Identifier
- St000756: Permutations ⟶ ℤ
Values
=>
[1]=>1
[1,2]=>3
[2,1]=>1
[1,2,3]=>6
[1,3,2]=>3
[2,1,3]=>4
[2,3,1]=>3
[3,1,2]=>1
[3,2,1]=>1
[1,2,3,4]=>10
[1,2,4,3]=>6
[1,3,2,4]=>7
[1,3,4,2]=>6
[1,4,2,3]=>3
[1,4,3,2]=>3
[2,1,3,4]=>8
[2,1,4,3]=>4
[2,3,1,4]=>7
[2,3,4,1]=>6
[2,4,1,3]=>3
[2,4,3,1]=>3
[3,1,2,4]=>5
[3,1,4,2]=>4
[3,2,1,4]=>5
[3,2,4,1]=>4
[3,4,1,2]=>3
[3,4,2,1]=>3
[4,1,2,3]=>1
[4,1,3,2]=>1
[4,2,1,3]=>1
[4,2,3,1]=>1
[4,3,1,2]=>1
[4,3,2,1]=>1
[1,2,3,4,5]=>15
[1,2,3,5,4]=>10
[1,2,4,3,5]=>11
[1,2,4,5,3]=>10
[1,2,5,3,4]=>6
[1,2,5,4,3]=>6
[1,3,2,4,5]=>12
[1,3,2,5,4]=>7
[1,3,4,2,5]=>11
[1,3,4,5,2]=>10
[1,3,5,2,4]=>6
[1,3,5,4,2]=>6
[1,4,2,3,5]=>8
[1,4,2,5,3]=>7
[1,4,3,2,5]=>8
[1,4,3,5,2]=>7
[1,4,5,2,3]=>6
[1,4,5,3,2]=>6
[1,5,2,3,4]=>3
[1,5,2,4,3]=>3
[1,5,3,2,4]=>3
[1,5,3,4,2]=>3
[1,5,4,2,3]=>3
[1,5,4,3,2]=>3
[2,1,3,4,5]=>13
[2,1,3,5,4]=>8
[2,1,4,3,5]=>9
[2,1,4,5,3]=>8
[2,1,5,3,4]=>4
[2,1,5,4,3]=>4
[2,3,1,4,5]=>12
[2,3,1,5,4]=>7
[2,3,4,1,5]=>11
[2,3,4,5,1]=>10
[2,3,5,1,4]=>6
[2,3,5,4,1]=>6
[2,4,1,3,5]=>8
[2,4,1,5,3]=>7
[2,4,3,1,5]=>8
[2,4,3,5,1]=>7
[2,4,5,1,3]=>6
[2,4,5,3,1]=>6
[2,5,1,3,4]=>3
[2,5,1,4,3]=>3
[2,5,3,1,4]=>3
[2,5,3,4,1]=>3
[2,5,4,1,3]=>3
[2,5,4,3,1]=>3
[3,1,2,4,5]=>10
[3,1,2,5,4]=>5
[3,1,4,2,5]=>9
[3,1,4,5,2]=>8
[3,1,5,2,4]=>4
[3,1,5,4,2]=>4
[3,2,1,4,5]=>10
[3,2,1,5,4]=>5
[3,2,4,1,5]=>9
[3,2,4,5,1]=>8
[3,2,5,1,4]=>4
[3,2,5,4,1]=>4
[3,4,1,2,5]=>8
[3,4,1,5,2]=>7
[3,4,2,1,5]=>8
[3,4,2,5,1]=>7
[3,4,5,1,2]=>6
[3,4,5,2,1]=>6
[3,5,1,2,4]=>3
[3,5,1,4,2]=>3
[3,5,2,1,4]=>3
[3,5,2,4,1]=>3
[3,5,4,1,2]=>3
[3,5,4,2,1]=>3
[4,1,2,3,5]=>6
[4,1,2,5,3]=>5
[4,1,3,2,5]=>6
[4,1,3,5,2]=>5
[4,1,5,2,3]=>4
[4,1,5,3,2]=>4
[4,2,1,3,5]=>6
[4,2,1,5,3]=>5
[4,2,3,1,5]=>6
[4,2,3,5,1]=>5
[4,2,5,1,3]=>4
[4,2,5,3,1]=>4
[4,3,1,2,5]=>6
[4,3,1,5,2]=>5
[4,3,2,1,5]=>6
[4,3,2,5,1]=>5
[4,3,5,1,2]=>4
[4,3,5,2,1]=>4
[4,5,1,2,3]=>3
[4,5,1,3,2]=>3
[4,5,2,1,3]=>3
[4,5,2,3,1]=>3
[4,5,3,1,2]=>3
[4,5,3,2,1]=>3
[5,1,2,3,4]=>1
[5,1,2,4,3]=>1
[5,1,3,2,4]=>1
[5,1,3,4,2]=>1
[5,1,4,2,3]=>1
[5,1,4,3,2]=>1
[5,2,1,3,4]=>1
[5,2,1,4,3]=>1
[5,2,3,1,4]=>1
[5,2,3,4,1]=>1
[5,2,4,1,3]=>1
[5,2,4,3,1]=>1
[5,3,1,2,4]=>1
[5,3,1,4,2]=>1
[5,3,2,1,4]=>1
[5,3,2,4,1]=>1
[5,3,4,1,2]=>1
[5,3,4,2,1]=>1
[5,4,1,2,3]=>1
[5,4,1,3,2]=>1
[5,4,2,1,3]=>1
[5,4,2,3,1]=>1
[5,4,3,1,2]=>1
[5,4,3,2,1]=>1
[1,2,3,4,5,6]=>21
[1,2,3,4,6,5]=>15
[1,2,3,5,4,6]=>16
[1,2,3,5,6,4]=>15
[1,2,3,6,4,5]=>10
[1,2,3,6,5,4]=>10
[1,2,4,3,5,6]=>17
[1,2,4,3,6,5]=>11
[1,2,4,5,3,6]=>16
[1,2,4,5,6,3]=>15
[1,2,4,6,3,5]=>10
[1,2,4,6,5,3]=>10
[1,2,5,3,4,6]=>12
[1,2,5,3,6,4]=>11
[1,2,5,4,3,6]=>12
[1,2,5,4,6,3]=>11
[1,2,5,6,3,4]=>10
[1,2,5,6,4,3]=>10
[1,2,6,3,4,5]=>6
[1,2,6,3,5,4]=>6
[1,2,6,4,3,5]=>6
[1,2,6,4,5,3]=>6
[1,2,6,5,3,4]=>6
[1,2,6,5,4,3]=>6
[1,3,2,4,5,6]=>18
[1,3,2,4,6,5]=>12
[1,3,2,5,4,6]=>13
[1,3,2,5,6,4]=>12
[1,3,2,6,4,5]=>7
[1,3,2,6,5,4]=>7
