Identifier
- St000794: Permutations ⟶ ℤ
Values
=>
[1,2]=>0
[2,1]=>1
[1,2,3]=>0
[1,3,2]=>2
[2,1,3]=>1
[2,3,1]=>2
[3,1,2]=>1
[3,2,1]=>3
[1,2,3,4]=>0
[1,2,4,3]=>3
[1,3,2,4]=>2
[1,3,4,2]=>3
[1,4,2,3]=>2
[1,4,3,2]=>5
[2,1,3,4]=>1
[2,1,4,3]=>4
[2,3,1,4]=>2
[2,3,4,1]=>3
[2,4,1,3]=>2
[2,4,3,1]=>5
[3,1,2,4]=>1
[3,1,4,2]=>4
[3,2,1,4]=>3
[3,2,4,1]=>5
[3,4,1,2]=>2
[3,4,2,1]=>4
[4,1,2,3]=>1
[4,1,3,2]=>3
[4,2,1,3]=>3
[4,2,3,1]=>4
[4,3,1,2]=>4
[4,3,2,1]=>6
[1,2,3,4,5]=>0
[1,2,3,5,4]=>4
[1,2,4,3,5]=>3
[1,2,4,5,3]=>4
[1,2,5,3,4]=>3
[1,2,5,4,3]=>7
[1,3,2,4,5]=>2
[1,3,2,5,4]=>6
[1,3,4,2,5]=>3
[1,3,4,5,2]=>4
[1,3,5,2,4]=>3
[1,3,5,4,2]=>7
[1,4,2,3,5]=>2
[1,4,2,5,3]=>6
[1,4,3,2,5]=>5
[1,4,3,5,2]=>7
[1,4,5,2,3]=>3
[1,4,5,3,2]=>6
[1,5,2,3,4]=>2
[1,5,2,4,3]=>5
[1,5,3,2,4]=>5
[1,5,3,4,2]=>6
[1,5,4,2,3]=>6
[1,5,4,3,2]=>9
[2,1,3,4,5]=>1
[2,1,3,5,4]=>5
[2,1,4,3,5]=>4
[2,1,4,5,3]=>5
[2,1,5,3,4]=>4
[2,1,5,4,3]=>8
[2,3,1,4,5]=>2
[2,3,1,5,4]=>6
[2,3,4,1,5]=>3
[2,3,4,5,1]=>4
[2,3,5,1,4]=>3
[2,3,5,4,1]=>7
[2,4,1,3,5]=>2
[2,4,1,5,3]=>6
[2,4,3,1,5]=>5
[2,4,3,5,1]=>7
[2,4,5,1,3]=>3
[2,4,5,3,1]=>6
[2,5,1,3,4]=>2
[2,5,1,4,3]=>5
[2,5,3,1,4]=>5
[2,5,3,4,1]=>6
[2,5,4,1,3]=>6
[2,5,4,3,1]=>9
[3,1,2,4,5]=>1
[3,1,2,5,4]=>5
[3,1,4,2,5]=>4
[3,1,4,5,2]=>5
[3,1,5,2,4]=>4
[3,1,5,4,2]=>8
[3,2,1,4,5]=>3
[3,2,1,5,4]=>7
[3,2,4,1,5]=>5
[3,2,4,5,1]=>6
[3,2,5,1,4]=>5
[3,2,5,4,1]=>9
[3,4,1,2,5]=>2
[3,4,1,5,2]=>6
[3,4,2,1,5]=>4
[3,4,2,5,1]=>7
[3,4,5,1,2]=>3
[3,4,5,2,1]=>5
[3,5,1,2,4]=>2
[3,5,1,4,2]=>5
[3,5,2,1,4]=>4
[3,5,2,4,1]=>6
[3,5,4,1,2]=>6
[3,5,4,2,1]=>8
[4,1,2,3,5]=>1
[4,1,2,5,3]=>5
[4,1,3,2,5]=>3
[4,1,3,5,2]=>5
[4,1,5,2,3]=>4
[4,1,5,3,2]=>7
[4,2,1,3,5]=>3
[4,2,1,5,3]=>7
[4,2,3,1,5]=>4
[4,2,3,5,1]=>6
[4,2,5,1,3]=>5
[4,2,5,3,1]=>8
[4,3,1,2,5]=>4
[4,3,1,5,2]=>8
[4,3,2,1,5]=>6
[4,3,2,5,1]=>9
[4,3,5,1,2]=>6
[4,3,5,2,1]=>8
[4,5,1,2,3]=>2
[4,5,1,3,2]=>4
[4,5,2,1,3]=>4
[4,5,2,3,1]=>5
[4,5,3,1,2]=>5
[4,5,3,2,1]=>7
[5,1,2,3,4]=>1
[5,1,2,4,3]=>4
[5,1,3,2,4]=>3
[5,1,3,4,2]=>4
[5,1,4,2,3]=>3
[5,1,4,3,2]=>6
[5,2,1,3,4]=>3
[5,2,1,4,3]=>6
[5,2,3,1,4]=>4
[5,2,3,4,1]=>5
[5,2,4,1,3]=>4
[5,2,4,3,1]=>7
[5,3,1,2,4]=>4
[5,3,1,4,2]=>7
[5,3,2,1,4]=>6
[5,3,2,4,1]=>8
[5,3,4,1,2]=>5
[5,3,4,2,1]=>7
[5,4,1,2,3]=>5
[5,4,1,3,2]=>7
[5,4,2,1,3]=>7
[5,4,2,3,1]=>8
[5,4,3,1,2]=>8
[5,4,3,2,1]=>10
[1,2,3,4,5,6]=>0
[1,2,3,4,6,5]=>5
[1,2,3,5,4,6]=>4
[1,2,3,5,6,4]=>5
[1,2,3,6,4,5]=>4
[1,2,3,6,5,4]=>9
[1,2,4,3,5,6]=>3
[1,2,4,3,6,5]=>8
[1,2,4,5,3,6]=>4
[1,2,4,5,6,3]=>5
[1,2,4,6,3,5]=>4
[1,2,4,6,5,3]=>9
[1,2,5,3,4,6]=>3
[1,2,5,3,6,4]=>8
[1,2,5,4,3,6]=>7
[1,2,5,4,6,3]=>9
[1,2,5,6,3,4]=>4
[1,2,5,6,4,3]=>8
[1,2,6,3,4,5]=>3
[1,2,6,3,5,4]=>7
[1,2,6,4,3,5]=>7
[1,2,6,4,5,3]=>8
[1,2,6,5,3,4]=>8
[1,2,6,5,4,3]=>12
[1,3,2,4,5,6]=>2
[1,3,2,4,6,5]=>7
[1,3,2,5,4,6]=>6
[1,3,2,5,6,4]=>7
[1,3,2,6,4,5]=>6
[1,3,2,6,5,4]=>11
[1,3,4,2,5,6]=>3
[1,3,4,2,6,5]=>8
[1,3,4,5,2,6]=>4
[1,3,4,5,6,2]=>5
[1,3,4,6,2,5]=>4
