Identifier
- St001220: Permutations ⟶ ℤ
Values
=>
[1,2]=>1
[2,1]=>1
[1,2,3]=>1
[1,3,2]=>1
[2,1,3]=>1
[2,3,1]=>1
[3,1,2]=>1
[3,2,1]=>2
[1,2,3,4]=>1
[1,2,4,3]=>1
[1,3,2,4]=>1
[1,3,4,2]=>1
[1,4,2,3]=>1
[1,4,3,2]=>2
[2,1,3,4]=>1
[2,1,4,3]=>2
[2,3,1,4]=>1
[2,3,4,1]=>1
[2,4,1,3]=>2
[2,4,3,1]=>2
[3,1,2,4]=>1
[3,1,4,2]=>2
[3,2,1,4]=>2
[3,2,4,1]=>2
[3,4,1,2]=>2
[3,4,2,1]=>3
[4,1,2,3]=>1
[4,1,3,2]=>2
[4,2,1,3]=>2
[4,2,3,1]=>3
[4,3,1,2]=>3
[4,3,2,1]=>6
[1,2,3,4,5]=>1
[1,2,3,5,4]=>1
[1,2,4,3,5]=>1
[1,2,4,5,3]=>1
[1,2,5,3,4]=>1
[1,2,5,4,3]=>2
[1,3,2,4,5]=>1
[1,3,2,5,4]=>2
[1,3,4,2,5]=>1
[1,3,4,5,2]=>1
[1,3,5,2,4]=>2
[1,3,5,4,2]=>2
[1,4,2,3,5]=>1
[1,4,2,5,3]=>2
[1,4,3,2,5]=>2
[1,4,3,5,2]=>2
[1,4,5,2,3]=>2
[1,4,5,3,2]=>3
[1,5,2,3,4]=>1
[1,5,2,4,3]=>2
[1,5,3,2,4]=>2
[1,5,3,4,2]=>3
[1,5,4,2,3]=>3
[1,5,4,3,2]=>6
[2,1,3,4,5]=>1
[2,1,3,5,4]=>2
[2,1,4,3,5]=>2
[2,1,4,5,3]=>2
[2,1,5,3,4]=>2
[2,1,5,4,3]=>4
[2,3,1,4,5]=>1
[2,3,1,5,4]=>2
[2,3,4,1,5]=>1
[2,3,4,5,1]=>1
[2,3,5,1,4]=>2
[2,3,5,4,1]=>2
[2,4,1,3,5]=>2
[2,4,1,5,3]=>2
[2,4,3,1,5]=>2
[2,4,3,5,1]=>2
[2,4,5,1,3]=>2
[2,4,5,3,1]=>3
[2,5,1,3,4]=>2
[2,5,1,4,3]=>4
[2,5,3,1,4]=>3
[2,5,3,4,1]=>3
[2,5,4,1,3]=>4
[2,5,4,3,1]=>6
[3,1,2,4,5]=>1
[3,1,2,5,4]=>2
[3,1,4,2,5]=>2
[3,1,4,5,2]=>2
[3,1,5,2,4]=>2
[3,1,5,4,2]=>4
[3,2,1,4,5]=>2
[3,2,1,5,4]=>4
[3,2,4,1,5]=>2
[3,2,4,5,1]=>2
[3,2,5,1,4]=>4
[3,2,5,4,1]=>4
[3,4,1,2,5]=>2
[3,4,1,5,2]=>2
[3,4,2,1,5]=>3
[3,4,2,5,1]=>3
[3,4,5,1,2]=>2
[3,4,5,2,1]=>4
[3,5,1,2,4]=>2
[3,5,1,4,2]=>4
[3,5,2,1,4]=>4
[3,5,2,4,1]=>5
[3,5,4,1,2]=>4
[3,5,4,2,1]=>8
[4,1,2,3,5]=>1
[4,1,2,5,3]=>2
[4,1,3,2,5]=>2
[4,1,3,5,2]=>3
[4,1,5,2,3]=>2
[4,1,5,3,2]=>4
[4,2,1,3,5]=>2
[4,2,1,5,3]=>4
[4,2,3,1,5]=>3
[4,2,3,5,1]=>3
[4,2,5,1,3]=>4
[4,2,5,3,1]=>5
[4,3,1,2,5]=>3
[4,3,1,5,2]=>4
[4,3,2,1,5]=>6
[4,3,2,5,1]=>6
[4,3,5,1,2]=>4
[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]=>6
[4,5,3,1,2]=>6
[4,5,3,2,1]=>11
[5,1,2,3,4]=>1
[5,1,2,4,3]=>2
[5,1,3,2,4]=>2
[5,1,3,4,2]=>3
[5,1,4,2,3]=>3
[5,1,4,3,2]=>6