[1,3,4,2,5,6]=>17
[1,3,4,2,6,5]=>11
[1,3,4,5,2,6]=>16
[1,3,4,5,6,2]=>15
[1,3,4,6,2,5]=>10
[1,3,4,6,5,2]=>10
[1,3,5,2,4,6]=>12
[1,3,5,2,6,4]=>11
[1,3,5,4,2,6]=>12
[1,3,5,4,6,2]=>11
[1,3,5,6,2,4]=>10
[1,3,5,6,4,2]=>10
[1,3,6,2,4,5]=>6
[1,3,6,2,5,4]=>6
[1,3,6,4,2,5]=>6
[1,3,6,4,5,2]=>6
[1,3,6,5,2,4]=>6
[1,3,6,5,4,2]=>6
[1,4,2,3,5,6]=>14
[1,4,2,3,6,5]=>8
[1,4,2,5,3,6]=>13
[1,4,2,5,6,3]=>12
[1,4,2,6,3,5]=>7
[1,4,2,6,5,3]=>7
[1,4,3,2,5,6]=>14
[1,4,3,2,6,5]=>8
[1,4,3,5,2,6]=>13
[1,4,3,5,6,2]=>12
[1,4,3,6,2,5]=>7
[1,4,3,6,5,2]=>7
[1,4,5,2,3,6]=>12
[1,4,5,2,6,3]=>11
[1,4,5,3,2,6]=>12
[1,4,5,3,6,2]=>11
[1,4,5,6,2,3]=>10
[1,4,5,6,3,2]=>10
[1,4,6,2,3,5]=>6
[1,4,6,2,5,3]=>6
[1,4,6,3,2,5]=>6
[1,4,6,3,5,2]=>6
[1,4,6,5,2,3]=>6
[1,4,6,5,3,2]=>6
[1,5,2,3,4,6]=>9
[1,5,2,3,6,4]=>8
[1,5,2,4,3,6]=>9
[1,5,2,4,6,3]=>8
[1,5,2,6,3,4]=>7
[1,5,2,6,4,3]=>7
[1,5,3,2,4,6]=>9
[1,5,3,2,6,4]=>8
[1,5,3,4,2,6]=>9
[1,5,3,4,6,2]=>8
[1,5,3,6,2,4]=>7
[1,5,3,6,4,2]=>7
[1,5,4,2,3,6]=>9
[1,5,4,2,6,3]=>8
[1,5,4,3,2,6]=>9
[1,5,4,3,6,2]=>8
[1,5,4,6,2,3]=>7
[1,5,4,6,3,2]=>7
[1,5,6,2,3,4]=>6
[1,5,6,2,4,3]=>6
[1,5,6,3,2,4]=>6
[1,5,6,3,4,2]=>6
[1,5,6,4,2,3]=>6
[1,5,6,4,3,2]=>6
[1,6,2,3,4,5]=>3
[1,6,2,3,5,4]=>3
[1,6,2,4,3,5]=>3
[1,6,2,4,5,3]=>3
[1,6,2,5,3,4]=>3
[1,6,2,5,4,3]=>3
[1,6,3,2,4,5]=>3
[1,6,3,2,5,4]=>3
[1,6,3,4,2,5]=>3
[1,6,3,4,5,2]=>3
[1,6,3,5,2,4]=>3
[1,6,3,5,4,2]=>3
[1,6,4,2,3,5]=>3
[1,6,4,2,5,3]=>3
[1,6,4,3,2,5]=>3
[1,6,4,3,5,2]=>3
[1,6,4,5,2,3]=>3
[1,6,4,5,3,2]=>3
[1,6,5,2,3,4]=>3
[1,6,5,2,4,3]=>3
[1,6,5,3,2,4]=>3
[1,6,5,3,4,2]=>3
[1,6,5,4,2,3]=>3
[1,6,5,4,3,2]=>3
[2,1,3,4,5,6]=>19
[2,1,3,4,6,5]=>13
[2,1,3,5,4,6]=>14
[2,1,3,5,6,4]=>13
[2,1,3,6,4,5]=>8
[2,1,3,6,5,4]=>8
[2,1,4,3,5,6]=>15
[2,1,4,3,6,5]=>9
[2,1,4,5,3,6]=>14
[2,1,4,5,6,3]=>13
[2,1,4,6,3,5]=>8
[2,1,4,6,5,3]=>8
[2,1,5,3,4,6]=>10
[2,1,5,3,6,4]=>9
[2,1,5,4,3,6]=>10
[2,1,5,4,6,3]=>9
[2,1,5,6,3,4]=>8
[2,1,5,6,4,3]=>8
[2,1,6,3,4,5]=>4
[2,1,6,3,5,4]=>4
[2,1,6,4,3,5]=>4
[2,1,6,4,5,3]=>4
[2,1,6,5,3,4]=>4
[2,1,6,5,4,3]=>4
[2,3,1,4,5,6]=>18
[2,3,1,4,6,5]=>12
[2,3,1,5,4,6]=>13
[2,3,1,5,6,4]=>12
[2,3,1,6,4,5]=>7
[2,3,1,6,5,4]=>7
[2,3,4,1,5,6]=>17
[2,3,4,1,6,5]=>11
[2,3,4,5,1,6]=>16
[2,3,4,5,6,1]=>15
[2,3,4,6,1,5]=>10
[2,3,4,6,5,1]=>10
[2,3,5,1,4,6]=>12
[2,3,5,1,6,4]=>11
[2,3,5,4,1,6]=>12
[2,3,5,4,6,1]=>11
[2,3,5,6,1,4]=>10
[2,3,5,6,4,1]=>10
[2,3,6,1,4,5]=>6
[2,3,6,1,5,4]=>6
[2,3,6,4,1,5]=>6
[2,3,6,4,5,1]=>6
[2,3,6,5,1,4]=>6
[2,3,6,5,4,1]=>6
[2,4,1,3,5,6]=>14
[2,4,1,3,6,5]=>8
[2,4,1,5,3,6]=>13
[2,4,1,5,6,3]=>12
[2,4,1,6,3,5]=>7
[2,4,1,6,5,3]=>7
[2,4,3,1,5,6]=>14
[2,4,3,1,6,5]=>8
[2,4,3,5,1,6]=>13
[2,4,3,5,6,1]=>12
[2,4,3,6,1,5]=>7
[2,4,3,6,5,1]=>7
[2,4,5,1,3,6]=>12
[2,4,5,1,6,3]=>11
[2,4,5,3,1,6]=>12
[2,4,5,3,6,1]=>11
[2,4,5,6,1,3]=>10
[2,4,5,6,3,1]=>10
[2,4,6,1,3,5]=>6
[2,4,6,1,5,3]=>6
[2,4,6,3,1,5]=>6
[2,4,6,3,5,1]=>6
[2,4,6,5,1,3]=>6