[1,3,4,6,5,2]=>9
[1,3,5,2,4,6]=>3
[1,3,5,2,6,4]=>8
[1,3,5,4,2,6]=>7
[1,3,5,4,6,2]=>9
[1,3,5,6,2,4]=>4
[1,3,5,6,4,2]=>8
[1,3,6,2,4,5]=>3
[1,3,6,2,5,4]=>7
[1,3,6,4,2,5]=>7
[1,3,6,4,5,2]=>8
[1,3,6,5,2,4]=>8
[1,3,6,5,4,2]=>12
[1,4,2,3,5,6]=>2
[1,4,2,3,6,5]=>7
[1,4,2,5,3,6]=>6
[1,4,2,5,6,3]=>7
[1,4,2,6,3,5]=>6
[1,4,2,6,5,3]=>11
[1,4,3,2,5,6]=>5
[1,4,3,2,6,5]=>10
[1,4,3,5,2,6]=>7
[1,4,3,5,6,2]=>8
[1,4,3,6,2,5]=>7
[1,4,3,6,5,2]=>12
[1,4,5,2,3,6]=>3
[1,4,5,2,6,3]=>8
[1,4,5,3,2,6]=>6
[1,4,5,3,6,2]=>9
[1,4,5,6,2,3]=>4
[1,4,5,6,3,2]=>7
[1,4,6,2,3,5]=>3
[1,4,6,2,5,3]=>7
[1,4,6,3,2,5]=>6
[1,4,6,3,5,2]=>8
[1,4,6,5,2,3]=>8
[1,4,6,5,3,2]=>11
[1,5,2,3,4,6]=>2
[1,5,2,3,6,4]=>7
[1,5,2,4,3,6]=>5
[1,5,2,4,6,3]=>7
[1,5,2,6,3,4]=>6
[1,5,2,6,4,3]=>10
[1,5,3,2,4,6]=>5
[1,5,3,2,6,4]=>10
[1,5,3,4,2,6]=>6
[1,5,3,4,6,2]=>8
[1,5,3,6,2,4]=>7
[1,5,3,6,4,2]=>11
[1,5,4,2,3,6]=>6
[1,5,4,2,6,3]=>11
[1,5,4,3,2,6]=>9
[1,5,4,3,6,2]=>12
[1,5,4,6,2,3]=>8
[1,5,4,6,3,2]=>11
[1,5,6,2,3,4]=>3
[1,5,6,2,4,3]=>6
[1,5,6,3,2,4]=>6
[1,5,6,3,4,2]=>7
[1,5,6,4,2,3]=>7
[1,5,6,4,3,2]=>10
[1,6,2,3,4,5]=>2
[1,6,2,3,5,4]=>6
[1,6,2,4,3,5]=>5
[1,6,2,4,5,3]=>6
[1,6,2,5,3,4]=>5
[1,6,2,5,4,3]=>9
[1,6,3,2,4,5]=>5
[1,6,3,2,5,4]=>9
[1,6,3,4,2,5]=>6
[1,6,3,4,5,2]=>7
[1,6,3,5,2,4]=>6
[1,6,3,5,4,2]=>10
[1,6,4,2,3,5]=>6
[1,6,4,2,5,3]=>10
[1,6,4,3,2,5]=>9
[1,6,4,3,5,2]=>11
[1,6,4,5,2,3]=>7
[1,6,4,5,3,2]=>10
[1,6,5,2,3,4]=>7
[1,6,5,2,4,3]=>10
[1,6,5,3,2,4]=>10
[1,6,5,3,4,2]=>11
[1,6,5,4,2,3]=>11
[1,6,5,4,3,2]=>14
[2,1,3,4,5,6]=>1
[2,1,3,4,6,5]=>6
[2,1,3,5,4,6]=>5
[2,1,3,5,6,4]=>6
[2,1,3,6,4,5]=>5
[2,1,3,6,5,4]=>10
[2,1,4,3,5,6]=>4
[2,1,4,3,6,5]=>9
[2,1,4,5,3,6]=>5
[2,1,4,5,6,3]=>6
[2,1,4,6,3,5]=>5
[2,1,4,6,5,3]=>10
[2,1,5,3,4,6]=>4
[2,1,5,3,6,4]=>9
[2,1,5,4,3,6]=>8
[2,1,5,4,6,3]=>10
[2,1,5,6,3,4]=>5
[2,1,5,6,4,3]=>9
[2,1,6,3,4,5]=>4
[2,1,6,3,5,4]=>8
[2,1,6,4,3,5]=>8
[2,1,6,4,5,3]=>9
[2,1,6,5,3,4]=>9
[2,1,6,5,4,3]=>13
[2,3,1,4,5,6]=>2
[2,3,1,4,6,5]=>7
[2,3,1,5,4,6]=>6
[2,3,1,5,6,4]=>7
[2,3,1,6,4,5]=>6
[2,3,1,6,5,4]=>11
[2,3,4,1,5,6]=>3
[2,3,4,1,6,5]=>8
[2,3,4,5,1,6]=>4
[2,3,4,5,6,1]=>5
[2,3,4,6,1,5]=>4
[2,3,4,6,5,1]=>9
[2,3,5,1,4,6]=>3
[2,3,5,1,6,4]=>8
[2,3,5,4,1,6]=>7
[2,3,5,4,6,1]=>9
[2,3,5,6,1,4]=>4
[2,3,5,6,4,1]=>8
[2,3,6,1,4,5]=>3
[2,3,6,1,5,4]=>7
[2,3,6,4,1,5]=>7
[2,3,6,4,5,1]=>8
[2,3,6,5,1,4]=>8
[2,3,6,5,4,1]=>12
[2,4,1,3,5,6]=>2
[2,4,1,3,6,5]=>7
[2,4,1,5,3,6]=>6
[2,4,1,5,6,3]=>7
[2,4,1,6,3,5]=>6
[2,4,1,6,5,3]=>11
[2,4,3,1,5,6]=>5
[2,4,3,1,6,5]=>10
[2,4,3,5,1,6]=>7
[2,4,3,5,6,1]=>8
[2,4,3,6,1,5]=>7
[2,4,3,6,5,1]=>12
[2,4,5,1,3,6]=>3
[2,4,5,1,6,3]=>8
[2,4,5,3,1,6]=>6
[2,4,5,3,6,1]=>9
[2,4,5,6,1,3]=>4
[2,4,5,6,3,1]=>7
[2,4,6,1,3,5]=>3
[2,4,6,1,5,3]=>7
[2,4,6,3,1,5]=>6
[2,4,6,3,5,1]=>8
[2,4,6,5,1,3]=>8
[2,4,6,5,3,1]=>11
[2,5,1,3,4,6]=>2
[2,5,1,3,6,4]=>7
[2,5,1,4,3,6]=>5
[2,5,1,4,6,3]=>7
[2,5,1,6,3,4]=>6
[2,5,1,6,4,3]=>10
[2,5,3,1,4,6]=>5
[2,5,3,1,6,4]=>10