[5,2,1,3,4]=>2
[5,2,1,4,3]=>4
[5,2,3,1,4]=>3
[5,2,3,4,1]=>4
[5,2,4,1,3]=>5
[5,2,4,3,1]=>8
[5,3,1,2,4]=>3
[5,3,1,4,2]=>5
[5,3,2,1,4]=>6
[5,3,2,4,1]=>8
[5,3,4,1,2]=>6
[5,3,4,2,1]=>11
[5,4,1,2,3]=>4
[5,4,1,3,2]=>8
[5,4,2,1,3]=>8
[5,4,2,3,1]=>11
[5,4,3,1,2]=>11
[5,4,3,2,1]=>22
[1,2,3,4,5,6]=>1
[1,2,3,4,6,5]=>1
[1,2,3,5,4,6]=>1
[1,2,3,5,6,4]=>1
[1,2,3,6,4,5]=>1
[1,2,3,6,5,4]=>2
[1,2,4,3,5,6]=>1
[1,2,4,3,6,5]=>2
[1,2,4,5,3,6]=>1
[1,2,4,5,6,3]=>1
[1,2,4,6,3,5]=>2
[1,2,4,6,5,3]=>2
[1,2,5,3,4,6]=>1
[1,2,5,3,6,4]=>2
[1,2,5,4,3,6]=>2
[1,2,5,4,6,3]=>2
[1,2,5,6,3,4]=>2
[1,2,5,6,4,3]=>3
[1,2,6,3,4,5]=>1
[1,2,6,3,5,4]=>2
[1,2,6,4,3,5]=>2
[1,2,6,4,5,3]=>3
[1,2,6,5,3,4]=>3
[1,2,6,5,4,3]=>6
[1,3,2,4,5,6]=>1
[1,3,2,4,6,5]=>2
[1,3,2,5,4,6]=>2
[1,3,2,5,6,4]=>2
[1,3,2,6,4,5]=>2
[1,3,2,6,5,4]=>4
[1,3,4,2,5,6]=>1
[1,3,4,2,6,5]=>2
[1,3,4,5,2,6]=>1
[1,3,4,5,6,2]=>1
[1,3,4,6,2,5]=>2
[1,3,4,6,5,2]=>2
[1,3,5,2,4,6]=>2
[1,3,5,2,6,4]=>2
[1,3,5,4,2,6]=>2
[1,3,5,4,6,2]=>2
[1,3,5,6,2,4]=>2
[1,3,5,6,4,2]=>3
[1,3,6,2,4,5]=>2
[1,3,6,2,5,4]=>4
[1,3,6,4,2,5]=>3
[1,3,6,4,5,2]=>3
[1,3,6,5,2,4]=>4
[1,3,6,5,4,2]=>6
[1,4,2,3,5,6]=>1
[1,4,2,3,6,5]=>2
[1,4,2,5,3,6]=>2
[1,4,2,5,6,3]=>2
[1,4,2,6,3,5]=>2
[1,4,2,6,5,3]=>4
[1,4,3,2,5,6]=>2
[1,4,3,2,6,5]=>4
[1,4,3,5,2,6]=>2
[1,4,3,5,6,2]=>2
[1,4,3,6,2,5]=>4
[1,4,3,6,5,2]=>4
[1,4,5,2,3,6]=>2
[1,4,5,2,6,3]=>2
[1,4,5,3,2,6]=>3
[1,4,5,3,6,2]=>3
[1,4,5,6,2,3]=>2
[1,4,5,6,3,2]=>4
[1,4,6,2,3,5]=>2
[1,4,6,2,5,3]=>4
[1,4,6,3,2,5]=>4
[1,4,6,3,5,2]=>5
[1,4,6,5,2,3]=>4
[1,4,6,5,3,2]=>8
[1,5,2,3,4,6]=>1
[1,5,2,3,6,4]=>2
[1,5,2,4,3,6]=>2
[1,5,2,4,6,3]=>3
[1,5,2,6,3,4]=>2
[1,5,2,6,4,3]=>4
[1,5,3,2,4,6]=>2
[1,5,3,2,6,4]=>4
[1,5,3,4,2,6]=>3
[1,5,3,4,6,2]=>3
[1,5,3,6,2,4]=>4
[1,5,3,6,4,2]=>5
[1,5,4,2,3,6]=>3
[1,5,4,2,6,3]=>4
[1,5,4,3,2,6]=>6
[1,5,4,3,6,2]=>6
[1,5,4,6,2,3]=>4
[1,5,4,6,3,2]=>8
[1,5,6,2,3,4]=>2
[1,5,6,2,4,3]=>4
[1,5,6,3,2,4]=>4
[1,5,6,3,4,2]=>6
[1,5,6,4,2,3]=>6
[1,5,6,4,3,2]=>11
[1,6,2,3,4,5]=>1
[1,6,2,3,5,4]=>2
[1,6,2,4,3,5]=>2