[2,4,6,5,3,1]=>6
[2,5,1,3,4,6]=>9
[2,5,1,3,6,4]=>8
[2,5,1,4,3,6]=>9
[2,5,1,4,6,3]=>8
[2,5,1,6,3,4]=>7
[2,5,1,6,4,3]=>7
[2,5,3,1,4,6]=>9
[2,5,3,1,6,4]=>8
[2,5,3,4,1,6]=>9
[2,5,3,4,6,1]=>8
[2,5,3,6,1,4]=>7
[2,5,3,6,4,1]=>7
[2,5,4,1,3,6]=>9
[2,5,4,1,6,3]=>8
[2,5,4,3,1,6]=>9
[2,5,4,3,6,1]=>8
[2,5,4,6,1,3]=>7
[2,5,4,6,3,1]=>7
[2,5,6,1,3,4]=>6
[2,5,6,1,4,3]=>6
[2,5,6,3,1,4]=>6
[2,5,6,3,4,1]=>6
[2,5,6,4,1,3]=>6
[2,5,6,4,3,1]=>6
[2,6,1,3,4,5]=>3
[2,6,1,3,5,4]=>3
[2,6,1,4,3,5]=>3
[2,6,1,4,5,3]=>3
[2,6,1,5,3,4]=>3
[2,6,1,5,4,3]=>3
[2,6,3,1,4,5]=>3
[2,6,3,1,5,4]=>3
[2,6,3,4,1,5]=>3
[2,6,3,4,5,1]=>3
[2,6,3,5,1,4]=>3
[2,6,3,5,4,1]=>3
[2,6,4,1,3,5]=>3
[2,6,4,1,5,3]=>3
[2,6,4,3,1,5]=>3
[2,6,4,3,5,1]=>3
[2,6,4,5,1,3]=>3
[2,6,4,5,3,1]=>3
[2,6,5,1,3,4]=>3
[2,6,5,1,4,3]=>3
[2,6,5,3,1,4]=>3
[2,6,5,3,4,1]=>3
[2,6,5,4,1,3]=>3
[2,6,5,4,3,1]=>3
[3,1,2,4,5,6]=>16
[3,1,2,4,6,5]=>10
[3,1,2,5,4,6]=>11
[3,1,2,5,6,4]=>10
[3,1,2,6,4,5]=>5
[3,1,2,6,5,4]=>5
[3,1,4,2,5,6]=>15
[3,1,4,2,6,5]=>9
[3,1,4,5,2,6]=>14
[3,1,4,5,6,2]=>13
[3,1,4,6,2,5]=>8
[3,1,4,6,5,2]=>8
[3,1,5,2,4,6]=>10
[3,1,5,2,6,4]=>9
[3,1,5,4,2,6]=>10
[3,1,5,4,6,2]=>9
[3,1,5,6,2,4]=>8
[3,1,5,6,4,2]=>8
[3,1,6,2,4,5]=>4
[3,1,6,2,5,4]=>4
[3,1,6,4,2,5]=>4
[3,1,6,4,5,2]=>4
[3,1,6,5,2,4]=>4
[3,1,6,5,4,2]=>4
[3,2,1,4,5,6]=>16
[3,2,1,4,6,5]=>10
[3,2,1,5,4,6]=>11
[3,2,1,5,6,4]=>10
[3,2,1,6,4,5]=>5
[3,2,1,6,5,4]=>5
[3,2,4,1,5,6]=>15
[3,2,4,1,6,5]=>9
[3,2,4,5,1,6]=>14
[3,2,4,5,6,1]=>13
[3,2,4,6,1,5]=>8
[3,2,4,6,5,1]=>8
[3,2,5,1,4,6]=>10
[3,2,5,1,6,4]=>9
[3,2,5,4,1,6]=>10
[3,2,5,4,6,1]=>9
[3,2,5,6,1,4]=>8
[3,2,5,6,4,1]=>8
[3,2,6,1,4,5]=>4
[3,2,6,1,5,4]=>4
[3,2,6,4,1,5]=>4
[3,2,6,4,5,1]=>4
[3,2,6,5,1,4]=>4
[3,2,6,5,4,1]=>4
[3,4,1,2,5,6]=>14
[3,4,1,2,6,5]=>8
[3,4,1,5,2,6]=>13
[3,4,1,5,6,2]=>12
[3,4,1,6,2,5]=>7
[3,4,1,6,5,2]=>7
[3,4,2,1,5,6]=>14
[3,4,2,1,6,5]=>8
[3,4,2,5,1,6]=>13
[3,4,2,5,6,1]=>12
[3,4,2,6,1,5]=>7
[3,4,2,6,5,1]=>7
[3,4,5,1,2,6]=>12
[3,4,5,1,6,2]=>11
[3,4,5,2,1,6]=>12
[3,4,5,2,6,1]=>11
[3,4,5,6,1,2]=>10
[3,4,5,6,2,1]=>10
[3,4,6,1,2,5]=>6
[3,4,6,1,5,2]=>6
[3,4,6,2,1,5]=>6
[3,4,6,2,5,1]=>6
[3,4,6,5,1,2]=>6
[3,4,6,5,2,1]=>6
[3,5,1,2,4,6]=>9
[3,5,1,2,6,4]=>8
[3,5,1,4,2,6]=>9
[3,5,1,4,6,2]=>8
[3,5,1,6,2,4]=>7
[3,5,1,6,4,2]=>7
[3,5,2,1,4,6]=>9
[3,5,2,1,6,4]=>8
[3,5,2,4,1,6]=>9
[3,5,2,4,6,1]=>8
[3,5,2,6,1,4]=>7
[3,5,2,6,4,1]=>7
[3,5,4,1,2,6]=>9
[3,5,4,1,6,2]=>8
[3,5,4,2,1,6]=>9
[3,5,4,2,6,1]=>8
[3,5,4,6,1,2]=>7
[3,5,4,6,2,1]=>7
[3,5,6,1,2,4]=>6
[3,5,6,1,4,2]=>6
[3,5,6,2,1,4]=>6
[3,5,6,2,4,1]=>6
[3,5,6,4,1,2]=>6
[3,5,6,4,2,1]=>6
[3,6,1,2,4,5]=>3
[3,6,1,2,5,4]=>3
[3,6,1,4,2,5]=>3
[3,6,1,4,5,2]=>3
[3,6,1,5,2,4]=>3
[3,6,1,5,4,2]=>3
[3,6,2,1,4,5]=>3
[3,6,2,1,5,4]=>3
[3,6,2,4,1,5]=>3
[3,6,2,4,5,1]=>3
[3,6,2,5,1,4]=>3
[3,6,2,5,4,1]=>3
[3,6,4,1,2,5]=>3
[3,6,4,1,5,2]=>3
[3,6,4,2,1,5]=>3
[3,6,4,2,5,1]=>3
[3,6,4,5,1,2]=>3
