Identifier
- St001976: Permutations ⟶ ℤ
Values
=>
[1,2]=>0
[2,1]=>1
[1,2,3]=>0
[1,3,2]=>3
[2,1,3]=>1
[2,3,1]=>3
[3,1,2]=>1
[3,2,1]=>4
[1,2,3,4]=>0
[1,2,4,3]=>6
[1,3,2,4]=>3
[1,3,4,2]=>6
[1,4,2,3]=>3
[1,4,3,2]=>9
[2,1,3,4]=>1
[2,1,4,3]=>7
[2,3,1,4]=>3
[2,3,4,1]=>6
[2,4,1,3]=>3
[2,4,3,1]=>9
[3,1,2,4]=>1
[3,1,4,2]=>7
[3,2,1,4]=>4
[3,2,4,1]=>7
[3,4,1,2]=>3
[3,4,2,1]=>9
[4,1,2,3]=>1
[4,1,3,2]=>7
[4,2,1,3]=>4
[4,2,3,1]=>7
[4,3,1,2]=>4
[4,3,2,1]=>10
[1,2,3,4,5]=>0
[1,2,3,5,4]=>10
[1,2,4,3,5]=>6
[1,2,4,5,3]=>10
[1,2,5,3,4]=>6
[1,2,5,4,3]=>16
[1,3,2,4,5]=>3
[1,3,2,5,4]=>13
[1,3,4,2,5]=>6
[1,3,4,5,2]=>10
[1,3,5,2,4]=>6
[1,3,5,4,2]=>16
[1,4,2,3,5]=>3
[1,4,2,5,3]=>13
[1,4,3,2,5]=>9
[1,4,3,5,2]=>13
[1,4,5,2,3]=>6
[1,4,5,3,2]=>16
[1,5,2,3,4]=>3
[1,5,2,4,3]=>13
[1,5,3,2,4]=>9
[1,5,3,4,2]=>13
[1,5,4,2,3]=>9
[1,5,4,3,2]=>19
[2,1,3,4,5]=>1
[2,1,3,5,4]=>11
[2,1,4,3,5]=>7
[2,1,4,5,3]=>11
[2,1,5,3,4]=>7
[2,1,5,4,3]=>17
[2,3,1,4,5]=>3
[2,3,1,5,4]=>13
[2,3,4,1,5]=>6
[2,3,4,5,1]=>10
[2,3,5,1,4]=>6
[2,3,5,4,1]=>16
[2,4,1,3,5]=>3
[2,4,1,5,3]=>13
[2,4,3,1,5]=>9
[2,4,3,5,1]=>13
[2,4,5,1,3]=>6
[2,4,5,3,1]=>16
[2,5,1,3,4]=>3
[2,5,1,4,3]=>13
[2,5,3,1,4]=>9
[2,5,3,4,1]=>13
[2,5,4,1,3]=>9
[2,5,4,3,1]=>19
[3,1,2,4,5]=>1
[3,1,2,5,4]=>11
[3,1,4,2,5]=>7
[3,1,4,5,2]=>11
[3,1,5,2,4]=>7
[3,1,5,4,2]=>17
[3,2,1,4,5]=>4
[3,2,1,5,4]=>14
[3,2,4,1,5]=>7
[3,2,4,5,1]=>11
[3,2,5,1,4]=>7
[3,2,5,4,1]=>17
[3,4,1,2,5]=>3
[3,4,1,5,2]=>13
[3,4,2,1,5]=>9
[3,4,2,5,1]=>13
[3,4,5,1,2]=>6
[3,4,5,2,1]=>16
[3,5,1,2,4]=>3
[3,5,1,4,2]=>13
[3,5,2,1,4]=>9
[3,5,2,4,1]=>13
[3,5,4,1,2]=>9
[3,5,4,2,1]=>19
[4,1,2,3,5]=>1
[4,1,2,5,3]=>11
[4,1,3,2,5]=>7
[4,1,3,5,2]=>11
[4,1,5,2,3]=>7
[4,1,5,3,2]=>17
[4,2,1,3,5]=>4
[4,2,1,5,3]=>14
[4,2,3,1,5]=>7
[4,2,3,5,1]=>11
[4,2,5,1,3]=>7
[4,2,5,3,1]=>17
[4,3,1,2,5]=>4
[4,3,1,5,2]=>14
[4,3,2,1,5]=>10
[4,3,2,5,1]=>14
[4,3,5,1,2]=>7
[4,3,5,2,1]=>17
[4,5,1,2,3]=>3
[4,5,1,3,2]=>13
[4,5,2,1,3]=>9
[4,5,2,3,1]=>13
[4,5,3,1,2]=>9
[4,5,3,2,1]=>19
[5,1,2,3,4]=>1
[5,1,2,4,3]=>11
[5,1,3,2,4]=>7
[5,1,3,4,2]=>11
[5,1,4,2,3]=>7
[5,1,4,3,2]=>17
[5,2,1,3,4]=>4
