
[1,2,6,4,5,3]=>26
[1,2,6,5,3,4]=>26
[1,2,6,5,4,3]=>25
[1,3,2,4,5,6]=>34
[1,3,2,4,6,5]=>33
[1,3,2,5,4,6]=>33
[1,3,2,5,6,4]=>31
[1,3,2,6,4,5]=>31
[1,3,2,6,5,4]=>30
[1,3,4,2,5,6]=>32
[1,3,4,2,6,5]=>31
[1,3,4,5,2,6]=>29
[1,3,4,5,6,2]=>25
[1,3,4,6,2,5]=>27
[1,3,4,6,5,2]=>24
[1,3,5,2,4,6]=>30
[1,3,5,2,6,4]=>28
[1,3,5,4,2,6]=>28
[1,3,5,4,6,2]=>24
[1,3,5,6,2,4]=>24
[1,3,5,6,4,2]=>22
[1,3,6,2,4,5]=>27
[1,3,6,2,5,4]=>26
[1,3,6,4,2,5]=>25
[1,3,6,4,5,2]=>22
[1,3,6,5,2,4]=>23
[1,3,6,5,4,2]=>21
[1,4,2,3,5,6]=>32
[1,4,2,3,6,5]=>31
[1,4,2,5,3,6]=>30
[1,4,2,5,6,3]=>27
[1,4,2,6,3,5]=>28
[1,4,2,6,5,3]=>26
[1,4,3,2,5,6]=>31
[1,4,3,2,6,5]=>30
[1,4,3,5,2,6]=>28
[1,4,3,5,6,2]=>24
[1,4,3,6,2,5]=>26
[1,4,3,6,5,2]=>23
[1,4,5,2,3,6]=>27
[1,4,5,2,6,3]=>24
[1,4,5,3,2,6]=>26
[1,4,5,3,6,2]=>22
[1,4,5,6,2,3]=>20
[1,4,5,6,3,2]=>19
[1,4,6,2,3,5]=>24
[1,4,6,2,5,3]=>22
[1,4,6,3,2,5]=>23
[1,4,6,3,5,2]=>20
[1,4,6,5,2,3]=>19
[1,4,6,5,3,2]=>18
[1,5,2,3,4,6]=>29
[1,5,2,3,6,4]=>27
[1,5,2,4,3,6]=>28
[1,5,2,4,6,3]=>25
[1,5,2,6,3,4]=>24
[1,5,2,6,4,3]=>23
[1,5,3,2,4,6]=>28
[1,5,3,2,6,4]=>26
[1,5,3,4,2,6]=>26
[1,5,3,4,6,2]=>22
[1,5,3,6,2,4]=>22
[1,5,3,6,4,2]=>20
[1,5,4,2,3,6]=>26
[1,5,4,2,6,3]=>23
[1,5,4,3,2,6]=>25
[1,5,4,3,6,2]=>21
[1,5,4,6,2,3]=>19
[1,5,4,6,3,2]=>18
[1,5,6,2,3,4]=>20
[1,5,6,2,4,3]=>19
[1,5,6,3,2,4]=>19
[1,5,6,3,4,2]=>17
[1,5,6,4,2,3]=>17
[1,5,6,4,3,2]=>16
[1,6,2,3,4,5]=>25
[1,6,2,3,5,4]=>24
[1,6,2,4,3,5]=>24
[1,6,2,4,5,3]=>22
[1,6,2,5,3,4]=>22
[1,6,2,5,4,3]=>21
[1,6,3,2,4,5]=>24
[1,6,3,2,5,4]=>23
[1,6,3,4,2,5]=>22
[1,6,3,4,5,2]=>19
[1,6,3,5,2,4]=>20
[1,6,3,5,4,2]=>18
[1,6,4,2,3,5]=>22
[1,6,4,2,5,3]=>20
[1,6,4,3,2,5]=>21
[1,6,4,3,5,2]=>18
[1,6,4,5,2,3]=>17
[1,6,4,5,3,2]=>16
[1,6,5,2,3,4]=>19
[1,6,5,2,4,3]=>18
[1,6,5,3,2,4]=>18
[1,6,5,3,4,2]=>16
[1,6,5,4,2,3]=>16
[1,6,5,4,3,2]=>15
[2,1,3,4,5,6]=>34
[2,1,3,4,6,5]=>33
[2,1,3,5,4,6]=>33
[2,1,3,5,6,4]=>31
[2,1,3,6,4,5]=>31
[2,1,3,6,5,4]=>30
[2,1,4,3,5,6]=>33
[2,1,4,3,6,5]=>32
[2,1,4,5,3,6]=>31
[2,1,4,5,6,3]=>28
[2,1,4,6,3,5]=>29
[2,1,4,6,5,3]=>27
[2,1,5,3,4,6]=>31
[2,1,5,3,6,4]=>29
[2,1,5,4,3,6]=>30
[2,1,5,4,6,3]=>27
[2,1,5,6,3,4]=>26
[2,1,5,6,4,3]=>25
[2,1,6,3,4,5]=>28
[2,1,6,3,5,4]=>27
[2,1,6,4,3,5]=>27
[2,1,6,4,5,3]=>25
[2,1,6,5,3,4]=>25
[2,1,6,5,4,3]=>24
[2,3,1,4,5,6]=>32
[2,3,1,4,6,5]=>31
[2,3,1,5,4,6]=>31
[2,3,1,5,6,4]=>29
[2,3,1,6,4,5]=>29
[2,3,1,6,5,4]=>28
[2,3,4,1,5,6]=>29
[2,3,4,1,6,5]=>28
[2,3,4,5,1,6]=>25
[2,3,4,5,6,1]=>20
[2,3,4,6,1,5]=>23
[2,3,4,6,5,1]=>19
[2,3,5,1,4,6]=>27
[2,3,5,1,6,4]=>25
[2,3,5,4,1,6]=>24