[3,6,4,5,2,1]=>3
[3,6,5,1,2,4]=>3
[3,6,5,1,4,2]=>3
[3,6,5,2,1,4]=>3
[3,6,5,2,4,1]=>3
[3,6,5,4,1,2]=>3
[3,6,5,4,2,1]=>3
[4,1,2,3,5,6]=>12
[4,1,2,3,6,5]=>6
[4,1,2,5,3,6]=>11
[4,1,2,5,6,3]=>10
[4,1,2,6,3,5]=>5
[4,1,2,6,5,3]=>5
[4,1,3,2,5,6]=>12
[4,1,3,2,6,5]=>6
[4,1,3,5,2,6]=>11
[4,1,3,5,6,2]=>10
[4,1,3,6,2,5]=>5
[4,1,3,6,5,2]=>5
[4,1,5,2,3,6]=>10
[4,1,5,2,6,3]=>9
[4,1,5,3,2,6]=>10
[4,1,5,3,6,2]=>9
[4,1,5,6,2,3]=>8
[4,1,5,6,3,2]=>8
[4,1,6,2,3,5]=>4
[4,1,6,2,5,3]=>4
[4,1,6,3,2,5]=>4
[4,1,6,3,5,2]=>4
[4,1,6,5,2,3]=>4
[4,1,6,5,3,2]=>4
[4,2,1,3,5,6]=>12
[4,2,1,3,6,5]=>6
[4,2,1,5,3,6]=>11
[4,2,1,5,6,3]=>10
[4,2,1,6,3,5]=>5
[4,2,1,6,5,3]=>5
[4,2,3,1,5,6]=>12
[4,2,3,1,6,5]=>6
[4,2,3,5,1,6]=>11
[4,2,3,5,6,1]=>10
[4,2,3,6,1,5]=>5
[4,2,3,6,5,1]=>5
[4,2,5,1,3,6]=>10
[4,2,5,1,6,3]=>9
[4,2,5,3,1,6]=>10
[4,2,5,3,6,1]=>9
[4,2,5,6,1,3]=>8
[4,2,5,6,3,1]=>8
[4,2,6,1,3,5]=>4
[4,2,6,1,5,3]=>4
[4,2,6,3,1,5]=>4
[4,2,6,3,5,1]=>4
[4,2,6,5,1,3]=>4
[4,2,6,5,3,1]=>4
[4,3,1,2,5,6]=>12
[4,3,1,2,6,5]=>6
[4,3,1,5,2,6]=>11
[4,3,1,5,6,2]=>10
[4,3,1,6,2,5]=>5
[4,3,1,6,5,2]=>5
[4,3,2,1,5,6]=>12
[4,3,2,1,6,5]=>6
[4,3,2,5,1,6]=>11
[4,3,2,5,6,1]=>10
[4,3,2,6,1,5]=>5
[4,3,2,6,5,1]=>5
[4,3,5,1,2,6]=>10
[4,3,5,1,6,2]=>9
[4,3,5,2,1,6]=>10
[4,3,5,2,6,1]=>9
[4,3,5,6,1,2]=>8
[4,3,5,6,2,1]=>8
[4,3,6,1,2,5]=>4
[4,3,6,1,5,2]=>4
[4,3,6,2,1,5]=>4
[4,3,6,2,5,1]=>4
[4,3,6,5,1,2]=>4
[4,3,6,5,2,1]=>4
[4,5,1,2,3,6]=>9
[4,5,1,2,6,3]=>8
[4,5,1,3,2,6]=>9
[4,5,1,3,6,2]=>8
[4,5,1,6,2,3]=>7
[4,5,1,6,3,2]=>7
[4,5,2,1,3,6]=>9
[4,5,2,1,6,3]=>8
[4,5,2,3,1,6]=>9
[4,5,2,3,6,1]=>8
[4,5,2,6,1,3]=>7
[4,5,2,6,3,1]=>7
[4,5,3,1,2,6]=>9
[4,5,3,1,6,2]=>8
[4,5,3,2,1,6]=>9
[4,5,3,2,6,1]=>8
[4,5,3,6,1,2]=>7
[4,5,3,6,2,1]=>7
[4,5,6,1,2,3]=>6
[4,5,6,1,3,2]=>6
[4,5,6,2,1,3]=>6
[4,5,6,2,3,1]=>6
[4,5,6,3,1,2]=>6
[4,5,6,3,2,1]=>6
[4,6,1,2,3,5]=>3
[4,6,1,2,5,3]=>3
[4,6,1,3,2,5]=>3
[4,6,1,3,5,2]=>3
[4,6,1,5,2,3]=>3
[4,6,1,5,3,2]=>3
[4,6,2,1,3,5]=>3
[4,6,2,1,5,3]=>3
[4,6,2,3,1,5]=>3
[4,6,2,3,5,1]=>3
[4,6,2,5,1,3]=>3
[4,6,2,5,3,1]=>3
[4,6,3,1,2,5]=>3
[4,6,3,1,5,2]=>3
[4,6,3,2,1,5]=>3
[4,6,3,2,5,1]=>3
[4,6,3,5,1,2]=>3
[4,6,3,5,2,1]=>3
[4,6,5,1,2,3]=>3
[4,6,5,1,3,2]=>3
[4,6,5,2,1,3]=>3
[4,6,5,2,3,1]=>3
[4,6,5,3,1,2]=>3
[4,6,5,3,2,1]=>3
[5,1,2,3,4,6]=>7
[5,1,2,3,6,4]=>6
[5,1,2,4,3,6]=>7
[5,1,2,4,6,3]=>6
[5,1,2,6,3,4]=>5
[5,1,2,6,4,3]=>5
[5,1,3,2,4,6]=>7
[5,1,3,2,6,4]=>6
[5,1,3,4,2,6]=>7
[5,1,3,4,6,2]=>6
[5,1,3,6,2,4]=>5
[5,1,3,6,4,2]=>5
[5,1,4,2,3,6]=>7
[5,1,4,2,6,3]=>6
[5,1,4,3,2,6]=>7
[5,1,4,3,6,2]=>6
[5,1,4,6,2,3]=>5
[5,1,4,6,3,2]=>5
[5,1,6,2,3,4]=>4
[5,1,6,2,4,3]=>4
[5,1,6,3,2,4]=>4
[5,1,6,3,4,2]=>4
[5,1,6,4,2,3]=>4
[5,1,6,4,3,2]=>4
[5,2,1,3,4,6]=>7
[5,2,1,3,6,4]=>6
[5,2,1,4,3,6]=>7
[5,2,1,4,6,3]=>6
[5,2,1,6,3,4]=>5
[5,2,1,6,4,3]=>5
[5,2,3,1,4,6]=>7
[5,2,3,1,6,4]=>6
[5,2,3,4,1,6]=>7
[5,2,3,4,6,1]=>6
[5,2,3,6,1,4]=>5
[5,2,3,6,4,1]=>5