[5,2,1,4,3]=>14
[5,2,3,1,4]=>7
[5,2,3,4,1]=>11
[5,2,4,1,3]=>7
[5,2,4,3,1]=>17
[5,3,1,2,4]=>4
[5,3,1,4,2]=>14
[5,3,2,1,4]=>10
[5,3,2,4,1]=>14
[5,3,4,1,2]=>7
[5,3,4,2,1]=>17
[5,4,1,2,3]=>4
[5,4,1,3,2]=>14
[5,4,2,1,3]=>10
[5,4,2,3,1]=>14
[5,4,3,1,2]=>10
[5,4,3,2,1]=>20
[1,2,3,4,5,6]=>0
[1,2,3,4,6,5]=>15
[1,2,3,5,4,6]=>10
[1,2,3,5,6,4]=>15
[1,2,3,6,4,5]=>10
[1,2,3,6,5,4]=>25
[1,2,4,3,5,6]=>6
[1,2,4,3,6,5]=>21
[1,2,4,5,3,6]=>10
[1,2,4,5,6,3]=>15
[1,2,4,6,3,5]=>10
[1,2,4,6,5,3]=>25
[1,2,5,3,4,6]=>6
[1,2,5,3,6,4]=>21
[1,2,5,4,3,6]=>16
[1,2,5,4,6,3]=>21
[1,2,5,6,3,4]=>10
[1,2,5,6,4,3]=>25
[1,2,6,3,4,5]=>6
[1,2,6,3,5,4]=>21
[1,2,6,4,3,5]=>16
[1,2,6,4,5,3]=>21
[1,2,6,5,3,4]=>16
[1,2,6,5,4,3]=>31
[1,3,2,4,5,6]=>3
[1,3,2,4,6,5]=>18
[1,3,2,5,4,6]=>13
[1,3,2,5,6,4]=>18
[1,3,2,6,4,5]=>13
[1,3,2,6,5,4]=>28
[1,3,4,2,5,6]=>6
[1,3,4,2,6,5]=>21
[1,3,4,5,2,6]=>10
[1,3,4,5,6,2]=>15
[1,3,4,6,2,5]=>10
[1,3,4,6,5,2]=>25
[1,3,5,2,4,6]=>6
[1,3,5,2,6,4]=>21
[1,3,5,4,2,6]=>16
[1,3,5,4,6,2]=>21
[1,3,5,6,2,4]=>10
[1,3,5,6,4,2]=>25
[1,3,6,2,4,5]=>6
[1,3,6,2,5,4]=>21
[1,3,6,4,2,5]=>16
[1,3,6,4,5,2]=>21
[1,3,6,5,2,4]=>16
[1,3,6,5,4,2]=>31
[1,4,2,3,5,6]=>3
[1,4,2,3,6,5]=>18
[1,4,2,5,3,6]=>13
[1,4,2,5,6,3]=>18
[1,4,2,6,3,5]=>13
[1,4,2,6,5,3]=>28
[1,4,3,2,5,6]=>9
[1,4,3,2,6,5]=>24
[1,4,3,5,2,6]=>13
[1,4,3,5,6,2]=>18
[1,4,3,6,2,5]=>13
[1,4,3,6,5,2]=>28
[1,4,5,2,3,6]=>6
[1,4,5,2,6,3]=>21
[1,4,5,3,2,6]=>16
[1,4,5,3,6,2]=>21
[1,4,5,6,2,3]=>10
[1,4,5,6,3,2]=>25
[1,4,6,2,3,5]=>6
[1,4,6,2,5,3]=>21
[1,4,6,3,2,5]=>16
[1,4,6,3,5,2]=>21
[1,4,6,5,2,3]=>16
[1,4,6,5,3,2]=>31
[1,5,2,3,4,6]=>3
[1,5,2,3,6,4]=>18
[1,5,2,4,3,6]=>13
[1,5,2,4,6,3]=>18
[1,5,2,6,3,4]=>13
[1,5,2,6,4,3]=>28
[1,5,3,2,4,6]=>9
[1,5,3,2,6,4]=>24
[1,5,3,4,2,6]=>13
[1,5,3,4,6,2]=>18
[1,5,3,6,2,4]=>13
[1,5,3,6,4,2]=>28
[1,5,4,2,3,6]=>9
[1,5,4,2,6,3]=>24
[1,5,4,3,2,6]=>19
[1,5,4,3,6,2]=>24
[1,5,4,6,2,3]=>13
[1,5,4,6,3,2]=>28
[1,5,6,2,3,4]=>6
[1,5,6,2,4,3]=>21
[1,5,6,3,2,4]=>16
[1,5,6,3,4,2]=>21
[1,5,6,4,2,3]=>16
[1,5,6,4,3,2]=>31
[1,6,2,3,4,5]=>3
[1,6,2,3,5,4]=>18
[1,6,2,4,3,5]=>13
[1,6,2,4,5,3]=>18
[1,6,2,5,3,4]=>13