[2,5,3,4,1,6]=>6
[2,5,3,4,6,1]=>8
[2,5,3,6,1,4]=>7
[2,5,3,6,4,1]=>11
[2,5,4,1,3,6]=>6
[2,5,4,1,6,3]=>11
[2,5,4,3,1,6]=>9
[2,5,4,3,6,1]=>12
[2,5,4,6,1,3]=>8
[2,5,4,6,3,1]=>11
[2,5,6,1,3,4]=>3
[2,5,6,1,4,3]=>6
[2,5,6,3,1,4]=>6
[2,5,6,3,4,1]=>7
[2,5,6,4,1,3]=>7
[2,5,6,4,3,1]=>10
[2,6,1,3,4,5]=>2
[2,6,1,3,5,4]=>6
[2,6,1,4,3,5]=>5
[2,6,1,4,5,3]=>6
[2,6,1,5,3,4]=>5
[2,6,1,5,4,3]=>9
[2,6,3,1,4,5]=>5
[2,6,3,1,5,4]=>9
[2,6,3,4,1,5]=>6
[2,6,3,4,5,1]=>7
[2,6,3,5,1,4]=>6
[2,6,3,5,4,1]=>10
[2,6,4,1,3,5]=>6
[2,6,4,1,5,3]=>10
[2,6,4,3,1,5]=>9
[2,6,4,3,5,1]=>11
[2,6,4,5,1,3]=>7
[2,6,4,5,3,1]=>10
[2,6,5,1,3,4]=>7
[2,6,5,1,4,3]=>10
[2,6,5,3,1,4]=>10
[2,6,5,3,4,1]=>11
[2,6,5,4,1,3]=>11
[2,6,5,4,3,1]=>14
[3,1,2,4,5,6]=>1
[3,1,2,4,6,5]=>6
[3,1,2,5,4,6]=>5
[3,1,2,5,6,4]=>6
[3,1,2,6,4,5]=>5
[3,1,2,6,5,4]=>10
[3,1,4,2,5,6]=>4
[3,1,4,2,6,5]=>9
[3,1,4,5,2,6]=>5
[3,1,4,5,6,2]=>6
[3,1,4,6,2,5]=>5
[3,1,4,6,5,2]=>10
[3,1,5,2,4,6]=>4
[3,1,5,2,6,4]=>9
[3,1,5,4,2,6]=>8
[3,1,5,4,6,2]=>10
[3,1,5,6,2,4]=>5
[3,1,5,6,4,2]=>9
[3,1,6,2,4,5]=>4
[3,1,6,2,5,4]=>8
[3,1,6,4,2,5]=>8
[3,1,6,4,5,2]=>9
[3,1,6,5,2,4]=>9
[3,1,6,5,4,2]=>13
[3,2,1,4,5,6]=>3
[3,2,1,4,6,5]=>8
[3,2,1,5,4,6]=>7
[3,2,1,5,6,4]=>8
[3,2,1,6,4,5]=>7
[3,2,1,6,5,4]=>12
[3,2,4,1,5,6]=>5
[3,2,4,1,6,5]=>10
[3,2,4,5,1,6]=>6
[3,2,4,5,6,1]=>7
[3,2,4,6,1,5]=>6
[3,2,4,6,5,1]=>11
[3,2,5,1,4,6]=>5
[3,2,5,1,6,4]=>10
[3,2,5,4,1,6]=>9
[3,2,5,4,6,1]=>11
[3,2,5,6,1,4]=>6
[3,2,5,6,4,1]=>10
[3,2,6,1,4,5]=>5
[3,2,6,1,5,4]=>9
[3,2,6,4,1,5]=>9
[3,2,6,4,5,1]=>10
[3,2,6,5,1,4]=>10
[3,2,6,5,4,1]=>14
[3,4,1,2,5,6]=>2
[3,4,1,2,6,5]=>7
[3,4,1,5,2,6]=>6
[3,4,1,5,6,2]=>7
[3,4,1,6,2,5]=>6
[3,4,1,6,5,2]=>11
[3,4,2,1,5,6]=>4
[3,4,2,1,6,5]=>9
[3,4,2,5,1,6]=>7
[3,4,2,5,6,1]=>8
[3,4,2,6,1,5]=>7
[3,4,2,6,5,1]=>12
[3,4,5,1,2,6]=>3
[3,4,5,1,6,2]=>8
[3,4,5,2,1,6]=>5
[3,4,5,2,6,1]=>9
[3,4,5,6,1,2]=>4
[3,4,5,6,2,1]=>6
[3,4,6,1,2,5]=>3
[3,4,6,1,5,2]=>7
[3,4,6,2,1,5]=>5
[3,4,6,2,5,1]=>8
[3,4,6,5,1,2]=>8
[3,4,6,5,2,1]=>10
[3,5,1,2,4,6]=>2
[3,5,1,2,6,4]=>7
[3,5,1,4,2,6]=>5
[3,5,1,4,6,2]=>7
[3,5,1,6,2,4]=>6
[3,5,1,6,4,2]=>10
[3,5,2,1,4,6]=>4
[3,5,2,1,6,4]=>9
[3,5,2,4,1,6]=>6
[3,5,2,4,6,1]=>8
[3,5,2,6,1,4]=>7
[3,5,2,6,4,1]=>11
[3,5,4,1,2,6]=>6
[3,5,4,1,6,2]=>11
[3,5,4,2,1,6]=>8
[3,5,4,2,6,1]=>12
[3,5,4,6,1,2]=>8
[3,5,4,6,2,1]=>10
[3,5,6,1,2,4]=>3
[3,5,6,1,4,2]=>6
[3,5,6,2,1,4]=>5
[3,5,6,2,4,1]=>7
[3,5,6,4,1,2]=>7
[3,5,6,4,2,1]=>9
[3,6,1,2,4,5]=>2
[3,6,1,2,5,4]=>6
[3,6,1,4,2,5]=>5
[3,6,1,4,5,2]=>6
[3,6,1,5,2,4]=>5
[3,6,1,5,4,2]=>9
[3,6,2,1,4,5]=>4
[3,6,2,1,5,4]=>8
[3,6,2,4,1,5]=>6
[3,6,2,4,5,1]=>7
[3,6,2,5,1,4]=>6
[3,6,2,5,4,1]=>10
[3,6,4,1,2,5]=>6
[3,6,4,1,5,2]=>10
[3,6,4,2,1,5]=>8
[3,6,4,2,5,1]=>11
[3,6,4,5,1,2]=>7
[3,6,4,5,2,1]=>9
[3,6,5,1,2,4]=>7
[3,6,5,1,4,2]=>10
[3,6,5,2,1,4]=>9
[3,6,5,2,4,1]=>11
[3,6,5,4,1,2]=>11
[3,6,5,4,2,1]=>13
[4,1,2,3,5,6]=>1
[4,1,2,3,6,5]=>6
[4,1,2,5,3,6]=>5
[4,1,2,5,6,3]=>6