[1,6,2,4,5,3]=>3
[1,6,2,5,3,4]=>3
[1,6,2,5,4,3]=>6
[1,6,3,2,4,5]=>2
[1,6,3,2,5,4]=>4
[1,6,3,4,2,5]=>3
[1,6,3,4,5,2]=>4
[1,6,3,5,2,4]=>5
[1,6,3,5,4,2]=>8
[1,6,4,2,3,5]=>3
[1,6,4,2,5,3]=>5
[1,6,4,3,2,5]=>6
[1,6,4,3,5,2]=>8
[1,6,4,5,2,3]=>6
[1,6,4,5,3,2]=>11
[1,6,5,2,3,4]=>4
[1,6,5,2,4,3]=>8
[1,6,5,3,2,4]=>8
[1,6,5,3,4,2]=>11
[1,6,5,4,2,3]=>11
[1,6,5,4,3,2]=>22
[2,1,3,4,5,6]=>1
[2,1,3,4,6,5]=>2
[2,1,3,5,4,6]=>2
[2,1,3,5,6,4]=>2
[2,1,3,6,4,5]=>2
[2,1,3,6,5,4]=>4
[2,1,4,3,5,6]=>2
[2,1,4,3,6,5]=>3
[2,1,4,5,3,6]=>2
[2,1,4,5,6,3]=>2
[2,1,4,6,3,5]=>3
[2,1,4,6,5,3]=>4
[2,1,5,3,4,6]=>2
[2,1,5,3,6,4]=>3
[2,1,5,4,3,6]=>4
[2,1,5,4,6,3]=>4
[2,1,5,6,3,4]=>3
[2,1,5,6,4,3]=>6
[2,1,6,3,4,5]=>2
[2,1,6,3,5,4]=>4
[2,1,6,4,3,5]=>4
[2,1,6,4,5,3]=>6
[2,1,6,5,3,4]=>6
[2,1,6,5,4,3]=>11
[2,3,1,4,5,6]=>1
[2,3,1,4,6,5]=>2
[2,3,1,5,4,6]=>2
[2,3,1,5,6,4]=>3
[2,3,1,6,4,5]=>3
[2,3,1,6,5,4]=>5
[2,3,4,1,5,6]=>1
[2,3,4,1,6,5]=>2
[2,3,4,5,1,6]=>1
[2,3,4,5,6,1]=>1
[2,3,4,6,1,5]=>2
[2,3,4,6,5,1]=>2
[2,3,5,1,4,6]=>2
[2,3,5,1,6,4]=>3
[2,3,5,4,1,6]=>2
[2,3,5,4,6,1]=>2
[2,3,5,6,1,4]=>3
[2,3,5,6,4,1]=>3
[2,3,6,1,4,5]=>3
[2,3,6,1,5,4]=>5
[2,3,6,4,1,5]=>3
[2,3,6,4,5,1]=>3
[2,3,6,5,1,4]=>5
[2,3,6,5,4,1]=>6
[2,4,1,3,5,6]=>2
[2,4,1,3,6,5]=>3
[2,4,1,5,3,6]=>2
[2,4,1,5,6,3]=>3
[2,4,1,6,3,5]=>3
[2,4,1,6,5,3]=>5
[2,4,3,1,5,6]=>2
[2,4,3,1,6,5]=>4
[2,4,3,5,1,6]=>2
[2,4,3,5,6,1]=>2
[2,4,3,6,1,5]=>4
[2,4,3,6,5,1]=>4
[2,4,5,1,3,6]=>2
[2,4,5,1,6,3]=>3
[2,4,5,3,1,6]=>3
[2,4,5,3,6,1]=>3
[2,4,5,6,1,3]=>3
[2,4,5,6,3,1]=>4
[2,4,6,1,3,5]=>3
[2,4,6,1,5,3]=>5
[2,4,6,3,1,5]=>5
[2,4,6,3,5,1]=>5
[2,4,6,5,1,3]=>5
[2,4,6,5,3,1]=>8
[2,5,1,3,4,6]=>2
[2,5,1,3,6,4]=>3
[2,5,1,4,3,6]=>4
[2,5,1,4,6,3]=>4
[2,5,1,6,3,4]=>3
[2,5,1,6,4,3]=>6
[2,5,3,1,4,6]=>3
[2,5,3,1,6,4]=>4
[2,5,3,4,1,6]=>3
[2,5,3,4,6,1]=>3
[2,5,3,6,1,4]=>4
[2,5,3,6,4,1]=>5
[2,5,4,1,3,6]=>4
[2,5,4,1,6,3]=>5
[2,5,4,3,1,6]=>6
[2,5,4,3,6,1]=>6
[2,5,4,6,1,3]=>5
[2,5,4,6,3,1]=>8
[2,5,6,1,3,4]=>3
[2,5,6,1,4,3]=>6
[2,5,6,3,1,4]=>5
[2,5,6,3,4,1]=>6