[1,6,2,5,4,3]=>28
[1,6,3,2,4,5]=>9
[1,6,3,2,5,4]=>24
[1,6,3,4,2,5]=>13
[1,6,3,4,5,2]=>18
[1,6,3,5,2,4]=>13
[1,6,3,5,4,2]=>28
[1,6,4,2,3,5]=>9
[1,6,4,2,5,3]=>24
[1,6,4,3,2,5]=>19
[1,6,4,3,5,2]=>24
[1,6,4,5,2,3]=>13
[1,6,4,5,3,2]=>28
[1,6,5,2,3,4]=>9
[1,6,5,2,4,3]=>24
[1,6,5,3,2,4]=>19
[1,6,5,3,4,2]=>24
[1,6,5,4,2,3]=>19
[1,6,5,4,3,2]=>34
[2,1,3,4,5,6]=>1
[2,1,3,4,6,5]=>16
[2,1,3,5,4,6]=>11
[2,1,3,5,6,4]=>16
[2,1,3,6,4,5]=>11
[2,1,3,6,5,4]=>26
[2,1,4,3,5,6]=>7
[2,1,4,3,6,5]=>22
[2,1,4,5,3,6]=>11
[2,1,4,5,6,3]=>16
[2,1,4,6,3,5]=>11
[2,1,4,6,5,3]=>26
[2,1,5,3,4,6]=>7
[2,1,5,3,6,4]=>22
[2,1,5,4,3,6]=>17
[2,1,5,4,6,3]=>22
[2,1,5,6,3,4]=>11
[2,1,5,6,4,3]=>26
[2,1,6,3,4,5]=>7
[2,1,6,3,5,4]=>22
[2,1,6,4,3,5]=>17
[2,1,6,4,5,3]=>22
[2,1,6,5,3,4]=>17
[2,1,6,5,4,3]=>32
[2,3,1,4,5,6]=>3
[2,3,1,4,6,5]=>18
[2,3,1,5,4,6]=>13
[2,3,1,5,6,4]=>18
[2,3,1,6,4,5]=>13
[2,3,1,6,5,4]=>28
[2,3,4,1,5,6]=>6
[2,3,4,1,6,5]=>21
[2,3,4,5,1,6]=>10
[2,3,4,5,6,1]=>15
[2,3,4,6,1,5]=>10
[2,3,4,6,5,1]=>25
[2,3,5,1,4,6]=>6
[2,3,5,1,6,4]=>21
[2,3,5,4,1,6]=>16
[2,3,5,4,6,1]=>21
[2,3,5,6,1,4]=>10
[2,3,5,6,4,1]=>25
[2,3,6,1,4,5]=>6
[2,3,6,1,5,4]=>21
[2,3,6,4,1,5]=>16
[2,3,6,4,5,1]=>21
[2,3,6,5,1,4]=>16
[2,3,6,5,4,1]=>31
[2,4,1,3,5,6]=>3
[2,4,1,3,6,5]=>18
[2,4,1,5,3,6]=>13
[2,4,1,5,6,3]=>18
[2,4,1,6,3,5]=>13
[2,4,1,6,5,3]=>28
[2,4,3,1,5,6]=>9
[2,4,3,1,6,5]=>24
[2,4,3,5,1,6]=>13
[2,4,3,5,6,1]=>18
[2,4,3,6,1,5]=>13
[2,4,3,6,5,1]=>28
[2,4,5,1,3,6]=>6
[2,4,5,1,6,3]=>21
[2,4,5,3,1,6]=>16
[2,4,5,3,6,1]=>21
[2,4,5,6,1,3]=>10
[2,4,5,6,3,1]=>25
[2,4,6,1,3,5]=>6
[2,4,6,1,5,3]=>21
[2,4,6,3,1,5]=>16
[2,4,6,3,5,1]=>21
[2,4,6,5,1,3]=>16
[2,4,6,5,3,1]=>31
[2,5,1,3,4,6]=>3
[2,5,1,3,6,4]=>18
[2,5,1,4,3,6]=>13
[2,5,1,4,6,3]=>18
[2,5,1,6,3,4]=>13
[2,5,1,6,4,3]=>28
[2,5,3,1,4,6]=>9
[2,5,3,1,6,4]=>24
[2,5,3,4,1,6]=>13
[2,5,3,4,6,1]=>18
[2,5,3,6,1,4]=>13
[2,5,3,6,4,1]=>28
[2,5,4,1,3,6]=>9
[2,5,4,1,6,3]=>24
[2,5,4,3,1,6]=>19
[2,5,4,3,6,1]=>24
[2,5,4,6,1,3]=>13
[2,5,4,6,3,1]=>28
[2,5,6,1,3,4]=>6
[2,5,6,1,4,3]=>21
[2,5,6,3,1,4]=>16
[2,5,6,3,4,1]=>21
[2,5,6,4,1,3]=>16
[2,5,6,4,3,1]=>31