[5,2,4,1,3,6]=>7
[5,2,4,1,6,3]=>6
[5,2,4,3,1,6]=>7
[5,2,4,3,6,1]=>6
[5,2,4,6,1,3]=>5
[5,2,4,6,3,1]=>5
[5,2,6,1,3,4]=>4
[5,2,6,1,4,3]=>4
[5,2,6,3,1,4]=>4
[5,2,6,3,4,1]=>4
[5,2,6,4,1,3]=>4
[5,2,6,4,3,1]=>4
[5,3,1,2,4,6]=>7
[5,3,1,2,6,4]=>6
[5,3,1,4,2,6]=>7
[5,3,1,4,6,2]=>6
[5,3,1,6,2,4]=>5
[5,3,1,6,4,2]=>5
[5,3,2,1,4,6]=>7
[5,3,2,1,6,4]=>6
[5,3,2,4,1,6]=>7
[5,3,2,4,6,1]=>6
[5,3,2,6,1,4]=>5
[5,3,2,6,4,1]=>5
[5,3,4,1,2,6]=>7
[5,3,4,1,6,2]=>6
[5,3,4,2,1,6]=>7
[5,3,4,2,6,1]=>6
[5,3,4,6,1,2]=>5
[5,3,4,6,2,1]=>5
[5,3,6,1,2,4]=>4
[5,3,6,1,4,2]=>4
[5,3,6,2,1,4]=>4
[5,3,6,2,4,1]=>4
[5,3,6,4,1,2]=>4
[5,3,6,4,2,1]=>4
[5,4,1,2,3,6]=>7
[5,4,1,2,6,3]=>6
[5,4,1,3,2,6]=>7
[5,4,1,3,6,2]=>6
[5,4,1,6,2,3]=>5
[5,4,1,6,3,2]=>5
[5,4,2,1,3,6]=>7
[5,4,2,1,6,3]=>6
[5,4,2,3,1,6]=>7
[5,4,2,3,6,1]=>6
[5,4,2,6,1,3]=>5
[5,4,2,6,3,1]=>5
[5,4,3,1,2,6]=>7
[5,4,3,1,6,2]=>6
[5,4,3,2,1,6]=>7
[5,4,3,2,6,1]=>6
[5,4,3,6,1,2]=>5
[5,4,3,6,2,1]=>5
[5,4,6,1,2,3]=>4
[5,4,6,1,3,2]=>4
[5,4,6,2,1,3]=>4
[5,4,6,2,3,1]=>4
[5,4,6,3,1,2]=>4
[5,4,6,3,2,1]=>4
[5,6,1,2,3,4]=>3
[5,6,1,2,4,3]=>3
[5,6,1,3,2,4]=>3
[5,6,1,3,4,2]=>3
[5,6,1,4,2,3]=>3
[5,6,1,4,3,2]=>3
[5,6,2,1,3,4]=>3
[5,6,2,1,4,3]=>3
[5,6,2,3,1,4]=>3
[5,6,2,3,4,1]=>3
[5,6,2,4,1,3]=>3
[5,6,2,4,3,1]=>3
[5,6,3,1,2,4]=>3
[5,6,3,1,4,2]=>3
[5,6,3,2,1,4]=>3
[5,6,3,2,4,1]=>3
[5,6,3,4,1,2]=>3
[5,6,3,4,2,1]=>3
[5,6,4,1,2,3]=>3
[5,6,4,1,3,2]=>3
[5,6,4,2,1,3]=>3
[5,6,4,2,3,1]=>3
[5,6,4,3,1,2]=>3
[5,6,4,3,2,1]=>3
[6,1,2,3,4,5]=>1
[6,1,2,3,5,4]=>1
[6,1,2,4,3,5]=>1
[6,1,2,4,5,3]=>1
[6,1,2,5,3,4]=>1
[6,1,2,5,4,3]=>1
[6,1,3,2,4,5]=>1
[6,1,3,2,5,4]=>1
[6,1,3,4,2,5]=>1
[6,1,3,4,5,2]=>1
[6,1,3,5,2,4]=>1
[6,1,3,5,4,2]=>1
[6,1,4,2,3,5]=>1
[6,1,4,2,5,3]=>1
[6,1,4,3,2,5]=>1
[6,1,4,3,5,2]=>1
[6,1,4,5,2,3]=>1
[6,1,4,5,3,2]=>1
[6,1,5,2,3,4]=>1
[6,1,5,2,4,3]=>1
[6,1,5,3,2,4]=>1
[6,1,5,3,4,2]=>1
[6,1,5,4,2,3]=>1
[6,1,5,4,3,2]=>1
[6,2,1,3,4,5]=>1
[6,2,1,3,5,4]=>1
[6,2,1,4,3,5]=>1
[6,2,1,4,5,3]=>1
[6,2,1,5,3,4]=>1
[6,2,1,5,4,3]=>1
[6,2,3,1,4,5]=>1
[6,2,3,1,5,4]=>1
[6,2,3,4,1,5]=>1
[6,2,3,4,5,1]=>1
[6,2,3,5,1,4]=>1
[6,2,3,5,4,1]=>1
[6,2,4,1,3,5]=>1
[6,2,4,1,5,3]=>1
[6,2,4,3,1,5]=>1
[6,2,4,3,5,1]=>1
[6,2,4,5,1,3]=>1
[6,2,4,5,3,1]=>1
[6,2,5,1,3,4]=>1
[6,2,5,1,4,3]=>1
[6,2,5,3,1,4]=>1
[6,2,5,3,4,1]=>1
[6,2,5,4,1,3]=>1
[6,2,5,4,3,1]=>1
[6,3,1,2,4,5]=>1
[6,3,1,2,5,4]=>1
[6,3,1,4,2,5]=>1
[6,3,1,4,5,2]=>1
[6,3,1,5,2,4]=>1
[6,3,1,5,4,2]=>1
[6,3,2,1,4,5]=>1
[6,3,2,1,5,4]=>1
[6,3,2,4,1,5]=>1
[6,3,2,4,5,1]=>1
[6,3,2,5,1,4]=>1
[6,3,2,5,4,1]=>1
[6,3,4,1,2,5]=>1
[6,3,4,1,5,2]=>1
[6,3,4,2,1,5]=>1
[6,3,4,2,5,1]=>1
[6,3,4,5,1,2]=>1
[6,3,4,5,2,1]=>1
[6,3,5,1,2,4]=>1
[6,3,5,1,4,2]=>1
[6,3,5,2,1,4]=>1
[6,3,5,2,4,1]=>1
[6,3,5,4,1,2]=>1
[6,3,5,4,2,1]=>1
[6,4,1,2,3,5]=>1
[6,4,1,2,5,3]=>1
[6,4,1,3,2,5]=>1
[6,4,1,3,5,2]=>1
[6,4,1,5,2,3]=>1
[6,4,1,5,3,2]=>1
[6,4,2,1,3,5]=>1
[6,4,2,1,5,3]=>1
[6,4,2,3,1,5]=>1