[2,5,6,4,1,3]=>7
[2,5,6,4,3,1]=>12
[2,6,1,3,4,5]=>2
[2,6,1,3,5,4]=>4
[2,6,1,4,3,5]=>4
[2,6,1,4,5,3]=>6
[2,6,1,5,3,4]=>6
[2,6,1,5,4,3]=>11
[2,6,3,1,4,5]=>3
[2,6,3,1,5,4]=>6
[2,6,3,4,1,5]=>4
[2,6,3,4,5,1]=>4
[2,6,3,5,1,4]=>6
[2,6,3,5,4,1]=>8
[2,6,4,1,3,5]=>5
[2,6,4,1,5,3]=>7
[2,6,4,3,1,5]=>7
[2,6,4,3,5,1]=>8
[2,6,4,5,1,3]=>7
[2,6,4,5,3,1]=>12
[2,6,5,1,3,4]=>6
[2,6,5,1,4,3]=>12
[2,6,5,3,1,4]=>9
[2,6,5,3,4,1]=>12
[2,6,5,4,1,3]=>14
[2,6,5,4,3,1]=>23
[3,1,2,4,5,6]=>1
[3,1,2,4,6,5]=>2
[3,1,2,5,4,6]=>2
[3,1,2,5,6,4]=>3
[3,1,2,6,4,5]=>3
[3,1,2,6,5,4]=>5
[3,1,4,2,5,6]=>2
[3,1,4,2,6,5]=>3
[3,1,4,5,2,6]=>2
[3,1,4,5,6,2]=>2
[3,1,4,6,2,5]=>3
[3,1,4,6,5,2]=>4
[3,1,5,2,4,6]=>2
[3,1,5,2,6,4]=>3
[3,1,5,4,2,6]=>4
[3,1,5,4,6,2]=>4
[3,1,5,6,2,4]=>3
[3,1,5,6,4,2]=>6
[3,1,6,2,4,5]=>3
[3,1,6,2,5,4]=>5
[3,1,6,4,2,5]=>4
[3,1,6,4,5,2]=>6
[3,1,6,5,2,4]=>6
[3,1,6,5,4,2]=>11
[3,2,1,4,5,6]=>2
[3,2,1,4,6,5]=>4
[3,2,1,5,4,6]=>4
[3,2,1,5,6,4]=>5
[3,2,1,6,4,5]=>5
[3,2,1,6,5,4]=>10
[3,2,4,1,5,6]=>2
[3,2,4,1,6,5]=>4
[3,2,4,5,1,6]=>2
[3,2,4,5,6,1]=>2
[3,2,4,6,1,5]=>4
[3,2,4,6,5,1]=>4
[3,2,5,1,4,6]=>4
[3,2,5,1,6,4]=>5
[3,2,5,4,1,6]=>4
[3,2,5,4,6,1]=>4
[3,2,5,6,1,4]=>5
[3,2,5,6,4,1]=>6
[3,2,6,1,4,5]=>5
[3,2,6,1,5,4]=>10
[3,2,6,4,1,5]=>6
[3,2,6,4,5,1]=>6
[3,2,6,5,1,4]=>10
[3,2,6,5,4,1]=>12
[3,4,1,2,5,6]=>2
[3,4,1,2,6,5]=>3
[3,4,1,5,2,6]=>2
[3,4,1,5,6,2]=>3
[3,4,1,6,2,5]=>3
[3,4,1,6,5,2]=>5
[3,4,2,1,5,6]=>3
[3,4,2,1,6,5]=>6
[3,4,2,5,1,6]=>3
[3,4,2,5,6,1]=>3
[3,4,2,6,1,5]=>6
[3,4,2,6,5,1]=>6
[3,4,5,1,2,6]=>2
[3,4,5,1,6,2]=>3
[3,4,5,2,1,6]=>4
[3,4,5,2,6,1]=>4
[3,4,5,6,1,2]=>3
[3,4,5,6,2,1]=>5
[3,4,6,1,2,5]=>3
[3,4,6,1,5,2]=>5
[3,4,6,2,1,5]=>6
[3,4,6,2,5,1]=>7
[3,4,6,5,1,2]=>5
[3,4,6,5,2,1]=>10
[3,5,1,2,4,6]=>2
[3,5,1,2,6,4]=>3
[3,5,1,4,2,6]=>4
[3,5,1,4,6,2]=>4
[3,5,1,6,2,4]=>3
[3,5,1,6,4,2]=>6
[3,5,2,1,4,6]=>4
[3,5,2,1,6,4]=>6
[3,5,2,4,1,6]=>5
[3,5,2,4,6,1]=>5
[3,5,2,6,1,4]=>6
[3,5,2,6,4,1]=>8
[3,5,4,1,2,6]=>4
[3,5,4,1,6,2]=>5
[3,5,4,2,1,6]=>8
[3,5,4,2,6,1]=>8
[3,5,4,6,1,2]=>5