[4,1,2,6,3,5]=>5
[4,1,2,6,5,3]=>10
[4,1,3,2,5,6]=>3
[4,1,3,2,6,5]=>8
[4,1,3,5,2,6]=>5
[4,1,3,5,6,2]=>6
[4,1,3,6,2,5]=>5
[4,1,3,6,5,2]=>10
[4,1,5,2,3,6]=>4
[4,1,5,2,6,3]=>9
[4,1,5,3,2,6]=>7
[4,1,5,3,6,2]=>10
[4,1,5,6,2,3]=>5
[4,1,5,6,3,2]=>8
[4,1,6,2,3,5]=>4
[4,1,6,2,5,3]=>8
[4,1,6,3,2,5]=>7
[4,1,6,3,5,2]=>9
[4,1,6,5,2,3]=>9
[4,1,6,5,3,2]=>12
[4,2,1,3,5,6]=>3
[4,2,1,3,6,5]=>8
[4,2,1,5,3,6]=>7
[4,2,1,5,6,3]=>8
[4,2,1,6,3,5]=>7
[4,2,1,6,5,3]=>12
[4,2,3,1,5,6]=>4
[4,2,3,1,6,5]=>9
[4,2,3,5,1,6]=>6
[4,2,3,5,6,1]=>7
[4,2,3,6,1,5]=>6
[4,2,3,6,5,1]=>11
[4,2,5,1,3,6]=>5
[4,2,5,1,6,3]=>10
[4,2,5,3,1,6]=>8
[4,2,5,3,6,1]=>11
[4,2,5,6,1,3]=>6
[4,2,5,6,3,1]=>9
[4,2,6,1,3,5]=>5
[4,2,6,1,5,3]=>9
[4,2,6,3,1,5]=>8
[4,2,6,3,5,1]=>10
[4,2,6,5,1,3]=>10
[4,2,6,5,3,1]=>13
[4,3,1,2,5,6]=>4
[4,3,1,2,6,5]=>9
[4,3,1,5,2,6]=>8
[4,3,1,5,6,2]=>9
[4,3,1,6,2,5]=>8
[4,3,1,6,5,2]=>13
[4,3,2,1,5,6]=>6
[4,3,2,1,6,5]=>11
[4,3,2,5,1,6]=>9
[4,3,2,5,6,1]=>10
[4,3,2,6,1,5]=>9
[4,3,2,6,5,1]=>14
[4,3,5,1,2,6]=>6
[4,3,5,1,6,2]=>11
[4,3,5,2,1,6]=>8
[4,3,5,2,6,1]=>12
[4,3,5,6,1,2]=>7
[4,3,5,6,2,1]=>9
[4,3,6,1,2,5]=>6
[4,3,6,1,5,2]=>10
[4,3,6,2,1,5]=>8
[4,3,6,2,5,1]=>11
[4,3,6,5,1,2]=>11
[4,3,6,5,2,1]=>13
[4,5,1,2,3,6]=>2
[4,5,1,2,6,3]=>7
[4,5,1,3,2,6]=>4
[4,5,1,3,6,2]=>7
[4,5,1,6,2,3]=>6
[4,5,1,6,3,2]=>9
[4,5,2,1,3,6]=>4
[4,5,2,1,6,3]=>9
[4,5,2,3,1,6]=>5
[4,5,2,3,6,1]=>8
[4,5,2,6,1,3]=>7
[4,5,2,6,3,1]=>10
[4,5,3,1,2,6]=>5
[4,5,3,1,6,2]=>10
[4,5,3,2,1,6]=>7
[4,5,3,2,6,1]=>11
[4,5,3,6,1,2]=>8
[4,5,3,6,2,1]=>10
[4,5,6,1,2,3]=>3
[4,5,6,1,3,2]=>5
[4,5,6,2,1,3]=>5
[4,5,6,2,3,1]=>6
[4,5,6,3,1,2]=>6
[4,5,6,3,2,1]=>8
[4,6,1,2,3,5]=>2
[4,6,1,2,5,3]=>6
[4,6,1,3,2,5]=>4
[4,6,1,3,5,2]=>6
[4,6,1,5,2,3]=>5
[4,6,1,5,3,2]=>8
[4,6,2,1,3,5]=>4
[4,6,2,1,5,3]=>8
[4,6,2,3,1,5]=>5
[4,6,2,3,5,1]=>7
[4,6,2,5,1,3]=>6
[4,6,2,5,3,1]=>9
[4,6,3,1,2,5]=>5
[4,6,3,1,5,2]=>9
[4,6,3,2,1,5]=>7
[4,6,3,2,5,1]=>10
[4,6,3,5,1,2]=>7
[4,6,3,5,2,1]=>9
[4,6,5,1,2,3]=>7
[4,6,5,1,3,2]=>9
[4,6,5,2,1,3]=>9
[4,6,5,2,3,1]=>10
[4,6,5,3,1,2]=>10
[4,6,5,3,2,1]=>12
[5,1,2,3,4,6]=>1
[5,1,2,3,6,4]=>6
[5,1,2,4,3,6]=>4
[5,1,2,4,6,3]=>6
[5,1,2,6,3,4]=>5
[5,1,2,6,4,3]=>9
[5,1,3,2,4,6]=>3
[5,1,3,2,6,4]=>8
[5,1,3,4,2,6]=>4
[5,1,3,4,6,2]=>6
[5,1,3,6,2,4]=>5
[5,1,3,6,4,2]=>9
[5,1,4,2,3,6]=>3
[5,1,4,2,6,3]=>8
[5,1,4,3,2,6]=>6
[5,1,4,3,6,2]=>9
[5,1,4,6,2,3]=>5
[5,1,4,6,3,2]=>8
[5,1,6,2,3,4]=>4
[5,1,6,2,4,3]=>7
[5,1,6,3,2,4]=>7
[5,1,6,3,4,2]=>8
[5,1,6,4,2,3]=>8
[5,1,6,4,3,2]=>11
[5,2,1,3,4,6]=>3
[5,2,1,3,6,4]=>8
[5,2,1,4,3,6]=>6
[5,2,1,4,6,3]=>8
[5,2,1,6,3,4]=>7
[5,2,1,6,4,3]=>11
[5,2,3,1,4,6]=>4
[5,2,3,1,6,4]=>9
[5,2,3,4,1,6]=>5
[5,2,3,4,6,1]=>7
[5,2,3,6,1,4]=>6
[5,2,3,6,4,1]=>10
[5,2,4,1,3,6]=>4
[5,2,4,1,6,3]=>9
[5,2,4,3,1,6]=>7
[5,2,4,3,6,1]=>10
[5,2,4,6,1,3]=>6
[5,2,4,6,3,1]=>9
[5,2,6,1,3,4]=>5
[5,2,6,1,4,3]=>8
[5,2,6,3,1,4]=>8
[5,2,6,3,4,1]=>9
[5,2,6,4,1,3]=>9
[5,2,6,4,3,1]=>12
[5,3,1,2,4,6]=>4