[6,4,2,3,5,1]=>1
[6,4,2,5,1,3]=>1
[6,4,2,5,3,1]=>1
[6,4,3,1,2,5]=>1
[6,4,3,1,5,2]=>1
[6,4,3,2,1,5]=>1
[6,4,3,2,5,1]=>1
[6,4,3,5,1,2]=>1
[6,4,3,5,2,1]=>1
[6,4,5,1,2,3]=>1
[6,4,5,1,3,2]=>1
[6,4,5,2,1,3]=>1
[6,4,5,2,3,1]=>1
[6,4,5,3,1,2]=>1
[6,4,5,3,2,1]=>1
[6,5,1,2,3,4]=>1
[6,5,1,2,4,3]=>1
[6,5,1,3,2,4]=>1
[6,5,1,3,4,2]=>1
[6,5,1,4,2,3]=>1
[6,5,1,4,3,2]=>1
[6,5,2,1,3,4]=>1
[6,5,2,1,4,3]=>1
[6,5,2,3,1,4]=>1
[6,5,2,3,4,1]=>1
[6,5,2,4,1,3]=>1
[6,5,2,4,3,1]=>1
[6,5,3,1,2,4]=>1
[6,5,3,1,4,2]=>1
[6,5,3,2,1,4]=>1
[6,5,3,2,4,1]=>1
[6,5,3,4,1,2]=>1
[6,5,3,4,2,1]=>1
[6,5,4,1,2,3]=>1
[6,5,4,1,3,2]=>1
[6,5,4,2,1,3]=>1
[6,5,4,2,3,1]=>1
[6,5,4,3,1,2]=>1
[6,5,4,3,2,1]=>1
[1,2,3,4,5,6,7]=>28
[1,2,3,4,5,7,6]=>21
[1,2,3,4,6,5,7]=>22
[1,2,3,4,6,7,5]=>21
[1,2,3,4,7,5,6]=>15
[1,2,3,4,7,6,5]=>15
[1,2,3,5,4,6,7]=>23
[1,2,3,5,4,7,6]=>16
[1,2,3,5,6,4,7]=>22
[1,2,3,5,6,7,4]=>21
[1,2,3,5,7,4,6]=>15
[1,2,3,5,7,6,4]=>15
[1,2,3,6,4,5,7]=>17
[1,2,3,6,4,7,5]=>16
[1,2,3,6,5,4,7]=>17
[1,2,3,6,5,7,4]=>16
[1,2,3,6,7,4,5]=>15
[1,2,3,6,7,5,4]=>15
[1,2,3,7,4,5,6]=>10
[1,2,3,7,4,6,5]=>10
[1,2,3,7,5,4,6]=>10
[1,2,3,7,5,6,4]=>10
[1,2,3,7,6,4,5]=>10
[1,2,3,7,6,5,4]=>10
[1,2,4,3,5,6,7]=>24
[1,2,4,3,5,7,6]=>17
[1,2,4,3,6,5,7]=>18
[1,2,4,3,6,7,5]=>17
[1,2,4,3,7,5,6]=>11
[1,2,4,3,7,6,5]=>11
[1,2,4,5,3,6,7]=>23
[1,2,4,5,3,7,6]=>16
[1,2,4,5,6,3,7]=>22
[1,2,4,5,6,7,3]=>21
[1,2,4,5,7,3,6]=>15
[1,2,4,5,7,6,3]=>15
[1,2,4,6,3,5,7]=>17
[1,2,4,6,3,7,5]=>16
[1,2,4,6,5,3,7]=>17
[1,2,4,6,5,7,3]=>16
[1,2,4,6,7,3,5]=>15
[1,2,4,6,7,5,3]=>15
[1,2,4,7,3,5,6]=>10
[1,2,4,7,3,6,5]=>10
[1,2,4,7,5,3,6]=>10
[1,2,4,7,5,6,3]=>10
[1,2,4,7,6,3,5]=>10
[1,2,4,7,6,5,3]=>10
[1,2,5,3,4,6,7]=>19
[1,2,5,3,4,7,6]=>12
[1,2,5,3,6,4,7]=>18
[1,2,5,3,6,7,4]=>17
[1,2,5,3,7,4,6]=>11
[1,2,5,3,7,6,4]=>11
[1,2,5,4,3,6,7]=>19
[1,2,5,4,3,7,6]=>12
[1,2,5,4,6,3,7]=>18
[1,2,5,4,6,7,3]=>17
[1,2,5,4,7,3,6]=>11
[1,2,5,4,7,6,3]=>11
[1,2,5,6,3,4,7]=>17
[1,2,5,6,3,7,4]=>16
[1,2,5,6,4,3,7]=>17
[1,2,5,6,4,7,3]=>16
[1,2,5,6,7,3,4]=>15
[1,2,5,6,7,4,3]=>15
[1,2,5,7,3,4,6]=>10
[1,2,5,7,3,6,4]=>10
[1,2,5,7,4,3,6]=>10
[1,2,5,7,4,6,3]=>10
[1,2,5,7,6,3,4]=>10
[1,2,5,7,6,4,3]=>10
[1,2,6,3,4,5,7]=>13
[1,2,6,3,4,7,5]=>12
[1,2,6,3,5,4,7]=>13
[1,2,6,3,5,7,4]=>12
[1,2,6,3,7,4,5]=>11
[1,2,6,3,7,5,4]=>11
[1,2,6,4,3,5,7]=>13
[1,2,6,4,3,7,5]=>12
[1,2,6,4,5,3,7]=>13
[1,2,6,4,5,7,3]=>12
[1,2,6,4,7,3,5]=>11
[1,2,6,4,7,5,3]=>11
[1,2,6,5,3,4,7]=>13
[1,2,6,5,3,7,4]=>12
[1,2,6,5,4,3,7]=>13
[1,2,6,5,4,7,3]=>12
[1,2,6,5,7,3,4]=>11
[1,2,6,5,7,4,3]=>11
[1,2,6,7,3,4,5]=>10
[1,2,6,7,3,5,4]=>10
[1,2,6,7,4,3,5]=>10
[1,2,6,7,4,5,3]=>10
[1,2,6,7,5,3,4]=>10
[1,2,6,7,5,4,3]=>10
[1,2,7,3,4,5,6]=>6
[1,2,7,3,4,6,5]=>6
[1,2,7,3,5,4,6]=>6
[1,2,7,3,5,6,4]=>6
[1,2,7,3,6,4,5]=>6
[1,2,7,3,6,5,4]=>6
[1,2,7,4,3,5,6]=>6
[1,2,7,4,3,6,5]=>6
[1,2,7,4,5,3,6]=>6
[1,2,7,4,5,6,3]=>6
[1,2,7,4,6,3,5]=>6