[2,6,1,3,4,5]=>3
[2,6,1,3,5,4]=>18
[2,6,1,4,3,5]=>13
[2,6,1,4,5,3]=>18
[2,6,1,5,3,4]=>13
[2,6,1,5,4,3]=>28
[2,6,3,1,4,5]=>9
[2,6,3,1,5,4]=>24
[2,6,3,4,1,5]=>13
[2,6,3,4,5,1]=>18
[2,6,3,5,1,4]=>13
[2,6,3,5,4,1]=>28
[2,6,4,1,3,5]=>9
[2,6,4,1,5,3]=>24
[2,6,4,3,1,5]=>19
[2,6,4,3,5,1]=>24
[2,6,4,5,1,3]=>13
[2,6,4,5,3,1]=>28
[2,6,5,1,3,4]=>9
[2,6,5,1,4,3]=>24
[2,6,5,3,1,4]=>19
[2,6,5,3,4,1]=>24
[2,6,5,4,1,3]=>19
[2,6,5,4,3,1]=>34
[3,1,2,4,5,6]=>1
[3,1,2,4,6,5]=>16
[3,1,2,5,4,6]=>11
[3,1,2,5,6,4]=>16
[3,1,2,6,4,5]=>11
[3,1,2,6,5,4]=>26
[3,1,4,2,5,6]=>7
[3,1,4,2,6,5]=>22
[3,1,4,5,2,6]=>11
[3,1,4,5,6,2]=>16
[3,1,4,6,2,5]=>11
[3,1,4,6,5,2]=>26
[3,1,5,2,4,6]=>7
[3,1,5,2,6,4]=>22
[3,1,5,4,2,6]=>17
[3,1,5,4,6,2]=>22
[3,1,5,6,2,4]=>11
[3,1,5,6,4,2]=>26
[3,1,6,2,4,5]=>7
[3,1,6,2,5,4]=>22
[3,1,6,4,2,5]=>17
[3,1,6,4,5,2]=>22
[3,1,6,5,2,4]=>17
[3,1,6,5,4,2]=>32
[3,2,1,4,5,6]=>4
[3,2,1,4,6,5]=>19
[3,2,1,5,4,6]=>14
[3,2,1,5,6,4]=>19
[3,2,1,6,4,5]=>14
[3,2,1,6,5,4]=>29
[3,2,4,1,5,6]=>7
[3,2,4,1,6,5]=>22
[3,2,4,5,1,6]=>11
[3,2,4,5,6,1]=>16
[3,2,4,6,1,5]=>11
[3,2,4,6,5,1]=>26
[3,2,5,1,4,6]=>7
[3,2,5,1,6,4]=>22
[3,2,5,4,1,6]=>17
[3,2,5,4,6,1]=>22
[3,2,5,6,1,4]=>11
[3,2,5,6,4,1]=>26
[3,2,6,1,4,5]=>7
[3,2,6,1,5,4]=>22
[3,2,6,4,1,5]=>17
[3,2,6,4,5,1]=>22
[3,2,6,5,1,4]=>17
[3,2,6,5,4,1]=>32
[3,4,1,2,5,6]=>3
[3,4,1,2,6,5]=>18
[3,4,1,5,2,6]=>13
[3,4,1,5,6,2]=>18
[3,4,1,6,2,5]=>13
[3,4,1,6,5,2]=>28
[3,4,2,1,5,6]=>9
[3,4,2,1,6,5]=>24
[3,4,2,5,1,6]=>13
[3,4,2,5,6,1]=>18
[3,4,2,6,1,5]=>13
[3,4,2,6,5,1]=>28
[3,4,5,1,2,6]=>6
[3,4,5,1,6,2]=>21
[3,4,5,2,1,6]=>16
[3,4,5,2,6,1]=>21
[3,4,5,6,1,2]=>10
[3,4,5,6,2,1]=>25
[3,4,6,1,2,5]=>6
[3,4,6,1,5,2]=>21
[3,4,6,2,1,5]=>16
[3,4,6,2,5,1]=>21
[3,4,6,5,1,2]=>16
[3,4,6,5,2,1]=>31
[3,5,1,2,4,6]=>3
[3,5,1,2,6,4]=>18
[3,5,1,4,2,6]=>13
[3,5,1,4,6,2]=>18
[3,5,1,6,2,4]=>13
[3,5,1,6,4,2]=>28
[3,5,2,1,4,6]=>9
[3,5,2,1,6,4]=>24
[3,5,2,4,1,6]=>13
[3,5,2,4,6,1]=>18
[3,5,2,6,1,4]=>13
[3,5,2,6,4,1]=>28
[3,5,4,1,2,6]=>9
[3,5,4,1,6,2]=>24
[3,5,4,2,1,6]=>19
[3,5,4,2,6,1]=>24
[3,5,4,6,1,2]=>13
[3,5,4,6,2,1]=>28
[3,5,6,1,2,4]=>6