[5,3,1,2,6,4]=>9
[5,3,1,4,2,6]=>7
[5,3,1,4,6,2]=>9
[5,3,1,6,2,4]=>8
[5,3,1,6,4,2]=>12
[5,3,2,1,4,6]=>6
[5,3,2,1,6,4]=>11
[5,3,2,4,1,6]=>8
[5,3,2,4,6,1]=>10
[5,3,2,6,1,4]=>9
[5,3,2,6,4,1]=>13
[5,3,4,1,2,6]=>5
[5,3,4,1,6,2]=>10
[5,3,4,2,1,6]=>7
[5,3,4,2,6,1]=>11
[5,3,4,6,1,2]=>7
[5,3,4,6,2,1]=>9
[5,3,6,1,2,4]=>6
[5,3,6,1,4,2]=>9
[5,3,6,2,1,4]=>8
[5,3,6,2,4,1]=>10
[5,3,6,4,1,2]=>10
[5,3,6,4,2,1]=>12
[5,4,1,2,3,6]=>5
[5,4,1,2,6,3]=>10
[5,4,1,3,2,6]=>7
[5,4,1,3,6,2]=>10
[5,4,1,6,2,3]=>9
[5,4,1,6,3,2]=>12
[5,4,2,1,3,6]=>7
[5,4,2,1,6,3]=>12
[5,4,2,3,1,6]=>8
[5,4,2,3,6,1]=>11
[5,4,2,6,1,3]=>10
[5,4,2,6,3,1]=>13
[5,4,3,1,2,6]=>8
[5,4,3,1,6,2]=>13
[5,4,3,2,1,6]=>10
[5,4,3,2,6,1]=>14
[5,4,3,6,1,2]=>11
[5,4,3,6,2,1]=>13
[5,4,6,1,2,3]=>7
[5,4,6,1,3,2]=>9
[5,4,6,2,1,3]=>9
[5,4,6,2,3,1]=>10
[5,4,6,3,1,2]=>10
[5,4,6,3,2,1]=>12
[5,6,1,2,3,4]=>2
[5,6,1,2,4,3]=>5
[5,6,1,3,2,4]=>4
[5,6,1,3,4,2]=>5
[5,6,1,4,2,3]=>4
[5,6,1,4,3,2]=>7
[5,6,2,1,3,4]=>4
[5,6,2,1,4,3]=>7
[5,6,2,3,1,4]=>5
[5,6,2,3,4,1]=>6
[5,6,2,4,1,3]=>5
[5,6,2,4,3,1]=>8
[5,6,3,1,2,4]=>5
[5,6,3,1,4,2]=>8
[5,6,3,2,1,4]=>7
[5,6,3,2,4,1]=>9
[5,6,3,4,1,2]=>6
[5,6,3,4,2,1]=>8
[5,6,4,1,2,3]=>6
[5,6,4,1,3,2]=>8
[5,6,4,2,1,3]=>8
[5,6,4,2,3,1]=>9
[5,6,4,3,1,2]=>9
[5,6,4,3,2,1]=>11
[6,1,2,3,4,5]=>1
[6,1,2,3,5,4]=>5
[6,1,2,4,3,5]=>4
[6,1,2,4,5,3]=>5
[6,1,2,5,3,4]=>4
[6,1,2,5,4,3]=>8
[6,1,3,2,4,5]=>3
[6,1,3,2,5,4]=>7
[6,1,3,4,2,5]=>4
[6,1,3,4,5,2]=>5
[6,1,3,5,2,4]=>4
[6,1,3,5,4,2]=>8
[6,1,4,2,3,5]=>3
[6,1,4,2,5,3]=>7
[6,1,4,3,2,5]=>6
[6,1,4,3,5,2]=>8
[6,1,4,5,2,3]=>4
[6,1,4,5,3,2]=>7
[6,1,5,2,3,4]=>3
[6,1,5,2,4,3]=>6
[6,1,5,3,2,4]=>6
[6,1,5,3,4,2]=>7
[6,1,5,4,2,3]=>7
[6,1,5,4,3,2]=>10
[6,2,1,3,4,5]=>3
[6,2,1,3,5,4]=>7
[6,2,1,4,3,5]=>6
[6,2,1,4,5,3]=>7
[6,2,1,5,3,4]=>6
[6,2,1,5,4,3]=>10
[6,2,3,1,4,5]=>4
[6,2,3,1,5,4]=>8
[6,2,3,4,1,5]=>5
[6,2,3,4,5,1]=>6
[6,2,3,5,1,4]=>5
[6,2,3,5,4,1]=>9
[6,2,4,1,3,5]=>4
[6,2,4,1,5,3]=>8
[6,2,4,3,1,5]=>7
[6,2,4,3,5,1]=>9
[6,2,4,5,1,3]=>5
[6,2,4,5,3,1]=>8
[6,2,5,1,3,4]=>4
[6,2,5,1,4,3]=>7
[6,2,5,3,1,4]=>7
[6,2,5,3,4,1]=>8
[6,2,5,4,1,3]=>8
[6,2,5,4,3,1]=>11
[6,3,1,2,4,5]=>4
[6,3,1,2,5,4]=>8
[6,3,1,4,2,5]=>7
[6,3,1,4,5,2]=>8
[6,3,1,5,2,4]=>7
[6,3,1,5,4,2]=>11
[6,3,2,1,4,5]=>6
[6,3,2,1,5,4]=>10
[6,3,2,4,1,5]=>8
[6,3,2,4,5,1]=>9
[6,3,2,5,1,4]=>8
[6,3,2,5,4,1]=>12
[6,3,4,1,2,5]=>5
[6,3,4,1,5,2]=>9
[6,3,4,2,1,5]=>7
[6,3,4,2,5,1]=>10
[6,3,4,5,1,2]=>6
[6,3,4,5,2,1]=>8
[6,3,5,1,2,4]=>5
[6,3,5,1,4,2]=>8
[6,3,5,2,1,4]=>7
[6,3,5,2,4,1]=>9
[6,3,5,4,1,2]=>9
[6,3,5,4,2,1]=>11
[6,4,1,2,3,5]=>5
[6,4,1,2,5,3]=>9
[6,4,1,3,2,5]=>7
[6,4,1,3,5,2]=>9
[6,4,1,5,2,3]=>8
[6,4,1,5,3,2]=>11
[6,4,2,1,3,5]=>7
[6,4,2,1,5,3]=>11
[6,4,2,3,1,5]=>8
[6,4,2,3,5,1]=>10
[6,4,2,5,1,3]=>9
[6,4,2,5,3,1]=>12
[6,4,3,1,2,5]=>8
[6,4,3,1,5,2]=>12
[6,4,3,2,1,5]=>10
[6,4,3,2,5,1]=>13
[6,4,3,5,1,2]=>10
[6,4,3,5,2,1]=>12
[6,4,5,1,2,3]=>6
[6,4,5,1,3,2]=>8
[6,4,5,2,1,3]=>8
[6,4,5,2,3,1]=>9