[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]=>6
[3,5,6,2,4,1]=>9
[3,5,6,4,1,2]=>7
[3,5,6,4,2,1]=>14
[3,6,1,2,4,5]=>3
[3,6,1,2,5,4]=>5
[3,6,1,4,2,5]=>4
[3,6,1,4,5,2]=>6
[3,6,1,5,2,4]=>6
[3,6,1,5,4,2]=>11
[3,6,2,1,4,5]=>5
[3,6,2,1,5,4]=>10
[3,6,2,4,1,5]=>6
[3,6,2,4,5,1]=>7
[3,6,2,5,1,4]=>10
[3,6,2,5,4,1]=>14
[3,6,4,1,2,5]=>5
[3,6,4,1,5,2]=>7
[3,6,4,2,1,5]=>9
[3,6,4,2,5,1]=>11
[3,6,4,5,1,2]=>7
[3,6,4,5,2,1]=>14
[3,6,5,1,2,4]=>6
[3,6,5,1,4,2]=>12
[3,6,5,2,1,4]=>12
[3,6,5,2,4,1]=>17
[3,6,5,4,1,2]=>14
[3,6,5,4,2,1]=>28
[4,1,2,3,5,6]=>1
[4,1,2,3,6,5]=>2
[4,1,2,5,3,6]=>2
[4,1,2,5,6,3]=>3
[4,1,2,6,3,5]=>3
[4,1,2,6,5,3]=>5
[4,1,3,2,5,6]=>2
[4,1,3,2,6,5]=>4
[4,1,3,5,2,6]=>3
[4,1,3,5,6,2]=>3
[4,1,3,6,2,5]=>4
[4,1,3,6,5,2]=>6
[4,1,5,2,3,6]=>2
[4,1,5,2,6,3]=>3
[4,1,5,3,2,6]=>4
[4,1,5,3,6,2]=>5
[4,1,5,6,2,3]=>3
[4,1,5,6,3,2]=>6
[4,1,6,2,3,5]=>3
[4,1,6,2,5,3]=>5
[4,1,6,3,2,5]=>5
[4,1,6,3,5,2]=>7
[4,1,6,5,2,3]=>6
[4,1,6,5,3,2]=>12
[4,2,1,3,5,6]=>2
[4,2,1,3,6,5]=>4
[4,2,1,5,3,6]=>4
[4,2,1,5,6,3]=>5
[4,2,1,6,3,5]=>5
[4,2,1,6,5,3]=>10
[4,2,3,1,5,6]=>3
[4,2,3,1,6,5]=>6
[4,2,3,5,1,6]=>3
[4,2,3,5,6,1]=>3
[4,2,3,6,1,5]=>6
[4,2,3,6,5,1]=>6
[4,2,5,1,3,6]=>4
[4,2,5,1,6,3]=>5
[4,2,5,3,1,6]=>5
[4,2,5,3,6,1]=>5
[4,2,5,6,1,3]=>5
[4,2,5,6,3,1]=>7
[4,2,6,1,3,5]=>5
[4,2,6,1,5,3]=>10
[4,2,6,3,1,5]=>7
[4,2,6,3,5,1]=>8
[4,2,6,5,1,3]=>10
[4,2,6,5,3,1]=>14
[4,3,1,2,5,6]=>3
[4,3,1,2,6,5]=>6
[4,3,1,5,2,6]=>4
[4,3,1,5,6,2]=>5
[4,3,1,6,2,5]=>6
[4,3,1,6,5,2]=>10
[4,3,2,1,5,6]=>6
[4,3,2,1,6,5]=>11
[4,3,2,5,1,6]=>6
[4,3,2,5,6,1]=>6
[4,3,2,6,1,5]=>11
[4,3,2,6,5,1]=>12
[4,3,5,1,2,6]=>4
[4,3,5,1,6,2]=>5
[4,3,5,2,1,6]=>8
[4,3,5,2,6,1]=>8
[4,3,5,6,1,2]=>5
[4,3,5,6,2,1]=>10
[4,3,6,1,2,5]=>6
[4,3,6,1,5,2]=>10
[4,3,6,2,1,5]=>12
[4,3,6,2,5,1]=>14
[4,3,6,5,1,2]=>10
[4,3,6,5,2,1]=>19
[4,5,1,2,3,6]=>2
[4,5,1,2,6,3]=>3
[4,5,1,3,2,6]=>4
[4,5,1,3,6,2]=>5
[4,5,1,6,2,3]=>3
[4,5,1,6,3,2]=>6
[4,5,2,1,3,6]=>4
[4,5,2,1,6,3]=>6
[4,5,2,3,1,6]=>6
[4,5,2,3,6,1]=>6
[4,5,2,6,1,3]=>6