[3,5,6,1,4,2]=>21
[3,5,6,2,1,4]=>16
[3,5,6,2,4,1]=>21
[3,5,6,4,1,2]=>16
[3,5,6,4,2,1]=>31
[3,6,1,2,4,5]=>3
[3,6,1,2,5,4]=>18
[3,6,1,4,2,5]=>13
[3,6,1,4,5,2]=>18
[3,6,1,5,2,4]=>13
[3,6,1,5,4,2]=>28
[3,6,2,1,4,5]=>9
[3,6,2,1,5,4]=>24
[3,6,2,4,1,5]=>13
[3,6,2,4,5,1]=>18
[3,6,2,5,1,4]=>13
[3,6,2,5,4,1]=>28
[3,6,4,1,2,5]=>9
[3,6,4,1,5,2]=>24
[3,6,4,2,1,5]=>19
[3,6,4,2,5,1]=>24
[3,6,4,5,1,2]=>13
[3,6,4,5,2,1]=>28
[3,6,5,1,2,4]=>9
[3,6,5,1,4,2]=>24
[3,6,5,2,1,4]=>19
[3,6,5,2,4,1]=>24
[3,6,5,4,1,2]=>19
[3,6,5,4,2,1]=>34
[4,1,2,3,5,6]=>1
[4,1,2,3,6,5]=>16
[4,1,2,5,3,6]=>11
[4,1,2,5,6,3]=>16
[4,1,2,6,3,5]=>11
[4,1,2,6,5,3]=>26
[4,1,3,2,5,6]=>7
[4,1,3,2,6,5]=>22
[4,1,3,5,2,6]=>11
[4,1,3,5,6,2]=>16
[4,1,3,6,2,5]=>11
[4,1,3,6,5,2]=>26
[4,1,5,2,3,6]=>7
[4,1,5,2,6,3]=>22
[4,1,5,3,2,6]=>17
[4,1,5,3,6,2]=>22
[4,1,5,6,2,3]=>11
[4,1,5,6,3,2]=>26
[4,1,6,2,3,5]=>7
[4,1,6,2,5,3]=>22
[4,1,6,3,2,5]=>17
[4,1,6,3,5,2]=>22
[4,1,6,5,2,3]=>17
[4,1,6,5,3,2]=>32
[4,2,1,3,5,6]=>4
[4,2,1,3,6,5]=>19
[4,2,1,5,3,6]=>14
[4,2,1,5,6,3]=>19
[4,2,1,6,3,5]=>14
[4,2,1,6,5,3]=>29
[4,2,3,1,5,6]=>7
[4,2,3,1,6,5]=>22
[4,2,3,5,1,6]=>11
[4,2,3,5,6,1]=>16
[4,2,3,6,1,5]=>11
[4,2,3,6,5,1]=>26
[4,2,5,1,3,6]=>7
[4,2,5,1,6,3]=>22
[4,2,5,3,1,6]=>17
[4,2,5,3,6,1]=>22
[4,2,5,6,1,3]=>11
[4,2,5,6,3,1]=>26
[4,2,6,1,3,5]=>7
[4,2,6,1,5,3]=>22
[4,2,6,3,1,5]=>17
[4,2,6,3,5,1]=>22
[4,2,6,5,1,3]=>17
[4,2,6,5,3,1]=>32
[4,3,1,2,5,6]=>4
[4,3,1,2,6,5]=>19
[4,3,1,5,2,6]=>14
[4,3,1,5,6,2]=>19
[4,3,1,6,2,5]=>14
[4,3,1,6,5,2]=>29
[4,3,2,1,5,6]=>10
[4,3,2,1,6,5]=>25
[4,3,2,5,1,6]=>14
[4,3,2,5,6,1]=>19
[4,3,2,6,1,5]=>14
[4,3,2,6,5,1]=>29
[4,3,5,1,2,6]=>7
[4,3,5,1,6,2]=>22
[4,3,5,2,1,6]=>17
[4,3,5,2,6,1]=>22
[4,3,5,6,1,2]=>11
[4,3,5,6,2,1]=>26
[4,3,6,1,2,5]=>7
[4,3,6,1,5,2]=>22
[4,3,6,2,1,5]=>17
[4,3,6,2,5,1]=>22
[4,3,6,5,1,2]=>17
[4,3,6,5,2,1]=>32
[4,5,1,2,3,6]=>3
[4,5,1,2,6,3]=>18
[4,5,1,3,2,6]=>13
[4,5,1,3,6,2]=>18
[4,5,1,6,2,3]=>13
[4,5,1,6,3,2]=>28
[4,5,2,1,3,6]=>9
[4,5,2,1,6,3]=>24
[4,5,2,3,1,6]=>13
[4,5,2,3,6,1]=>18
[4,5,2,6,1,3]=>13
[4,5,2,6,3,1]=>28
[4,5,3,1,2,6]=>9
[4,5,3,1,6,2]=>24