[2,3,5,4,6,1]=>19
[2,3,5,6,1,4]=>20
[2,3,5,6,4,1]=>17
[2,3,6,1,4,5]=>24
[2,3,6,1,5,4]=>23
[2,3,6,4,1,5]=>21
[2,3,6,4,5,1]=>17
[2,3,6,5,1,4]=>19
[2,3,6,5,4,1]=>16
[2,4,1,3,5,6]=>30
[2,4,1,3,6,5]=>29
[2,4,1,5,3,6]=>28
[2,4,1,5,6,3]=>25
[2,4,1,6,3,5]=>26
[2,4,1,6,5,3]=>24
[2,4,3,1,5,6]=>28
[2,4,3,1,6,5]=>27
[2,4,3,5,1,6]=>24
[2,4,3,5,6,1]=>19
[2,4,3,6,1,5]=>22
[2,4,3,6,5,1]=>18
[2,4,5,1,3,6]=>24
[2,4,5,1,6,3]=>21
[2,4,5,3,1,6]=>22
[2,4,5,3,6,1]=>17
[2,4,5,6,1,3]=>16
[2,4,5,6,3,1]=>14
[2,4,6,1,3,5]=>21
[2,4,6,1,5,3]=>19
[2,4,6,3,1,5]=>19
[2,4,6,3,5,1]=>15
[2,4,6,5,1,3]=>15
[2,4,6,5,3,1]=>13
[2,5,1,3,4,6]=>27
[2,5,1,3,6,4]=>25
[2,5,1,4,3,6]=>26
[2,5,1,4,6,3]=>23
[2,5,1,6,3,4]=>22
[2,5,1,6,4,3]=>21
[2,5,3,1,4,6]=>25
[2,5,3,1,6,4]=>23
[2,5,3,4,1,6]=>22
[2,5,3,4,6,1]=>17
[2,5,3,6,1,4]=>18
[2,5,3,6,4,1]=>15
[2,5,4,1,3,6]=>23
[2,5,4,1,6,3]=>20
[2,5,4,3,1,6]=>21
[2,5,4,3,6,1]=>16
[2,5,4,6,1,3]=>15
[2,5,4,6,3,1]=>13
[2,5,6,1,3,4]=>17
[2,5,6,1,4,3]=>16
[2,5,6,3,1,4]=>15
[2,5,6,3,4,1]=>12
[2,5,6,4,1,3]=>13
[2,5,6,4,3,1]=>11
[2,6,1,3,4,5]=>23
[2,6,1,3,5,4]=>22
[2,6,1,4,3,5]=>22
[2,6,1,4,5,3]=>20
[2,6,1,5,3,4]=>20
[2,6,1,5,4,3]=>19
[2,6,3,1,4,5]=>21
[2,6,3,1,5,4]=>20
[2,6,3,4,1,5]=>18
[2,6,3,4,5,1]=>14
[2,6,3,5,1,4]=>16
[2,6,3,5,4,1]=>13
[2,6,4,1,3,5]=>19
[2,6,4,1,5,3]=>17
[2,6,4,3,1,5]=>17
[2,6,4,3,5,1]=>13
[2,6,4,5,1,3]=>13
[2,6,4,5,3,1]=>11
[2,6,5,1,3,4]=>16
[2,6,5,1,4,3]=>15
[2,6,5,3,1,4]=>14
[2,6,5,3,4,1]=>11
[2,6,5,4,1,3]=>12
[2,6,5,4,3,1]=>10
[3,1,2,4,5,6]=>32
[3,1,2,4,6,5]=>31
[3,1,2,5,4,6]=>31
[3,1,2,5,6,4]=>29
[3,1,2,6,4,5]=>29
[3,1,2,6,5,4]=>28
[3,1,4,2,5,6]=>30
[3,1,4,2,6,5]=>29
[3,1,4,5,2,6]=>27
[3,1,4,5,6,2]=>23
[3,1,4,6,2,5]=>25
[3,1,4,6,5,2]=>22
[3,1,5,2,4,6]=>28
[3,1,5,2,6,4]=>26
[3,1,5,4,2,6]=>26
[3,1,5,4,6,2]=>22
[3,1,5,6,2,4]=>22
[3,1,5,6,4,2]=>20
[3,1,6,2,4,5]=>25
[3,1,6,2,5,4]=>24
[3,1,6,4,2,5]=>23
[3,1,6,4,5,2]=>20
[3,1,6,5,2,4]=>21
[3,1,6,5,4,2]=>19
[3,2,1,4,5,6]=>31
[3,2,1,4,6,5]=>30
[3,2,1,5,4,6]=>30
[3,2,1,5,6,4]=>28
[3,2,1,6,4,5]=>28
[3,2,1,6,5,4]=>27
[3,2,4,1,5,6]=>28
[3,2,4,1,6,5]=>27
[3,2,4,5,1,6]=>24
[3,2,4,5,6,1]=>19
[3,2,4,6,1,5]=>22
[3,2,4,6,5,1]=>18
[3,2,5,1,4,6]=>26
[3,2,5,1,6,4]=>24
[3,2,5,4,1,6]=>23
[3,2,5,4,6,1]=>18
[3,2,5,6,1,4]=>19
[3,2,5,6,4,1]=>16
[3,2,6,1,4,5]=>23
[3,2,6,1,5,4]=>22
[3,2,6,4,1,5]=>20
[3,2,6,4,5,1]=>16
[3,2,6,5,1,4]=>18
[3,2,6,5,4,1]=>15
[3,4,1,2,5,6]=>27
[3,4,1,2,6,5]=>26
[3,4,1,5,2,6]=>24
[3,4,1,5,6,2]=>20
[3,4,1,6,2,5]=>22
[3,4,1,6,5,2]=>19
[3,4,2,1,5,6]=>26
[3,4,2,1,6,5]=>25
[3,4,2,5,1,6]=>22