[4,5,2,6,3,1]=>9
[4,5,3,1,2,6]=>6
[4,5,3,1,6,2]=>7
[4,5,3,2,1,6]=>11
[4,5,3,2,6,1]=>12
[4,5,3,6,1,2]=>7
[4,5,3,6,2,1]=>14
[4,5,6,1,2,3]=>3
[4,5,6,1,3,2]=>6
[4,5,6,2,1,3]=>6
[4,5,6,2,3,1]=>9
[4,5,6,3,1,2]=>9
[4,5,6,3,2,1]=>18
[4,6,1,2,3,5]=>3
[4,6,1,2,5,3]=>5
[4,6,1,3,2,5]=>5
[4,6,1,3,5,2]=>7
[4,6,1,5,2,3]=>6
[4,6,1,5,3,2]=>12
[4,6,2,1,3,5]=>5
[4,6,2,1,5,3]=>10
[4,6,2,3,1,5]=>7
[4,6,2,3,5,1]=>9
[4,6,2,5,1,3]=>10
[4,6,2,5,3,1]=>15
[4,6,3,1,2,5]=>7
[4,6,3,1,5,2]=>12
[4,6,3,2,1,5]=>14
[4,6,3,2,5,1]=>17
[4,6,3,5,1,2]=>12
[4,6,3,5,2,1]=>23
[4,6,5,1,2,3]=>6
[4,6,5,1,3,2]=>12
[4,6,5,2,1,3]=>12
[4,6,5,2,3,1]=>18
[4,6,5,3,1,2]=>18
[4,6,5,3,2,1]=>35
[5,1,2,3,4,6]=>1
[5,1,2,3,6,4]=>2
[5,1,2,4,3,6]=>2
[5,1,2,4,6,3]=>3
[5,1,2,6,3,4]=>3
[5,1,2,6,4,3]=>5
[5,1,3,2,4,6]=>2
[5,1,3,2,6,4]=>4
[5,1,3,4,2,6]=>3
[5,1,3,4,6,2]=>4
[5,1,3,6,2,4]=>4
[5,1,3,6,4,2]=>6
[5,1,4,2,3,6]=>3
[5,1,4,2,6,3]=>5
[5,1,4,3,2,6]=>6
[5,1,4,3,6,2]=>7
[5,1,4,6,2,3]=>5
[5,1,4,6,3,2]=>9
[5,1,6,2,3,4]=>3
[5,1,6,2,4,3]=>5
[5,1,6,3,2,4]=>5
[5,1,6,3,4,2]=>7
[5,1,6,4,2,3]=>7
[5,1,6,4,3,2]=>14
[5,2,1,3,4,6]=>2
[5,2,1,3,6,4]=>4
[5,2,1,4,3,6]=>4
[5,2,1,4,6,3]=>6
[5,2,1,6,3,4]=>5
[5,2,1,6,4,3]=>10
[5,2,3,1,4,6]=>3
[5,2,3,1,6,4]=>6
[5,2,3,4,1,6]=>4
[5,2,3,4,6,1]=>4
[5,2,3,6,1,4]=>6
[5,2,3,6,4,1]=>7
[5,2,4,1,3,6]=>5
[5,2,4,1,6,3]=>7
[5,2,4,3,1,6]=>8
[5,2,4,3,6,1]=>8
[5,2,4,6,1,3]=>7
[5,2,4,6,3,1]=>11
[5,2,6,1,3,4]=>5
[5,2,6,1,4,3]=>10
[5,2,6,3,1,4]=>7
[5,2,6,3,4,1]=>9
[5,2,6,4,1,3]=>12
[5,2,6,4,3,1]=>17
[5,3,1,2,4,6]=>3
[5,3,1,2,6,4]=>6
[5,3,1,4,2,6]=>5
[5,3,1,4,6,2]=>6
[5,3,1,6,2,4]=>6
[5,3,1,6,4,2]=>10
[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]=>8
[5,3,2,6,1,4]=>11
[5,3,2,6,4,1]=>14
[5,3,4,1,2,6]=>6
[5,3,4,1,6,2]=>7
[5,3,4,2,1,6]=>11
[5,3,4,2,6,1]=>12
[5,3,4,6,1,2]=>7
[5,3,4,6,2,1]=>14
[5,3,6,1,2,4]=>6
[5,3,6,1,4,2]=>10
[5,3,6,2,1,4]=>12
[5,3,6,2,4,1]=>15
[5,3,6,4,1,2]=>12
[5,3,6,4,2,1]=>23
[5,4,1,2,3,6]=>4
[5,4,1,2,6,3]=>6
[5,4,1,3,2,6]=>8
[5,4,1,3,6,2]=>9
[5,4,1,6,2,3]=>6