[4,5,3,2,1,6]=>19
[4,5,3,2,6,1]=>24
[4,5,3,6,1,2]=>13
[4,5,3,6,2,1]=>28
[4,5,6,1,2,3]=>6
[4,5,6,1,3,2]=>21
[4,5,6,2,1,3]=>16
[4,5,6,2,3,1]=>21
[4,5,6,3,1,2]=>16
[4,5,6,3,2,1]=>31
[4,6,1,2,3,5]=>3
[4,6,1,2,5,3]=>18
[4,6,1,3,2,5]=>13
[4,6,1,3,5,2]=>18
[4,6,1,5,2,3]=>13
[4,6,1,5,3,2]=>28
[4,6,2,1,3,5]=>9
[4,6,2,1,5,3]=>24
[4,6,2,3,1,5]=>13
[4,6,2,3,5,1]=>18
[4,6,2,5,1,3]=>13
[4,6,2,5,3,1]=>28
[4,6,3,1,2,5]=>9
[4,6,3,1,5,2]=>24
[4,6,3,2,1,5]=>19
[4,6,3,2,5,1]=>24
[4,6,3,5,1,2]=>13
[4,6,3,5,2,1]=>28
[4,6,5,1,2,3]=>9
[4,6,5,1,3,2]=>24
[4,6,5,2,1,3]=>19
[4,6,5,2,3,1]=>24
[4,6,5,3,1,2]=>19
[4,6,5,3,2,1]=>34
[5,1,2,3,4,6]=>1
[5,1,2,3,6,4]=>16
[5,1,2,4,3,6]=>11
[5,1,2,4,6,3]=>16
[5,1,2,6,3,4]=>11
[5,1,2,6,4,3]=>26
[5,1,3,2,4,6]=>7
[5,1,3,2,6,4]=>22
[5,1,3,4,2,6]=>11
[5,1,3,4,6,2]=>16
[5,1,3,6,2,4]=>11
[5,1,3,6,4,2]=>26
[5,1,4,2,3,6]=>7
[5,1,4,2,6,3]=>22
[5,1,4,3,2,6]=>17
[5,1,4,3,6,2]=>22
[5,1,4,6,2,3]=>11
[5,1,4,6,3,2]=>26
[5,1,6,2,3,4]=>7
[5,1,6,2,4,3]=>22
[5,1,6,3,2,4]=>17
[5,1,6,3,4,2]=>22
[5,1,6,4,2,3]=>17
[5,1,6,4,3,2]=>32
[5,2,1,3,4,6]=>4
[5,2,1,3,6,4]=>19
[5,2,1,4,3,6]=>14
[5,2,1,4,6,3]=>19
[5,2,1,6,3,4]=>14
[5,2,1,6,4,3]=>29
[5,2,3,1,4,6]=>7
[5,2,3,1,6,4]=>22
[5,2,3,4,1,6]=>11
[5,2,3,4,6,1]=>16
[5,2,3,6,1,4]=>11
[5,2,3,6,4,1]=>26
[5,2,4,1,3,6]=>7
[5,2,4,1,6,3]=>22
[5,2,4,3,1,6]=>17
[5,2,4,3,6,1]=>22
[5,2,4,6,1,3]=>11
[5,2,4,6,3,1]=>26
[5,2,6,1,3,4]=>7
[5,2,6,1,4,3]=>22
[5,2,6,3,1,4]=>17
[5,2,6,3,4,1]=>22
[5,2,6,4,1,3]=>17
[5,2,6,4,3,1]=>32
[5,3,1,2,4,6]=>4
[5,3,1,2,6,4]=>19
[5,3,1,4,2,6]=>14
[5,3,1,4,6,2]=>19
[5,3,1,6,2,4]=>14
[5,3,1,6,4,2]=>29
[5,3,2,1,4,6]=>10
[5,3,2,1,6,4]=>25
[5,3,2,4,1,6]=>14
[5,3,2,4,6,1]=>19
[5,3,2,6,1,4]=>14
[5,3,2,6,4,1]=>29
[5,3,4,1,2,6]=>7
[5,3,4,1,6,2]=>22
[5,3,4,2,1,6]=>17
[5,3,4,2,6,1]=>22
[5,3,4,6,1,2]=>11
[5,3,4,6,2,1]=>26
[5,3,6,1,2,4]=>7
[5,3,6,1,4,2]=>22
[5,3,6,2,1,4]=>17
[5,3,6,2,4,1]=>22
[5,3,6,4,1,2]=>17
[5,3,6,4,2,1]=>32
[5,4,1,2,3,6]=>4
[5,4,1,2,6,3]=>19
[5,4,1,3,2,6]=>14
[5,4,1,3,6,2]=>19
[5,4,1,6,2,3]=>14
[5,4,1,6,3,2]=>29
[5,4,2,1,3,6]=>10
[5,4,2,1,6,3]=>25
[5,4,2,3,1,6]=>14