[3,4,2,5,6,1]=>17
[3,4,2,6,1,5]=>20
[3,4,2,6,5,1]=>16
[3,4,5,1,2,6]=>20
[3,4,5,1,6,2]=>16
[3,4,5,2,1,6]=>19
[3,4,5,2,6,1]=>14
[3,4,5,6,1,2]=>11
[3,4,5,6,2,1]=>10
[3,4,6,1,2,5]=>17
[3,4,6,1,5,2]=>14
[3,4,6,2,1,5]=>16
[3,4,6,2,5,1]=>12
[3,4,6,5,1,2]=>10
[3,4,6,5,2,1]=>9
[3,5,1,2,4,6]=>24
[3,5,1,2,6,4]=>22
[3,5,1,4,2,6]=>22
[3,5,1,4,6,2]=>18
[3,5,1,6,2,4]=>18
[3,5,1,6,4,2]=>16
[3,5,2,1,4,6]=>23
[3,5,2,1,6,4]=>21
[3,5,2,4,1,6]=>20
[3,5,2,4,6,1]=>15
[3,5,2,6,1,4]=>16
[3,5,2,6,4,1]=>13
[3,5,4,1,2,6]=>19
[3,5,4,1,6,2]=>15
[3,5,4,2,1,6]=>18
[3,5,4,2,6,1]=>13
[3,5,4,6,1,2]=>10
[3,5,4,6,2,1]=>9
[3,5,6,1,2,4]=>13
[3,5,6,1,4,2]=>11
[3,5,6,2,1,4]=>12
[3,5,6,2,4,1]=>9
[3,5,6,4,1,2]=>8
[3,5,6,4,2,1]=>7
[3,6,1,2,4,5]=>20
[3,6,1,2,5,4]=>19
[3,6,1,4,2,5]=>18
[3,6,1,4,5,2]=>15
[3,6,1,5,2,4]=>16
[3,6,1,5,4,2]=>14
[3,6,2,1,4,5]=>19
[3,6,2,1,5,4]=>18
[3,6,2,4,1,5]=>16
[3,6,2,4,5,1]=>12
[3,6,2,5,1,4]=>14
[3,6,2,5,4,1]=>11
[3,6,4,1,2,5]=>15
[3,6,4,1,5,2]=>12
[3,6,4,2,1,5]=>14
[3,6,4,2,5,1]=>10
[3,6,4,5,1,2]=>8
[3,6,4,5,2,1]=>7
[3,6,5,1,2,4]=>12
[3,6,5,1,4,2]=>10
[3,6,5,2,1,4]=>11
[3,6,5,2,4,1]=>8
[3,6,5,4,1,2]=>7
[3,6,5,4,2,1]=>6
[4,1,2,3,5,6]=>29
[4,1,2,3,6,5]=>28
[4,1,2,5,3,6]=>27
[4,1,2,5,6,3]=>24
[4,1,2,6,3,5]=>25
[4,1,2,6,5,3]=>23
[4,1,3,2,5,6]=>28
[4,1,3,2,6,5]=>27
[4,1,3,5,2,6]=>25
[4,1,3,5,6,2]=>21
[4,1,3,6,2,5]=>23
[4,1,3,6,5,2]=>20
[4,1,5,2,3,6]=>24
[4,1,5,2,6,3]=>21
[4,1,5,3,2,6]=>23
[4,1,5,3,6,2]=>19
[4,1,5,6,2,3]=>17
[4,1,5,6,3,2]=>16
[4,1,6,2,3,5]=>21
[4,1,6,2,5,3]=>19
[4,1,6,3,2,5]=>20
[4,1,6,3,5,2]=>17
[4,1,6,5,2,3]=>16
[4,1,6,5,3,2]=>15
[4,2,1,3,5,6]=>28
[4,2,1,3,6,5]=>27
[4,2,1,5,3,6]=>26
[4,2,1,5,6,3]=>23
[4,2,1,6,3,5]=>24
[4,2,1,6,5,3]=>22
[4,2,3,1,5,6]=>26
[4,2,3,1,6,5]=>25
[4,2,3,5,1,6]=>22
[4,2,3,5,6,1]=>17
[4,2,3,6,1,5]=>20
[4,2,3,6,5,1]=>16
[4,2,5,1,3,6]=>22
[4,2,5,1,6,3]=>19
[4,2,5,3,1,6]=>20
[4,2,5,3,6,1]=>15
[4,2,5,6,1,3]=>14
[4,2,5,6,3,1]=>12
[4,2,6,1,3,5]=>19
[4,2,6,1,5,3]=>17
[4,2,6,3,1,5]=>17
[4,2,6,3,5,1]=>13
[4,2,6,5,1,3]=>13
[4,2,6,5,3,1]=>11
[4,3,1,2,5,6]=>26
[4,3,1,2,6,5]=>25
[4,3,1,5,2,6]=>23
[4,3,1,5,6,2]=>19
[4,3,1,6,2,5]=>21
[4,3,1,6,5,2]=>18
[4,3,2,1,5,6]=>25
[4,3,2,1,6,5]=>24
[4,3,2,5,1,6]=>21
[4,3,2,5,6,1]=>16
[4,3,2,6,1,5]=>19
[4,3,2,6,5,1]=>15
[4,3,5,1,2,6]=>19
[4,3,5,1,6,2]=>15
[4,3,5,2,1,6]=>18
[4,3,5,2,6,1]=>13
[4,3,5,6,1,2]=>10
[4,3,5,6,2,1]=>9
[4,3,6,1,2,5]=>16
[4,3,6,1,5,2]=>13
[4,3,6,2,1,5]=>15
[4,3,6,2,5,1]=>11
[4,3,6,5,1,2]=>9
[4,3,6,5,2,1]=>8
[4,5,1,2,3,6]=>20
[4,5,1,2,6,3]=>17
[4,5,1,3,2,6]=>19
[4,5,1,3,6,2]=>15