[5,4,1,6,3,2]=>12
[5,4,2,1,3,6]=>8
[5,4,2,1,6,3]=>12
[5,4,2,3,1,6]=>11
[5,4,2,3,6,1]=>12
[5,4,2,6,1,3]=>12
[5,4,2,6,3,1]=>17
[5,4,3,1,2,6]=>11
[5,4,3,1,6,2]=>14
[5,4,3,2,1,6]=>22
[5,4,3,2,6,1]=>23
[5,4,3,6,1,2]=>14
[5,4,3,6,2,1]=>28
[5,4,6,1,2,3]=>6
[5,4,6,1,3,2]=>12
[5,4,6,2,1,3]=>12
[5,4,6,2,3,1]=>18
[5,4,6,3,1,2]=>18
[5,4,6,3,2,1]=>35
[5,6,1,2,3,4]=>3
[5,6,1,2,4,3]=>5
[5,6,1,3,2,4]=>5
[5,6,1,3,4,2]=>7
[5,6,1,4,2,3]=>7
[5,6,1,4,3,2]=>14
[5,6,2,1,3,4]=>5
[5,6,2,1,4,3]=>10
[5,6,2,3,1,4]=>7
[5,6,2,3,4,1]=>9
[5,6,2,4,1,3]=>12
[5,6,2,4,3,1]=>18
[5,6,3,1,2,4]=>7
[5,6,3,1,4,2]=>12
[5,6,3,2,1,4]=>14
[5,6,3,2,4,1]=>18
[5,6,3,4,1,2]=>14
[5,6,3,4,2,1]=>26
[5,6,4,1,2,3]=>9
[5,6,4,1,3,2]=>18
[5,6,4,2,1,3]=>18
[5,6,4,2,3,1]=>26
[5,6,4,3,1,2]=>26
[5,6,4,3,2,1]=>52
[6,1,2,3,4,5]=>1
[6,1,2,3,5,4]=>2
[6,1,2,4,3,5]=>2
[6,1,2,4,5,3]=>3
[6,1,2,5,3,4]=>3
[6,1,2,5,4,3]=>6
[6,1,3,2,4,5]=>2
[6,1,3,2,5,4]=>4
[6,1,3,4,2,5]=>3
[6,1,3,4,5,2]=>4
[6,1,3,5,2,4]=>5
[6,1,3,5,4,2]=>8
[6,1,4,2,3,5]=>3
[6,1,4,2,5,3]=>5
[6,1,4,3,2,5]=>6
[6,1,4,3,5,2]=>8
[6,1,4,5,2,3]=>6
[6,1,4,5,3,2]=>12
[6,1,5,2,3,4]=>4
[6,1,5,2,4,3]=>8
[6,1,5,3,2,4]=>8
[6,1,5,3,4,2]=>12
[6,1,5,4,2,3]=>12
[6,1,5,4,3,2]=>23
[6,2,1,3,4,5]=>2
[6,2,1,3,5,4]=>4
[6,2,1,4,3,5]=>4
[6,2,1,4,5,3]=>6
[6,2,1,5,3,4]=>6
[6,2,1,5,4,3]=>12
[6,2,3,1,4,5]=>3
[6,2,3,1,5,4]=>6
[6,2,3,4,1,5]=>4
[6,2,3,4,5,1]=>5
[6,2,3,5,1,4]=>7
[6,2,3,5,4,1]=>10
[6,2,4,1,3,5]=>5
[6,2,4,1,5,3]=>8
[6,2,4,3,1,5]=>8
[6,2,4,3,5,1]=>10
[6,2,4,5,1,3]=>9
[6,2,4,5,3,1]=>14
[6,2,5,1,3,4]=>7
[6,2,5,1,4,3]=>14
[6,2,5,3,1,4]=>11
[6,2,5,3,4,1]=>14
[6,2,5,4,1,3]=>17
[6,2,5,4,3,1]=>28
[6,3,1,2,4,5]=>3
[6,3,1,2,5,4]=>6
[6,3,1,4,2,5]=>5
[6,3,1,4,5,2]=>7
[6,3,1,5,2,4]=>8
[6,3,1,5,4,2]=>14
[6,3,2,1,4,5]=>6
[6,3,2,1,5,4]=>12
[6,3,2,4,1,5]=>8
[6,3,2,4,5,1]=>10
[6,3,2,5,1,4]=>14
[6,3,2,5,4,1]=>19
[6,3,4,1,2,5]=>6
[6,3,4,1,5,2]=>9
[6,3,4,2,1,5]=>12
[6,3,4,2,5,1]=>14
[6,3,4,5,1,2]=>9
[6,3,4,5,2,1]=>18
[6,3,5,1,2,4]=>9
[6,3,5,1,4,2]=>15
[6,3,5,2,1,4]=>17
[6,3,5,2,4,1]=>23