[5,4,2,3,6,1]=>19
[5,4,2,6,1,3]=>14
[5,4,2,6,3,1]=>29
[5,4,3,1,2,6]=>10
[5,4,3,1,6,2]=>25
[5,4,3,2,1,6]=>20
[5,4,3,2,6,1]=>25
[5,4,3,6,1,2]=>14
[5,4,3,6,2,1]=>29
[5,4,6,1,2,3]=>7
[5,4,6,1,3,2]=>22
[5,4,6,2,1,3]=>17
[5,4,6,2,3,1]=>22
[5,4,6,3,1,2]=>17
[5,4,6,3,2,1]=>32
[5,6,1,2,3,4]=>3
[5,6,1,2,4,3]=>18
[5,6,1,3,2,4]=>13
[5,6,1,3,4,2]=>18
[5,6,1,4,2,3]=>13
[5,6,1,4,3,2]=>28
[5,6,2,1,3,4]=>9
[5,6,2,1,4,3]=>24
[5,6,2,3,1,4]=>13
[5,6,2,3,4,1]=>18
[5,6,2,4,1,3]=>13
[5,6,2,4,3,1]=>28
[5,6,3,1,2,4]=>9
[5,6,3,1,4,2]=>24
[5,6,3,2,1,4]=>19
[5,6,3,2,4,1]=>24
[5,6,3,4,1,2]=>13
[5,6,3,4,2,1]=>28
[5,6,4,1,2,3]=>9
[5,6,4,1,3,2]=>24
[5,6,4,2,1,3]=>19
[5,6,4,2,3,1]=>24
[5,6,4,3,1,2]=>19
[5,6,4,3,2,1]=>34
[6,1,2,3,4,5]=>1
[6,1,2,3,5,4]=>16
[6,1,2,4,3,5]=>11
[6,1,2,4,5,3]=>16
[6,1,2,5,3,4]=>11
[6,1,2,5,4,3]=>26
[6,1,3,2,4,5]=>7
[6,1,3,2,5,4]=>22
[6,1,3,4,2,5]=>11
[6,1,3,4,5,2]=>16
[6,1,3,5,2,4]=>11
[6,1,3,5,4,2]=>26
[6,1,4,2,3,5]=>7
[6,1,4,2,5,3]=>22
[6,1,4,3,2,5]=>17
[6,1,4,3,5,2]=>22
[6,1,4,5,2,3]=>11
[6,1,4,5,3,2]=>26
[6,1,5,2,3,4]=>7
[6,1,5,2,4,3]=>22
[6,1,5,3,2,4]=>17
[6,1,5,3,4,2]=>22
[6,1,5,4,2,3]=>17
[6,1,5,4,3,2]=>32
[6,2,1,3,4,5]=>4
[6,2,1,3,5,4]=>19
[6,2,1,4,3,5]=>14
[6,2,1,4,5,3]=>19
[6,2,1,5,3,4]=>14
[6,2,1,5,4,3]=>29
[6,2,3,1,4,5]=>7
[6,2,3,1,5,4]=>22
[6,2,3,4,1,5]=>11
[6,2,3,4,5,1]=>16
[6,2,3,5,1,4]=>11
[6,2,3,5,4,1]=>26
[6,2,4,1,3,5]=>7
[6,2,4,1,5,3]=>22
[6,2,4,3,1,5]=>17
[6,2,4,3,5,1]=>22
[6,2,4,5,1,3]=>11
[6,2,4,5,3,1]=>26
[6,2,5,1,3,4]=>7
[6,2,5,1,4,3]=>22
[6,2,5,3,1,4]=>17
[6,2,5,3,4,1]=>22
[6,2,5,4,1,3]=>17
[6,2,5,4,3,1]=>32
[6,3,1,2,4,5]=>4
[6,3,1,2,5,4]=>19
[6,3,1,4,2,5]=>14
[6,3,1,4,5,2]=>19
[6,3,1,5,2,4]=>14
[6,3,1,5,4,2]=>29
[6,3,2,1,4,5]=>10
[6,3,2,1,5,4]=>25
[6,3,2,4,1,5]=>14
[6,3,2,4,5,1]=>19
[6,3,2,5,1,4]=>14
[6,3,2,5,4,1]=>29
[6,3,4,1,2,5]=>7
[6,3,4,1,5,2]=>22
[6,3,4,2,1,5]=>17
[6,3,4,2,5,1]=>22
[6,3,4,5,1,2]=>11
[6,3,4,5,2,1]=>26
[6,3,5,1,2,4]=>7
[6,3,5,1,4,2]=>22
[6,3,5,2,1,4]=>17
[6,3,5,2,4,1]=>22
[6,3,5,4,1,2]=>17
[6,3,5,4,2,1]=>32
[6,4,1,2,3,5]=>4
[6,4,1,2,5,3]=>19
[6,4,1,3,2,5]=>14
[6,4,1,3,5,2]=>19