[4,5,1,6,2,3]=>13
[4,5,1,6,3,2]=>12
[4,5,2,1,3,6]=>19
[4,5,2,1,6,3]=>16
[4,5,2,3,1,6]=>17
[4,5,2,3,6,1]=>12
[4,5,2,6,1,3]=>11
[4,5,2,6,3,1]=>9
[4,5,3,1,2,6]=>17
[4,5,3,1,6,2]=>13
[4,5,3,2,1,6]=>16
[4,5,3,2,6,1]=>11
[4,5,3,6,1,2]=>8
[4,5,3,6,2,1]=>7
[4,5,6,1,2,3]=>8
[4,5,6,1,3,2]=>7
[4,5,6,2,1,3]=>7
[4,5,6,2,3,1]=>5
[4,5,6,3,1,2]=>5
[4,5,6,3,2,1]=>4
[4,6,1,2,3,5]=>16
[4,6,1,2,5,3]=>14
[4,6,1,3,2,5]=>15
[4,6,1,3,5,2]=>12
[4,6,1,5,2,3]=>11
[4,6,1,5,3,2]=>10
[4,6,2,1,3,5]=>15
[4,6,2,1,5,3]=>13
[4,6,2,3,1,5]=>13
[4,6,2,3,5,1]=>9
[4,6,2,5,1,3]=>9
[4,6,2,5,3,1]=>7
[4,6,3,1,2,5]=>13
[4,6,3,1,5,2]=>10
[4,6,3,2,1,5]=>12
[4,6,3,2,5,1]=>8
[4,6,3,5,1,2]=>6
[4,6,3,5,2,1]=>5
[4,6,5,1,2,3]=>7
[4,6,5,1,3,2]=>6
[4,6,5,2,1,3]=>6
[4,6,5,2,3,1]=>4
[4,6,5,3,1,2]=>4
[4,6,5,3,2,1]=>3
[5,1,2,3,4,6]=>25
[5,1,2,3,6,4]=>23
[5,1,2,4,3,6]=>24
[5,1,2,4,6,3]=>21
[5,1,2,6,3,4]=>20
[5,1,2,6,4,3]=>19
[5,1,3,2,4,6]=>24
[5,1,3,2,6,4]=>22
[5,1,3,4,2,6]=>22
[5,1,3,4,6,2]=>18
[5,1,3,6,2,4]=>18
[5,1,3,6,4,2]=>16
[5,1,4,2,3,6]=>22
[5,1,4,2,6,3]=>19
[5,1,4,3,2,6]=>21
[5,1,4,3,6,2]=>17
[5,1,4,6,2,3]=>15
[5,1,4,6,3,2]=>14
[5,1,6,2,3,4]=>16
[5,1,6,2,4,3]=>15
[5,1,6,3,2,4]=>15
[5,1,6,3,4,2]=>13
[5,1,6,4,2,3]=>13
[5,1,6,4,3,2]=>12
[5,2,1,3,4,6]=>24
[5,2,1,3,6,4]=>22
[5,2,1,4,3,6]=>23
[5,2,1,4,6,3]=>20
[5,2,1,6,3,4]=>19
[5,2,1,6,4,3]=>18
[5,2,3,1,4,6]=>22
[5,2,3,1,6,4]=>20
[5,2,3,4,1,6]=>19
[5,2,3,4,6,1]=>14
[5,2,3,6,1,4]=>15
[5,2,3,6,4,1]=>12
[5,2,4,1,3,6]=>20
[5,2,4,1,6,3]=>17
[5,2,4,3,1,6]=>18
[5,2,4,3,6,1]=>13
[5,2,4,6,1,3]=>12
[5,2,4,6,3,1]=>10
[5,2,6,1,3,4]=>14
[5,2,6,1,4,3]=>13
[5,2,6,3,1,4]=>12
[5,2,6,3,4,1]=>9
[5,2,6,4,1,3]=>10
[5,2,6,4,3,1]=>8
[5,3,1,2,4,6]=>22
[5,3,1,2,6,4]=>20
[5,3,1,4,2,6]=>20
[5,3,1,4,6,2]=>16
[5,3,1,6,2,4]=>16
[5,3,1,6,4,2]=>14
[5,3,2,1,4,6]=>21
[5,3,2,1,6,4]=>19
[5,3,2,4,1,6]=>18
[5,3,2,4,6,1]=>13
[5,3,2,6,1,4]=>14
[5,3,2,6,4,1]=>11
[5,3,4,1,2,6]=>17
[5,3,4,1,6,2]=>13
[5,3,4,2,1,6]=>16
[5,3,4,2,6,1]=>11
[5,3,4,6,1,2]=>8
[5,3,4,6,2,1]=>7
[5,3,6,1,2,4]=>11
[5,3,6,1,4,2]=>9
[5,3,6,2,1,4]=>10
[5,3,6,2,4,1]=>7
[5,3,6,4,1,2]=>6
[5,3,6,4,2,1]=>5
[5,4,1,2,3,6]=>19
[5,4,1,2,6,3]=>16
[5,4,1,3,2,6]=>18
[5,4,1,3,6,2]=>14
[5,4,1,6,2,3]=>12
[5,4,1,6,3,2]=>11
[5,4,2,1,3,6]=>18
[5,4,2,1,6,3]=>15
[5,4,2,3,1,6]=>16
[5,4,2,3,6,1]=>11
[5,4,2,6,1,3]=>10
[5,4,2,6,3,1]=>8
[5,4,3,1,2,6]=>16
[5,4,3,1,6,2]=>12
[5,4,3,2,1,6]=>15
[5,4,3,2,6,1]=>10
[5,4,3,6,1,2]=>7
[5,4,3,6,2,1]=>6
[5,4,6,1,2,3]=>7
[5,4,6,1,3,2]=>6
[5,4,6,2,1,3]=>6
[5,4,6,2,3,1]=>4
[5,4,6,3,1,2]=>4
[5,4,6,3,2,1]=>3