[6,4,5,3,1,2]=>9
[6,4,5,3,2,1]=>11
[6,5,1,2,3,4]=>6
[6,5,1,2,4,3]=>9
[6,5,1,3,2,4]=>8
[6,5,1,3,4,2]=>9
[6,5,1,4,2,3]=>8
[6,5,1,4,3,2]=>11
[6,5,2,1,3,4]=>8
[6,5,2,1,4,3]=>11
[6,5,2,3,1,4]=>9
[6,5,2,3,4,1]=>10
[6,5,2,4,1,3]=>9
[6,5,2,4,3,1]=>12
[6,5,3,1,2,4]=>9
[6,5,3,1,4,2]=>12
[6,5,3,2,1,4]=>11
[6,5,3,2,4,1]=>13
[6,5,3,4,1,2]=>10
[6,5,3,4,2,1]=>12
[6,5,4,1,2,3]=>10
[6,5,4,1,3,2]=>12
[6,5,4,2,1,3]=>12
[6,5,4,2,3,1]=>13
[6,5,4,3,1,2]=>13
[6,5,4,3,2,1]=>15
[1,2,3,4,5,6,7]=>0
[1,2,3,4,5,7,6]=>6
[1,2,3,4,6,5,7]=>5
[1,2,3,4,6,7,5]=>6
[1,2,3,4,7,5,6]=>5
[1,2,3,4,7,6,5]=>11
[1,2,3,5,4,6,7]=>4
[1,2,3,5,4,7,6]=>10
[1,2,3,5,6,4,7]=>5
[1,2,3,5,6,7,4]=>6
[1,2,3,5,7,4,6]=>5
[1,2,3,5,7,6,4]=>11
[1,2,3,6,4,5,7]=>4
[1,2,3,6,4,7,5]=>10
[1,2,3,6,5,4,7]=>9
[1,2,3,6,5,7,4]=>11
[1,2,3,6,7,4,5]=>5
[1,2,3,6,7,5,4]=>10
[1,2,3,7,4,5,6]=>4
[1,2,3,7,4,6,5]=>9
[1,2,3,7,5,4,6]=>9
[1,2,3,7,5,6,4]=>10
[1,2,3,7,6,4,5]=>10
[1,2,3,7,6,5,4]=>15
[1,2,4,3,5,6,7]=>3
[1,2,4,3,5,7,6]=>9
[1,2,4,3,6,5,7]=>8
[1,2,4,3,6,7,5]=>9
[1,2,4,3,7,5,6]=>8
[1,2,4,3,7,6,5]=>14
[1,2,4,5,3,6,7]=>4
[1,2,4,5,3,7,6]=>10
[1,2,4,5,6,3,7]=>5
[1,2,4,5,6,7,3]=>6
[1,2,4,5,7,3,6]=>5
[1,2,4,5,7,6,3]=>11
[1,2,4,6,3,5,7]=>4
[1,2,4,6,3,7,5]=>10
[1,2,4,6,5,3,7]=>9
[1,2,4,6,5,7,3]=>11
[1,2,4,6,7,3,5]=>5
[1,2,4,6,7,5,3]=>10
[1,2,4,7,3,5,6]=>4
[1,2,4,7,3,6,5]=>9
[1,2,4,7,5,3,6]=>9
[1,2,4,7,5,6,3]=>10
[1,2,4,7,6,3,5]=>10
[1,2,4,7,6,5,3]=>15
[1,2,5,3,4,6,7]=>3
[1,2,5,3,4,7,6]=>9
[1,2,5,3,6,4,7]=>8
[1,2,5,3,6,7,4]=>9
[1,2,5,3,7,4,6]=>8
[1,2,5,3,7,6,4]=>14
[1,2,5,4,3,6,7]=>7
[1,2,5,4,3,7,6]=>13
[1,2,5,4,6,3,7]=>9
[1,2,5,4,6,7,3]=>10
[1,2,5,4,7,3,6]=>9
[1,2,5,4,7,6,3]=>15
[1,2,5,6,3,4,7]=>4
[1,2,5,6,3,7,4]=>10
[1,2,5,6,4,3,7]=>8
[1,2,5,6,4,7,3]=>11
[1,2,5,6,7,3,4]=>5
[1,2,5,6,7,4,3]=>9
[1,2,5,7,3,4,6]=>4
[1,2,5,7,3,6,4]=>9
[1,2,5,7,4,3,6]=>8
[1,2,5,7,4,6,3]=>10
[1,2,5,7,6,3,4]=>10
[1,2,5,7,6,4,3]=>14
[1,2,6,3,4,5,7]=>3
[1,2,6,3,4,7,5]=>9
[1,2,6,3,5,4,7]=>7
[1,2,6,3,5,7,4]=>9
[1,2,6,3,7,4,5]=>8
[1,2,6,3,7,5,4]=>13
[1,2,6,4,3,5,7]=>7
[1,2,6,4,3,7,5]=>13
[1,2,6,4,5,3,7]=>8
[1,2,6,4,5,7,3]=>10
[1,2,6,4,7,3,5]=>9
[1,2,6,4,7,5,3]=>14
[1,2,6,5,3,4,7]=>8
[1,2,6,5,3,7,4]=>14
[1,2,6,5,4,3,7]=>12
[1,2,6,5,4,7,3]=>15
[1,2,6,5,7,3,4]=>10
[1,2,6,5,7,4,3]=>14
[1,2,6,7,3,4,5]=>4
[1,2,6,7,3,5,4]=>8
[1,2,6,7,4,3,5]=>8
[1,2,6,7,4,5,3]=>9
[1,2,6,7,5,3,4]=>9
[1,2,6,7,5,4,3]=>13
[1,2,7,3,4,5,6]=>3
[1,2,7,3,4,6,5]=>8
[1,2,7,3,5,4,6]=>7
[1,2,7,3,5,6,4]=>8
[1,2,7,3,6,4,5]=>7
[1,2,7,3,6,5,4]=>12
[1,2,7,4,3,5,6]=>7
[1,2,7,4,3,6,5]=>12
[1,2,7,4,5,3,6]=>8
[1,2,7,4,5,6,3]=>9
[1,2,7,4,6,3,5]=>8
[1,2,7,4,6,5,3]=>13
[1,2,7,5,3,4,6]=>8
[1,2,7,5,3,6,4]=>13
[1,2,7,5,4,3,6]=>12
[1,2,7,5,4,6,3]=>14
[1,2,7,5,6,3,4]=>9
[1,2,7,5,6,4,3]=>13
[1,2,7,6,3,4,5]=>9
[1,2,7,6,3,5,4]=>13
[1,2,7,6,4,3,5]=>13
[1,2,7,6,4,5,3]=>14
[1,2,7,6,5,3,4]=>14
[1,2,7,6,5,4,3]=>18
[1,3,2,4,5,6,7]=>2
[1,3,2,4,5,7,6]=>8