[6,3,5,4,1,2]=>18
[6,3,5,4,2,1]=>35
[6,4,1,2,3,5]=>4
[6,4,1,2,5,3]=>7
[6,4,1,3,2,5]=>8
[6,4,1,3,5,2]=>11
[6,4,1,5,2,3]=>9
[6,4,1,5,3,2]=>17
[6,4,2,1,3,5]=>8
[6,4,2,1,5,3]=>14
[6,4,2,3,1,5]=>12
[6,4,2,3,5,1]=>14
[6,4,2,5,1,3]=>15
[6,4,2,5,3,1]=>23
[6,4,3,1,2,5]=>12
[6,4,3,1,5,2]=>17
[6,4,3,2,1,5]=>23
[6,4,3,2,5,1]=>28
[6,4,3,5,1,2]=>18
[6,4,3,5,2,1]=>35
[6,4,5,1,2,3]=>9
[6,4,5,1,3,2]=>18
[6,4,5,2,1,3]=>18
[6,4,5,2,3,1]=>26
[6,4,5,3,1,2]=>26
[6,4,5,3,2,1]=>52
[6,5,1,2,3,4]=>5
[6,5,1,2,4,3]=>10
[6,5,1,3,2,4]=>10
[6,5,1,3,4,2]=>14
[6,5,1,4,2,3]=>14
[6,5,1,4,3,2]=>28
[6,5,2,1,3,4]=>10
[6,5,2,1,4,3]=>19
[6,5,2,3,1,4]=>14
[6,5,2,3,4,1]=>18
[6,5,2,4,1,3]=>23
[6,5,2,4,3,1]=>35
[6,5,3,1,2,4]=>14
[6,5,3,1,4,2]=>23
[6,5,3,2,1,4]=>28
[6,5,3,2,4,1]=>35
[6,5,3,4,1,2]=>26
[6,5,3,4,2,1]=>52
[6,5,4,1,2,3]=>18
[6,5,4,1,3,2]=>35
[6,5,4,2,1,3]=>35
[6,5,4,2,3,1]=>52
[6,5,4,3,1,2]=>52
[6,5,4,3,2,1]=>101
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Description
The width of a permutation.
Let $w$ be a permutation. The interval $[e,w]$ in the weak order is ranked, and we define $r_i=r_i(w)$ to be the number of elements at rank $i$ in $[e,w]$, where $i \in \{0, \dots, \ell(w)\}$. The width of
$w$ is the maximum of $\{r_0,r_1,\ldots,r_{\ell(w)}\}$. See [1].
Let $w$ be a permutation. The interval $[e,w]$ in the weak order is ranked, and we define $r_i=r_i(w)$ to be the number of elements at rank $i$ in $[e,w]$, where $i \in \{0, \dots, \ell(w)\}$. The width of
$w$ is the maximum of $\{r_0,r_1,\ldots,r_{\ell(w)}\}$. See [1].
References
[1] Fishel, S., Milićević, E., Patrias, R., Tenner, B. E. Enumerations relating braid and commutation classes arXiv:1708.04372
Code
def statistic(pi):
S = SymmetricGroup(len(pi))
pi = S(pi)
P = S.weak_poset()
return P.subposet(P.principal_order_ideal(pi)).width()
Created
Jun 26, 2018 at 12:54 by Susanna Fishel
Updated
Jun 26, 2018 at 13:13 by Christian Stump
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