[5,6,1,2,3,4]=>11
[5,6,1,2,4,3]=>10
[5,6,1,3,2,4]=>10
[5,6,1,3,4,2]=>8
[5,6,1,4,2,3]=>8
[5,6,1,4,3,2]=>7
[5,6,2,1,3,4]=>10
[5,6,2,1,4,3]=>9
[5,6,2,3,1,4]=>8
[5,6,2,3,4,1]=>5
[5,6,2,4,1,3]=>6
[5,6,2,4,3,1]=>4
[5,6,3,1,2,4]=>8
[5,6,3,1,4,2]=>6
[5,6,3,2,1,4]=>7
[5,6,3,2,4,1]=>4
[5,6,3,4,1,2]=>3
[5,6,3,4,2,1]=>2
[5,6,4,1,2,3]=>5
[5,6,4,1,3,2]=>4
[5,6,4,2,1,3]=>4
[5,6,4,2,3,1]=>2
[5,6,4,3,1,2]=>2
[5,6,4,3,2,1]=>1
[6,1,2,3,4,5]=>20
[6,1,2,3,5,4]=>19
[6,1,2,4,3,5]=>19
[6,1,2,4,5,3]=>17
[6,1,2,5,3,4]=>17
[6,1,2,5,4,3]=>16
[6,1,3,2,4,5]=>19
[6,1,3,2,5,4]=>18
[6,1,3,4,2,5]=>17
[6,1,3,4,5,2]=>14
[6,1,3,5,2,4]=>15
[6,1,3,5,4,2]=>13
[6,1,4,2,3,5]=>17
[6,1,4,2,5,3]=>15
[6,1,4,3,2,5]=>16
[6,1,4,3,5,2]=>13
[6,1,4,5,2,3]=>12
[6,1,4,5,3,2]=>11
[6,1,5,2,3,4]=>14
[6,1,5,2,4,3]=>13
[6,1,5,3,2,4]=>13
[6,1,5,3,4,2]=>11
[6,1,5,4,2,3]=>11
[6,1,5,4,3,2]=>10
[6,2,1,3,4,5]=>19
[6,2,1,3,5,4]=>18
[6,2,1,4,3,5]=>18
[6,2,1,4,5,3]=>16
[6,2,1,5,3,4]=>16
[6,2,1,5,4,3]=>15
[6,2,3,1,4,5]=>17
[6,2,3,1,5,4]=>16
[6,2,3,4,1,5]=>14
[6,2,3,4,5,1]=>10
[6,2,3,5,1,4]=>12
[6,2,3,5,4,1]=>9
[6,2,4,1,3,5]=>15
[6,2,4,1,5,3]=>13
[6,2,4,3,1,5]=>13
[6,2,4,3,5,1]=>9
[6,2,4,5,1,3]=>9
[6,2,4,5,3,1]=>7
[6,2,5,1,3,4]=>12
[6,2,5,1,4,3]=>11
[6,2,5,3,1,4]=>10
[6,2,5,3,4,1]=>7
[6,2,5,4,1,3]=>8
[6,2,5,4,3,1]=>6
[6,3,1,2,4,5]=>17
[6,3,1,2,5,4]=>16
[6,3,1,4,2,5]=>15
[6,3,1,4,5,2]=>12
[6,3,1,5,2,4]=>13
[6,3,1,5,4,2]=>11
[6,3,2,1,4,5]=>16
[6,3,2,1,5,4]=>15
[6,3,2,4,1,5]=>13
[6,3,2,4,5,1]=>9
[6,3,2,5,1,4]=>11
[6,3,2,5,4,1]=>8
[6,3,4,1,2,5]=>12
[6,3,4,1,5,2]=>9
[6,3,4,2,1,5]=>11
[6,3,4,2,5,1]=>7
[6,3,4,5,1,2]=>5
[6,3,4,5,2,1]=>4
[6,3,5,1,2,4]=>9
[6,3,5,1,4,2]=>7
[6,3,5,2,1,4]=>8
[6,3,5,2,4,1]=>5
[6,3,5,4,1,2]=>4
[6,3,5,4,2,1]=>3
[6,4,1,2,3,5]=>14
[6,4,1,2,5,3]=>12
[6,4,1,3,2,5]=>13
[6,4,1,3,5,2]=>10
[6,4,1,5,2,3]=>9
[6,4,1,5,3,2]=>8
[6,4,2,1,3,5]=>13
[6,4,2,1,5,3]=>11
[6,4,2,3,1,5]=>11
[6,4,2,3,5,1]=>7
[6,4,2,5,1,3]=>7
[6,4,2,5,3,1]=>5
[6,4,3,1,2,5]=>11
[6,4,3,1,5,2]=>8
[6,4,3,2,1,5]=>10
[6,4,3,2,5,1]=>6
[6,4,3,5,1,2]=>4
[6,4,3,5,2,1]=>3
[6,4,5,1,2,3]=>5
[6,4,5,1,3,2]=>4
[6,4,5,2,1,3]=>4
[6,4,5,2,3,1]=>2
[6,4,5,3,1,2]=>2
[6,4,5,3,2,1]=>1
[6,5,1,2,3,4]=>10
[6,5,1,2,4,3]=>9
[6,5,1,3,2,4]=>9
[6,5,1,3,4,2]=>7
[6,5,1,4,2,3]=>7
[6,5,1,4,3,2]=>6
[6,5,2,1,3,4]=>9
[6,5,2,1,4,3]=>8
[6,5,2,3,1,4]=>7
[6,5,2,3,4,1]=>4
[6,5,2,4,1,3]=>5
[6,5,2,4,3,1]=>3
[6,5,3,1,2,4]=>7
[6,5,3,1,4,2]=>5
[6,5,3,2,1,4]=>6
[6,5,3,2,4,1]=>3
[6,5,3,4,1,2]=>2
[6,5,3,4,2,1]=>1
[6,5,4,1,2,3]=>4
[6,5,4,1,3,2]=>3
[6,5,4,2,1,3]=>3
[6,5,4,2,3,1]=>1