[1,3,2,4,6,5,7]=>7
[1,3,2,4,6,7,5]=>8
[1,3,2,4,7,5,6]=>7
[1,3,2,4,7,6,5]=>13
[1,3,2,5,4,6,7]=>6
[1,3,2,5,4,7,6]=>12
[1,3,2,5,6,4,7]=>7
[1,3,2,5,6,7,4]=>8
[1,3,2,5,7,4,6]=>7
[1,3,2,5,7,6,4]=>13
[1,3,2,6,4,5,7]=>6
[1,3,2,6,4,7,5]=>12
[1,3,2,6,5,4,7]=>11
[1,3,2,6,5,7,4]=>13
[1,3,2,6,7,4,5]=>7
[1,3,2,6,7,5,4]=>12
[1,3,2,7,4,5,6]=>6
[1,3,2,7,4,6,5]=>11
[1,3,2,7,5,4,6]=>11
[1,3,2,7,5,6,4]=>12
[1,3,2,7,6,4,5]=>12
[1,3,2,7,6,5,4]=>17
[1,3,4,2,5,6,7]=>3
[1,3,4,2,5,7,6]=>9
[1,3,4,2,6,5,7]=>8
[1,3,4,2,6,7,5]=>9
[1,3,4,2,7,5,6]=>8
[1,3,4,2,7,6,5]=>14
[1,3,4,5,2,6,7]=>4
[1,3,4,5,2,7,6]=>10
[1,3,4,5,6,2,7]=>5
[1,3,4,5,6,7,2]=>6
[1,3,4,5,7,2,6]=>5
[1,3,4,5,7,6,2]=>11
[1,3,4,6,2,5,7]=>4
[1,3,4,6,2,7,5]=>10
[1,3,4,6,5,2,7]=>9
[1,3,4,6,5,7,2]=>11
[1,3,4,6,7,2,5]=>5
[1,3,4,6,7,5,2]=>10
[1,3,4,7,2,5,6]=>4
[1,3,4,7,2,6,5]=>9
[1,3,4,7,5,2,6]=>9
[1,3,4,7,5,6,2]=>10
[1,3,4,7,6,2,5]=>10
[1,3,4,7,6,5,2]=>15
[1,3,5,2,4,6,7]=>3
[1,3,5,2,4,7,6]=>9
[1,3,5,2,6,4,7]=>8
[1,3,5,2,6,7,4]=>9
[1,3,5,2,7,4,6]=>8
[1,3,5,2,7,6,4]=>14
[1,3,5,4,2,6,7]=>7
[1,3,5,4,2,7,6]=>13
[1,3,5,4,6,2,7]=>9
[1,3,5,4,6,7,2]=>10
[1,3,5,4,7,2,6]=>9
[1,3,5,4,7,6,2]=>15
[1,3,5,6,2,4,7]=>4
[1,3,5,6,2,7,4]=>10
[1,3,5,6,4,2,7]=>8
[1,3,5,6,4,7,2]=>11
[1,3,5,6,7,2,4]=>5
[1,3,5,6,7,4,2]=>9
[1,3,5,7,2,4,6]=>4
[1,3,5,7,2,6,4]=>9
[1,3,5,7,4,2,6]=>8
[1,3,5,7,4,6,2]=>10
[1,3,5,7,6,2,4]=>10
[1,3,5,7,6,4,2]=>14
[1,3,6,2,4,5,7]=>3
[1,3,6,2,4,7,5]=>9
[1,3,6,2,5,4,7]=>7
[1,3,6,2,5,7,4]=>9
[1,3,6,2,7,4,5]=>8
[1,3,6,2,7,5,4]=>13
[1,3,6,4,2,5,7]=>7
[1,3,6,4,2,7,5]=>13
[1,3,6,4,5,2,7]=>8
[1,3,6,4,5,7,2]=>10
[1,3,6,4,7,2,5]=>9
[1,3,6,4,7,5,2]=>14
[1,3,6,5,2,4,7]=>8
[1,3,6,5,2,7,4]=>14
[1,3,6,5,4,2,7]=>12
[1,3,6,5,4,7,2]=>15
[1,3,6,5,7,2,4]=>10
[1,3,6,5,7,4,2]=>14
[1,3,6,7,2,4,5]=>4
[1,3,6,7,2,5,4]=>8
[1,3,6,7,4,2,5]=>8
[1,3,6,7,4,5,2]=>9
[1,3,6,7,5,2,4]=>9
[1,3,6,7,5,4,2]=>13
[1,3,7,2,4,5,6]=>3
[1,3,7,2,4,6,5]=>8
[1,3,7,2,5,4,6]=>7
[1,3,7,2,5,6,4]=>8
[1,3,7,2,6,4,5]=>7
[1,3,7,2,6,5,4]=>12
[1,3,7,4,2,5,6]=>7
[1,3,7,4,2,6,5]=>12
[1,3,7,4,5,2,6]=>8
[1,3,7,4,5,6,2]=>9
[1,3,7,4,6,2,5]=>8
[1,3,7,4,6,5,2]=>13
[1,3,7,5,2,4,6]=>8
[1,3,7,5,2,6,4]=>13
[1,3,7,5,4,2,6]=>12
[1,3,7,5,4,6,2]=>14
[1,3,7,5,6,2,4]=>9
[1,3,7,5,6,4,2]=>13
[1,3,7,6,2,4,5]=>9
[1,3,7,6,2,5,4]=>13
[1,3,7,6,4,2,5]=>13
[1,3,7,6,4,5,2]=>14
[1,3,7,6,5,2,4]=>14
[1,3,7,6,5,4,2]=>18
[1,4,2,3,5,6,7]=>2
[1,4,2,3,5,7,6]=>8
[1,4,2,3,6,5,7]=>7
[1,4,2,3,6,7,5]=>8
[1,4,2,3,7,5,6]=>7
[1,4,2,3,7,6,5]=>13
[1,4,2,5,3,6,7]=>6
[1,4,2,5,3,7,6]=>12
[1,4,2,5,6,3,7]=>7
[1,4,2,5,6,7,3]=>8
[1,4,2,5,7,3,6]=>7
[1,4,2,5,7,6,3]=>13
[1,4,2,6,3,5,7]=>6
[1,4,2,6,3,7,5]=>12
[1,4,2,6,5,3,7]=>11
[1,4,2,6,5,7,3]=>13
[1,4,2,6,7,3,5]=>7
[1,4,2,6,7,5,3]=>12
[1,4,2,7,3,5,6]=>6
[1,4,2,7,3,6,5]=>11
[1,4,2,7,5,3,6]=>11
[1,4,2,7,5,6,3]=>12
[1,4,2,7,6,3,5]=>12
[1,4,2,7,6,5,3]=>17
[1,4,3,2,5,6,7]=>5
[1,4,3,2,5,7,6]=>11
[1,4,3,2,6,5,7]=>10
[1,4,3,2,6,7,5]=>11
