Identifier
- St000616: Permutations ⟶ ℤ
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
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].
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
[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
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!