[6,5,4,3,1,2]=>1
[6,5,4,3,2,1]=>0
[1,2,3,4,5,6,7]=>56
[1,2,3,4,5,7,6]=>55
[1,2,3,4,6,5,7]=>55
[1,2,3,4,6,7,5]=>53
[1,2,3,4,7,5,6]=>53
[1,2,3,4,7,6,5]=>52
[1,2,3,5,4,6,7]=>55
[1,2,3,5,4,7,6]=>54
[1,2,3,5,6,4,7]=>53
[1,2,3,5,6,7,4]=>50
[1,2,3,5,7,4,6]=>51
[1,2,3,5,7,6,4]=>49
[1,2,3,6,4,5,7]=>53
[1,2,3,6,4,7,5]=>51
[1,2,3,6,5,4,7]=>52
[1,2,3,6,5,7,4]=>49
[1,2,3,6,7,4,5]=>48
[1,2,3,6,7,5,4]=>47
[1,2,3,7,4,5,6]=>50
[1,2,3,7,4,6,5]=>49
[1,2,3,7,5,4,6]=>49
[1,2,3,7,5,6,4]=>47
[1,2,3,7,6,4,5]=>47
[1,2,3,7,6,5,4]=>46
[1,2,4,3,5,6,7]=>55
[1,2,4,3,5,7,6]=>54
[1,2,4,3,6,5,7]=>54
[1,2,4,3,6,7,5]=>52
[1,2,4,3,7,5,6]=>52
[1,2,4,3,7,6,5]=>51
[1,2,4,5,3,6,7]=>53
[1,2,4,5,3,7,6]=>52
[1,2,4,5,6,3,7]=>50
[1,2,4,5,6,7,3]=>46
[1,2,4,5,7,3,6]=>48
[1,2,4,5,7,6,3]=>45
[1,2,4,6,3,5,7]=>51
[1,2,4,6,3,7,5]=>49
[1,2,4,6,5,3,7]=>49
[1,2,4,6,5,7,3]=>45
[1,2,4,6,7,3,5]=>45
[1,2,4,6,7,5,3]=>43
[1,2,4,7,3,5,6]=>48
[1,2,4,7,3,6,5]=>47
[1,2,4,7,5,3,6]=>46
[1,2,4,7,5,6,3]=>43
[1,2,4,7,6,3,5]=>44
[1,2,4,7,6,5,3]=>42
[1,2,5,3,4,6,7]=>53
[1,2,5,3,4,7,6]=>52
[1,2,5,3,6,4,7]=>51
[1,2,5,3,6,7,4]=>48
[1,2,5,3,7,4,6]=>49
[1,2,5,3,7,6,4]=>47
[1,2,5,4,3,6,7]=>52
[1,2,5,4,3,7,6]=>51
[1,2,5,4,6,3,7]=>49
[1,2,5,4,6,7,3]=>45
[1,2,5,4,7,3,6]=>47
[1,2,5,4,7,6,3]=>44
[1,2,5,6,3,4,7]=>48
[1,2,5,6,3,7,4]=>45
[1,2,5,6,4,3,7]=>47
[1,2,5,6,4,7,3]=>43
[1,2,5,6,7,3,4]=>41
[1,2,5,6,7,4,3]=>40
[1,2,5,7,3,4,6]=>45
[1,2,5,7,3,6,4]=>43
[1,2,5,7,4,3,6]=>44
[1,2,5,7,4,6,3]=>41
[1,2,5,7,6,3,4]=>40
[1,2,5,7,6,4,3]=>39
[1,2,6,3,4,5,7]=>50
[1,2,6,3,4,7,5]=>48
[1,2,6,3,5,4,7]=>49
[1,2,6,3,5,7,4]=>46
[1,2,6,3,7,4,5]=>45
[1,2,6,3,7,5,4]=>44
[1,2,6,4,3,5,7]=>49
[1,2,6,4,3,7,5]=>47
[1,2,6,4,5,3,7]=>47
[1,2,6,4,5,7,3]=>43
[1,2,6,4,7,3,5]=>43
[1,2,6,4,7,5,3]=>41
[1,2,6,5,3,4,7]=>47
[1,2,6,5,3,7,4]=>44
[1,2,6,5,4,3,7]=>46
[1,2,6,5,4,7,3]=>42
[1,2,6,5,7,3,4]=>40
[1,2,6,5,7,4,3]=>39
[1,2,6,7,3,4,5]=>41
[1,2,6,7,3,5,4]=>40
[1,2,6,7,4,3,5]=>40
[1,2,6,7,4,5,3]=>38
[1,2,6,7,5,3,4]=>38
[1,2,6,7,5,4,3]=>37
[1,2,7,3,4,5,6]=>46
[1,2,7,3,4,6,5]=>45
[1,2,7,3,5,4,6]=>45
[1,2,7,3,5,6,4]=>43
[1,2,7,3,6,4,5]=>43
[1,2,7,3,6,5,4]=>42
[1,2,7,4,3,5,6]=>45
[1,2,7,4,3,6,5]=>44
[1,2,7,4,5,3,6]=>43
[1,2,7,4,5,6,3]=>40
[1,2,7,4,6,3,5]=>41
[1,2,7,4,6,5,3]=>39
[1,2,7,5,3,4,6]=>43
[1,2,7,5,3,6,4]=>41
[1,2,7,5,4,3,6]=>42
[1,2,7,5,4,6,3]=>39
[1,2,7,5,6,3,4]=>38
[1,2,7,5,6,4,3]=>37
[1,2,7,6,3,4,5]=>40
[1,2,7,6,3,5,4]=>39
[1,2,7,6,4,3,5]=>39
[1,2,7,6,4,5,3]=>37
[1,2,7,6,5,3,4]=>37
[1,2,7,6,5,4,3]=>36
[1,3,2,4,5,6,7]=>55
[1,3,2,4,5,7,6]=>54
[1,3,2,4,6,5,7]=>54