[1,4,3,2,7,5,6]=>10
[1,4,3,2,7,6,5]=>16
[1,4,3,5,2,6,7]=>7
[1,4,3,5,2,7,6]=>13
[1,4,3,5,6,2,7]=>8
[1,4,3,5,6,7,2]=>9
[1,4,3,5,7,2,6]=>8
[1,4,3,5,7,6,2]=>14
[1,4,3,6,2,5,7]=>7
[1,4,3,6,2,7,5]=>13
[1,4,3,6,5,2,7]=>12
[1,4,3,6,5,7,2]=>14
[1,4,3,6,7,2,5]=>8
[1,4,3,6,7,5,2]=>13
[1,4,3,7,2,5,6]=>7
[1,4,3,7,2,6,5]=>12
[1,4,3,7,5,2,6]=>12
[1,4,3,7,5,6,2]=>13
[1,4,3,7,6,2,5]=>13
[1,4,3,7,6,5,2]=>18
[1,4,5,2,3,6,7]=>3
[1,4,5,2,3,7,6]=>9
[1,4,5,2,6,3,7]=>8
[1,4,5,2,6,7,3]=>9
[1,4,5,2,7,3,6]=>8
[1,4,5,2,7,6,3]=>14
[1,4,5,3,2,6,7]=>6
[1,4,5,3,2,7,6]=>12
[1,4,5,3,6,2,7]=>9
[1,4,5,3,6,7,2]=>10
[1,4,5,3,7,2,6]=>9
[1,4,5,3,7,6,2]=>15
[1,4,5,6,2,3,7]=>4
[1,4,5,6,2,7,3]=>10
[1,4,5,6,3,2,7]=>7
[1,4,5,6,3,7,2]=>11
[1,4,5,6,7,2,3]=>5
[1,4,5,6,7,3,2]=>8
[1,4,5,7,2,3,6]=>4
[1,4,5,7,2,6,3]=>9
[1,4,5,7,3,2,6]=>7
[1,4,5,7,3,6,2]=>10
[1,4,5,7,6,2,3]=>10
[1,4,5,7,6,3,2]=>13
[1,4,6,2,3,5,7]=>3
[1,4,6,2,3,7,5]=>9
[1,4,6,2,5,3,7]=>7
[1,4,6,2,5,7,3]=>9
[1,4,6,2,7,3,5]=>8
[1,4,6,2,7,5,3]=>13
[1,4,6,3,2,5,7]=>6
[1,4,6,3,2,7,5]=>12
[1,4,6,3,5,2,7]=>8
[1,4,6,3,5,7,2]=>10
[1,4,6,3,7,2,5]=>9
[1,4,6,3,7,5,2]=>14
[1,4,6,5,2,3,7]=>8
[1,4,6,5,2,7,3]=>14
[1,4,6,5,3,2,7]=>11
[1,4,6,5,3,7,2]=>15
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Description
The mak of a permutation.
According to [1], this is the sum of the number of occurrences of the vincular patterns $(2\underline{31})$, $(\underline{32}1)$, $(1\underline{32})$, $(\underline{21})$, where matches of the underlined letters must be adjacent.
According to [1], this is the sum of the number of occurrences of the vincular patterns $(2\underline{31})$, $(\underline{32}1)$, $(1\underline{32})$, $(\underline{21})$, where matches of the underlined letters must be adjacent.
References
[1] Babson, E., Steingr'ımsson, E. Generalized permutation patterns and a classification of the Mahonian statistics MathSciNet:1758852
Code
def statistic(pi):
mak_babson_data = [([2,3,1],[2]), ([3,2,1],[1]), ([1,3,2],[2]), ([2,1],[1])]
return sum(vincular_occurrences(pi, p, c) for p, c in mak_babson_data)
def vincular_occurrences(perm, pat, columns):
n = len(pat)
R = [(c, i) for c in columns for i in range(n+1)]
return mesh_pattern_occurrences(perm, pat, R=R)
def G(w):
return [ (x+1,y) for (x,y) in enumerate(w) ]
def mesh_pattern_occurrences(perm, pat, R=[]):
occs = 0
k = len(pat)
n = len(perm)
pat = G(pat)
perm = G(perm)
for H in Subsets(perm, k):
H = sorted(H)
X = dict(G(sorted(i for (i,_) in H)))
Y = dict(G(sorted(j for (_,j) in H)))
if H == [ (X[i], Y[j]) for (i,j) in pat ]:
X[0], X[k+1] = 0, n+1
Y[0], Y[k+1] = 0, n+1
shady = ( X[i] < x < X[i+1] and Y[j] < y < Y[j+1]
for (i,j) in R
for (x,y) in perm
)
if not any(shady):
occs = occs + 1
return occs
Created
May 16, 2017 at 13:43 by Martin Rubey
Updated
May 16, 2017 at 16:36 by Martin Rubey
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