[6,4,1,5,2,3]=>14
[6,4,1,5,3,2]=>29
[6,4,2,1,3,5]=>10
[6,4,2,1,5,3]=>25
[6,4,2,3,1,5]=>14
[6,4,2,3,5,1]=>19
[6,4,2,5,1,3]=>14
[6,4,2,5,3,1]=>29
[6,4,3,1,2,5]=>10
[6,4,3,1,5,2]=>25
[6,4,3,2,1,5]=>20
[6,4,3,2,5,1]=>25
[6,4,3,5,1,2]=>14
[6,4,3,5,2,1]=>29
[6,4,5,1,2,3]=>7
[6,4,5,1,3,2]=>22
[6,4,5,2,1,3]=>17
[6,4,5,2,3,1]=>22
[6,4,5,3,1,2]=>17
[6,4,5,3,2,1]=>32
[6,5,1,2,3,4]=>4
[6,5,1,2,4,3]=>19
[6,5,1,3,2,4]=>14
[6,5,1,3,4,2]=>19
[6,5,1,4,2,3]=>14
[6,5,1,4,3,2]=>29
[6,5,2,1,3,4]=>10
[6,5,2,1,4,3]=>25
[6,5,2,3,1,4]=>14
[6,5,2,3,4,1]=>19
[6,5,2,4,1,3]=>14
[6,5,2,4,3,1]=>29
[6,5,3,1,2,4]=>10
[6,5,3,1,4,2]=>25
[6,5,3,2,1,4]=>20
[6,5,3,2,4,1]=>25
[6,5,3,4,1,2]=>14
[6,5,3,4,2,1]=>29
[6,5,4,1,2,3]=>10
[6,5,4,1,3,2]=>25
[6,5,4,2,1,3]=>20
[6,5,4,2,3,1]=>25
[6,5,4,3,1,2]=>20
[6,5,4,3,2,1]=>35
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 bin statistic of a permutation.
The bin statistic of a permutation $\sigma$ is defined as
$$ \sum_{i\in Des(\sigma)} \binom{i + 1}{2}, $$
where $Des(\sigma)$ is the set of all indices $i$ such that $\sigma(i) > \sigma(i + 1)$.
The bin statistic of a permutation $\sigma$ is defined as
$$ \sum_{i\in Des(\sigma)} \binom{i + 1}{2}, $$
where $Des(\sigma)$ is the set of all indices $i$ such that $\sigma(i) > \sigma(i + 1)$.
References
[1] Bright, K. L., Savage, C. D. The geometry of lecture hall partitions and quadratic permutation statistics MathSciNet:2673867
[2] Alfes, C., Maglione, J., Voll, C. Symplectic Hecke eigenbases from Ehrhart polynomials .
[3] Savage, C. D. The mathematics of lecture hall partitions MathSciNet:3534075 DOI:10.1016/j.jcta.2016.06.006
[2] Alfes, C., Maglione, J., Voll, C. Symplectic Hecke eigenbases from Ehrhart polynomials .
[3] Savage, C. D. The mathematics of lecture hall partitions MathSciNet:3534075 DOI:10.1016/j.jcta.2016.06.006
Code
def statistic(pi):
return sum(binomial(i + 1, 2) for i in pi.descents())
Created
Sep 07, 2025 at 08:26 by Joshua Maglione
Updated
Sep 07, 2025 at 08:26 by Joshua Maglione
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!