[1,3,2,4,6,7,5]=>52
[1,3,2,4,7,5,6]=>52
[1,3,2,4,7,6,5]=>51
[1,3,2,5,4,6,7]=>54
[1,3,2,5,4,7,6]=>53
[1,3,2,5,6,4,7]=>52
[1,3,2,5,6,7,4]=>49
[1,3,2,5,7,4,6]=>50
[1,3,2,5,7,6,4]=>48
[1,3,2,6,4,5,7]=>52
[1,3,2,6,4,7,5]=>50
[1,3,2,6,5,4,7]=>51
[1,3,2,6,5,7,4]=>48
[1,3,2,6,7,4,5]=>47
[1,3,2,6,7,5,4]=>46
[1,3,2,7,4,5,6]=>49
[1,3,2,7,4,6,5]=>48
[1,3,2,7,5,4,6]=>48
[1,3,2,7,5,6,4]=>46
[1,3,2,7,6,4,5]=>46
[1,3,2,7,6,5,4]=>45
[1,3,4,2,5,6,7]=>53
[1,3,4,2,5,7,6]=>52
[1,3,4,2,6,5,7]=>52
[1,3,4,2,6,7,5]=>50
[1,3,4,2,7,5,6]=>50
[1,3,4,2,7,6,5]=>49
[1,3,4,5,2,6,7]=>50
[1,3,4,5,2,7,6]=>49
[1,3,4,5,6,2,7]=>46
[1,3,4,5,6,7,2]=>41
[1,3,4,5,7,2,6]=>44
[1,3,4,5,7,6,2]=>40
[1,3,4,6,2,5,7]=>48
[1,3,4,6,2,7,5]=>46
[1,3,4,6,5,2,7]=>45
[1,3,4,6,5,7,2]=>40
[1,3,4,6,7,2,5]=>41
[1,3,4,6,7,5,2]=>38
[1,3,4,7,2,5,6]=>45
[1,3,4,7,2,6,5]=>44
[1,3,4,7,5,2,6]=>42
[1,3,4,7,5,6,2]=>38
[1,3,4,7,6,2,5]=>40
[1,3,4,7,6,5,2]=>37
[1,3,5,2,4,6,7]=>51
[1,3,5,2,4,7,6]=>50
[1,3,5,2,6,4,7]=>49
[1,3,5,2,6,7,4]=>46
[1,3,5,2,7,4,6]=>47
[1,3,5,2,7,6,4]=>45
[1,3,5,4,2,6,7]=>49
[1,3,5,4,2,7,6]=>48
[1,3,5,4,6,2,7]=>45
[1,3,5,4,6,7,2]=>40
[1,3,5,4,7,2,6]=>43
[1,3,5,4,7,6,2]=>39
[1,3,5,6,2,4,7]=>45
[1,3,5,6,2,7,4]=>42
[1,3,5,6,4,2,7]=>43
[1,3,5,6,4,7,2]=>38
[1,3,5,6,7,2,4]=>37
[1,3,5,6,7,4,2]=>35
[1,3,5,7,2,4,6]=>42
[1,3,5,7,2,6,4]=>40
[1,3,5,7,4,2,6]=>40
[1,3,5,7,4,6,2]=>36
[1,3,5,7,6,2,4]=>36
[1,3,5,7,6,4,2]=>34
[1,3,6,2,4,5,7]=>48
[1,3,6,2,4,7,5]=>46
[1,3,6,2,5,4,7]=>47
[1,3,6,2,5,7,4]=>44
[1,3,6,2,7,4,5]=>43
[1,3,6,2,7,5,4]=>42
[1,3,6,4,2,5,7]=>46
[1,3,6,4,2,7,5]=>44
[1,3,6,4,5,2,7]=>43
[1,3,6,4,5,7,2]=>38
[1,3,6,4,7,2,5]=>39
[1,3,6,4,7,5,2]=>36
[1,3,6,5,2,4,7]=>44
[1,3,6,5,2,7,4]=>41
[1,3,6,5,4,2,7]=>42
[1,3,6,5,4,7,2]=>37
[1,3,6,5,7,2,4]=>36
[1,3,6,5,7,4,2]=>34
[1,3,6,7,2,4,5]=>38
[1,3,6,7,2,5,4]=>37
[1,3,6,7,4,2,5]=>36
[1,3,6,7,4,5,2]=>33
[1,3,6,7,5,2,4]=>34
[1,3,6,7,5,4,2]=>32
[1,3,7,2,4,5,6]=>44
[1,3,7,2,4,6,5]=>43
[1,3,7,2,5,4,6]=>43
[1,3,7,2,5,6,4]=>41
[1,3,7,2,6,4,5]=>41
[1,3,7,2,6,5,4]=>40
[1,3,7,4,2,5,6]=>42
[1,3,7,4,2,6,5]=>41
[1,3,7,4,5,2,6]=>39
[1,3,7,4,5,6,2]=>35
[1,3,7,4,6,2,5]=>37
[1,3,7,4,6,5,2]=>34
[1,3,7,5,2,4,6]=>40
[1,3,7,5,2,6,4]=>38
[1,3,7,5,4,2,6]=>38
[1,3,7,5,4,6,2]=>34
[1,3,7,5,6,2,4]=>34
[1,3,7,5,6,4,2]=>32
[1,3,7,6,2,4,5]=>37
[1,3,7,6,2,5,4]=>36
[1,3,7,6,4,2,5]=>35
[1,3,7,6,4,5,2]=>32
[1,3,7,6,5,2,4]=>33
[1,3,7,6,5,4,2]=>31
[1,4,2,3,5,6,7]=>53
[1,4,2,3,5,7,6]=>52
[1,4,2,3,6,5,7]=>52
[1,4,2,3,6,7,5]=>50
[1,4,2,3,7,5,6]=>50
[1,4,2,3,7,6,5]=>49
[1,4,2,5,3,6,7]=>51