[1,2,7,4,6,5,3]=>6
[1,2,7,5,3,4,6]=>6
[1,2,7,5,3,6,4]=>6
[1,2,7,5,4,3,6]=>6
[1,2,7,5,4,6,3]=>6
[1,2,7,5,6,3,4]=>6
[1,2,7,5,6,4,3]=>6
[1,2,7,6,3,4,5]=>6
[1,2,7,6,3,5,4]=>6
[1,2,7,6,4,3,5]=>6
[1,2,7,6,4,5,3]=>6
[1,2,7,6,5,3,4]=>6
[1,2,7,6,5,4,3]=>6
[1,3,2,4,5,6,7]=>25
[1,3,2,4,5,7,6]=>18
[1,3,2,4,6,5,7]=>19
[1,3,2,4,6,7,5]=>18
[1,3,2,4,7,5,6]=>12
[1,3,2,4,7,6,5]=>12
[1,3,2,5,4,6,7]=>20
[1,3,2,5,4,7,6]=>13
[1,3,2,5,6,4,7]=>19
[1,3,2,5,6,7,4]=>18
[1,3,2,5,7,4,6]=>12
[1,3,2,5,7,6,4]=>12
[1,3,2,6,4,5,7]=>14
[1,3,2,6,4,7,5]=>13
[1,3,2,6,5,4,7]=>14
[1,3,2,6,5,7,4]=>13
[1,3,2,6,7,4,5]=>12
[1,3,2,6,7,5,4]=>12
[1,3,2,7,4,5,6]=>7
[1,3,2,7,4,6,5]=>7
[1,3,2,7,5,4,6]=>7
[1,3,2,7,5,6,4]=>7
[1,3,2,7,6,4,5]=>7
[1,3,2,7,6,5,4]=>7
[1,3,4,2,5,6,7]=>24
[1,3,4,2,5,7,6]=>17
[1,3,4,2,6,5,7]=>18
[1,3,4,2,6,7,5]=>17
[1,3,4,2,7,5,6]=>11
[1,3,4,2,7,6,5]=>11
[1,3,4,5,2,6,7]=>23
[1,3,4,5,2,7,6]=>16
[1,3,4,5,6,2,7]=>22
[1,3,4,5,6,7,2]=>21
[1,3,4,5,7,2,6]=>15
[1,3,4,5,7,6,2]=>15
[1,3,4,6,2,5,7]=>17
[1,3,4,6,2,7,5]=>16
[1,3,4,6,5,2,7]=>17
[1,3,4,6,5,7,2]=>16
[1,3,4,6,7,2,5]=>15
[1,3,4,6,7,5,2]=>15
[1,3,4,7,2,5,6]=>10
[1,3,4,7,2,6,5]=>10
[1,3,4,7,5,2,6]=>10
[1,3,4,7,5,6,2]=>10
[1,3,4,7,6,2,5]=>10
[1,3,4,7,6,5,2]=>10
[1,3,5,2,4,6,7]=>19
[1,3,5,2,4,7,6]=>12
[1,3,5,2,6,4,7]=>18
[1,3,5,2,6,7,4]=>17
[1,3,5,2,7,4,6]=>11
[1,3,5,2,7,6,4]=>11
[1,3,5,4,2,6,7]=>19
[1,3,5,4,2,7,6]=>12
[1,3,5,4,6,2,7]=>18
[1,3,5,4,6,7,2]=>17
[1,3,5,4,7,2,6]=>11
[1,3,5,4,7,6,2]=>11
[1,3,5,6,2,4,7]=>17
[1,3,5,6,2,7,4]=>16
[1,3,5,6,4,2,7]=>17
[1,3,5,6,4,7,2]=>16
[1,3,5,6,7,2,4]=>15
[1,3,5,6,7,4,2]=>15
[1,3,5,7,2,4,6]=>10
[1,3,5,7,2,6,4]=>10
[1,3,5,7,4,2,6]=>10
[1,3,5,7,4,6,2]=>10
[1,3,5,7,6,2,4]=>10
[1,3,5,7,6,4,2]=>10
[1,3,6,2,4,5,7]=>13
[1,3,6,2,4,7,5]=>12
[1,3,6,2,5,4,7]=>13
[1,3,6,2,5,7,4]=>12
[1,3,6,2,7,4,5]=>11
[1,3,6,2,7,5,4]=>11
[1,3,6,4,2,5,7]=>13
[1,3,6,4,2,7,5]=>12
[1,3,6,4,5,2,7]=>13
[1,3,6,4,5,7,2]=>12
[1,3,6,4,7,2,5]=>11
[1,3,6,4,7,5,2]=>11
[1,3,6,5,2,4,7]=>13
[1,3,6,5,2,7,4]=>12
[1,3,6,5,4,2,7]=>13
[1,3,6,5,4,7,2]=>12
[1,3,6,5,7,2,4]=>11
[1,3,6,5,7,4,2]=>11
[1,3,6,7,2,4,5]=>10
[1,3,6,7,2,5,4]=>10
[1,3,6,7,4,2,5]=>10
[1,3,6,7,4,5,2]=>10
[1,3,6,7,5,2,4]=>10
[1,3,6,7,5,4,2]=>10
[1,3,7,2,4,5,6]=>6
[1,3,7,2,4,6,5]=>6
[1,3,7,2,5,4,6]=>6
[1,3,7,2,5,6,4]=>6
[1,3,7,2,6,4,5]=>6
[1,3,7,2,6,5,4]=>6
[1,3,7,4,2,5,6]=>6
[1,3,7,4,2,6,5]=>6
[1,3,7,4,5,2,6]=>6
[1,3,7,4,5,6,2]=>6
[1,3,7,4,6,2,5]=>6
[1,3,7,4,6,5,2]=>6
[1,3,7,5,2,4,6]=>6
[1,3,7,5,2,6,4]=>6
[1,3,7,5,4,2,6]=>6
[1,3,7,5,4,6,2]=>6
[1,3,7,5,6,2,4]=>6
[1,3,7,5,6,4,2]=>6
[1,3,7,6,2,4,5]=>6
[1,3,7,6,2,5,4]=>6
[1,3,7,6,4,2,5]=>6
[1,3,7,6,4,5,2]=>6
[1,3,7,6,5,2,4]=>6
[1,3,7,6,5,4,2]=>6
[1,4,2,3,5,6,7]=>21
[1,4,2,3,5,7,6]=>14
[1,4,2,3,6,5,7]=>15
[1,4,2,3,6,7,5]=>14
[1,4,2,3,7,5,6]=>8
[1,4,2,3,7,6,5]=>8
[1,4,2,5,3,6,7]=>20
[1,4,2,5,3,7,6]=>13
[1,4,2,5,6,3,7]=>19