[1,4,2,5,3,7,6]=>50
[1,4,2,5,6,3,7]=>48
[1,4,2,5,6,7,3]=>44
[1,4,2,5,7,3,6]=>46
[1,4,2,5,7,6,3]=>43
[1,4,2,6,3,5,7]=>49
[1,4,2,6,3,7,5]=>47
[1,4,2,6,5,3,7]=>47
[1,4,2,6,5,7,3]=>43
[1,4,2,6,7,3,5]=>43
[1,4,2,6,7,5,3]=>41
[1,4,2,7,3,5,6]=>46
[1,4,2,7,3,6,5]=>45
[1,4,2,7,5,3,6]=>44
[1,4,2,7,5,6,3]=>41
[1,4,2,7,6,3,5]=>42
[1,4,2,7,6,5,3]=>40
[1,4,3,2,5,6,7]=>52
[1,4,3,2,5,7,6]=>51
[1,4,3,2,6,5,7]=>51
[1,4,3,2,6,7,5]=>49
[1,4,3,2,7,5,6]=>49
[1,4,3,2,7,6,5]=>48
[1,4,3,5,2,6,7]=>49
[1,4,3,5,2,7,6]=>48
[1,4,3,5,6,2,7]=>45
[1,4,3,5,6,7,2]=>40
[1,4,3,5,7,2,6]=>43
[1,4,3,5,7,6,2]=>39
[1,4,3,6,2,5,7]=>47
[1,4,3,6,2,7,5]=>45
[1,4,3,6,5,2,7]=>44
[1,4,3,6,5,7,2]=>39
[1,4,3,6,7,2,5]=>40
[1,4,3,6,7,5,2]=>37
[1,4,3,7,2,5,6]=>44
[1,4,3,7,2,6,5]=>43
[1,4,3,7,5,2,6]=>41
[1,4,3,7,5,6,2]=>37
[1,4,3,7,6,2,5]=>39
[1,4,3,7,6,5,2]=>36
[1,4,5,2,3,6,7]=>48
[1,4,5,2,3,7,6]=>47
[1,4,5,2,6,3,7]=>45
[1,4,5,2,6,7,3]=>41
[1,4,5,2,7,3,6]=>43
[1,4,5,2,7,6,3]=>40
[1,4,5,3,2,6,7]=>47
[1,4,5,3,2,7,6]=>46
[1,4,5,3,6,2,7]=>43
[1,4,5,3,6,7,2]=>38
[1,4,5,3,7,2,6]=>41
[1,4,5,3,7,6,2]=>37
[1,4,5,6,2,3,7]=>41
[1,4,5,6,2,7,3]=>37
[1,4,5,6,3,2,7]=>40
[1,4,5,6,3,7,2]=>35
[1,4,5,6,7,2,3]=>32
[1,4,5,6,7,3,2]=>31
[1,4,5,7,2,3,6]=>38
[1,4,5,7,2,6,3]=>35
[1,4,5,7,3,2,6]=>37
[1,4,5,7,3,6,2]=>33
[1,4,5,7,6,2,3]=>31
[1,4,5,7,6,3,2]=>30
[1,4,6,2,3,5,7]=>45
[1,4,6,2,3,7,5]=>43
[1,4,6,2,5,3,7]=>43
[1,4,6,2,5,7,3]=>39
[1,4,6,2,7,3,5]=>39
[1,4,6,2,7,5,3]=>37
[1,4,6,3,2,5,7]=>44
[1,4,6,3,2,7,5]=>42
[1,4,6,3,5,2,7]=>41
[1,4,6,3,5,7,2]=>36
[1,4,6,3,7,2,5]=>37
[1,4,6,3,7,5,2]=>34
[1,4,6,5,2,3,7]=>40
[1,4,6,5,2,7,3]=>36
[1,4,6,5,3,2,7]=>39
[1,4,6,5,3,7,2]=>34
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Description
The non-inversion sum of a permutation.
A pair $a < b$ is an noninversion of a permutation $\pi$ if $\pi(a) < \pi(b)$. The non-inversion sum is given by $\sum(b-a)$ over all non-inversions of $\pi$.
A pair $a < b$ is an noninversion of a permutation $\pi$ if $\pi(a) < \pi(b)$. The non-inversion sum is given by $\sum(b-a)$ over all non-inversions of $\pi$.
References
[1] Sack, J., Úlfarsson, H. Refined inversion statistics on permutations MathSciNet:2880660 arXiv:1106.1995
[2] The inversion sum of a permutation. St000055
[2] The inversion sum of a permutation. St000055
Code
def statistic(pi):
return sum( inv[1]-inv[0] for inv in pi.noninversions(2) )
Created
Dec 23, 2015 at 08:49 by Christian Stump
Updated
Sep 29, 2022 at 19:06 by Will Dowling
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