[1,4,2,5,6,7,3]=>18
[1,4,2,5,7,3,6]=>12
[1,4,2,5,7,6,3]=>12
[1,4,2,6,3,5,7]=>14
[1,4,2,6,3,7,5]=>13
[1,4,2,6,5,3,7]=>14
[1,4,2,6,5,7,3]=>13
[1,4,2,6,7,3,5]=>12
[1,4,2,6,7,5,3]=>12
[1,4,2,7,3,5,6]=>7
[1,4,2,7,3,6,5]=>7
[1,4,2,7,5,3,6]=>7
[1,4,2,7,5,6,3]=>7
[1,4,2,7,6,3,5]=>7
[1,4,2,7,6,5,3]=>7
[1,4,3,2,5,6,7]=>21
[1,4,3,2,5,7,6]=>14
[1,4,3,2,6,5,7]=>15
[1,4,3,2,6,7,5]=>14
[1,4,3,2,7,5,6]=>8
[1,4,3,2,7,6,5]=>8
[1,4,3,5,2,6,7]=>20
[1,4,3,5,2,7,6]=>13
[1,4,3,5,6,2,7]=>19
[1,4,3,5,6,7,2]=>18
[1,4,3,5,7,2,6]=>12
[1,4,3,5,7,6,2]=>12
[1,4,3,6,2,5,7]=>14
[1,4,3,6,2,7,5]=>13
[1,4,3,6,5,2,7]=>14
[1,4,3,6,5,7,2]=>13
[1,4,3,6,7,2,5]=>12
[1,4,3,6,7,5,2]=>12
[1,4,3,7,2,5,6]=>7
[1,4,3,7,2,6,5]=>7
[1,4,3,7,5,2,6]=>7
[1,4,3,7,5,6,2]=>7
[1,4,3,7,6,2,5]=>7
[1,4,3,7,6,5,2]=>7
[1,4,5,2,3,6,7]=>19
[1,4,5,2,3,7,6]=>12
[1,4,5,2,6,3,7]=>18
[1,4,5,2,6,7,3]=>17
[1,4,5,2,7,3,6]=>11
[1,4,5,2,7,6,3]=>11
[1,4,5,3,2,6,7]=>19
[1,4,5,3,2,7,6]=>12
[1,4,5,3,6,2,7]=>18
[1,4,5,3,6,7,2]=>17
[1,4,5,3,7,2,6]=>11
[1,4,5,3,7,6,2]=>11
[1,4,5,6,2,3,7]=>17
[1,4,5,6,2,7,3]=>16
[1,4,5,6,3,2,7]=>17
[1,4,5,6,3,7,2]=>16
[1,4,5,6,7,2,3]=>15
[1,4,5,6,7,3,2]=>15
[1,4,5,7,2,3,6]=>10
[1,4,5,7,2,6,3]=>10
[1,4,5,7,3,2,6]=>10
[1,4,5,7,3,6,2]=>10
[1,4,5,7,6,2,3]=>10
[1,4,5,7,6,3,2]=>10
[1,4,6,2,3,5,7]=>13
[1,4,6,2,3,7,5]=>12
[1,4,6,2,5,3,7]=>13
[1,4,6,2,5,7,3]=>12
[1,4,6,2,7,3,5]=>11
[1,4,6,2,7,5,3]=>11
[1,4,6,3,2,5,7]=>13
[1,4,6,3,2,7,5]=>12
[1,4,6,3,5,2,7]=>13
[1,4,6,3,5,7,2]=>12
[1,4,6,3,7,2,5]=>11
[1,4,6,3,7,5,2]=>11
[1,4,6,5,2,3,7]=>13
[1,4,6,5,2,7,3]=>12
[1,4,6,5,3,2,7]=>13
[1,4,6,5,3,7,2]=>12
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Description
The sum of the positions of the left to right maxima of a permutation.
The generating function for this statistic is $$\sum_{\pi\in\mathfrak S_n} q^{slrmax(pi)} = \prod_{k=1}^n (q^k+k-1),$$
see [prop. 2.6., 1].
The generating function for this statistic is $$\sum_{\pi\in\mathfrak S_n} q^{slrmax(pi)} = \prod_{k=1}^n (q^k+k-1),$$
see [prop. 2.6., 1].
References
[1] Kortchemski, I. Asymptotic behavior of permutation records arXiv:0804.0446
[2] Triangle read by rows: T(n,k) is the number of permutations of [n] for which the sum of the positions of the left-to-right maxima is k (1<=k<=n(n+1)/2). OEIS:A143946
[2] Triangle read by rows: T(n,k) is the number of permutations of [n] for which the sum of the positions of the left-to-right maxima is k (1<=k<=n(n+1)/2). OEIS:A143946
Code
def statistic(pi):
"""
sage: r=5; factor(sum(x^statistic(pi) for pi in Permutations(r)))
(x^5 + 4)*(x^4 + 3)*(x^3 + 2)*(x^2 + 1)*x
"""
pi = list(pi)
i = 0
res = 0
for j in range(len(pi)):
if pi[j] > i:
i = pi[j]
res += j+1
return res
Created
Apr 08, 2017 at 21:39 by Martin Rubey
Updated
May 03, 2019 at 12:57 by Henning Ulfarsson
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