- FindStat

edit this statistic or download as text // json

Identifier

St000530: Permutations ⟶ ℤ

Values

=>
                            
                            
                            
                            

                        [1,2]=>1
[2,1]=>1
[1,2,3]=>1
[1,3,2]=>2
[2,1,3]=>2
[2,3,1]=>2
[3,1,2]=>2
[3,2,1]=>1
[1,2,3,4]=>1
[1,2,4,3]=>3
[1,3,2,4]=>5
[1,3,4,2]=>3
[1,4,2,3]=>5
[1,4,3,2]=>3
[2,1,3,4]=>3
[2,1,4,3]=>5
[2,3,1,4]=>5
[2,3,4,1]=>3
[2,4,1,3]=>5
[2,4,3,1]=>3
[3,1,2,4]=>3
[3,1,4,2]=>5
[3,2,1,4]=>3
[3,2,4,1]=>5
[3,4,1,2]=>5
[3,4,2,1]=>3
[4,1,2,3]=>3
[4,1,3,2]=>5
[4,2,1,3]=>3
[4,2,3,1]=>5
[4,3,1,2]=>3
[4,3,2,1]=>1
[1,2,3,4,5]=>1
[1,2,3,5,4]=>4
[1,2,4,3,5]=>9
[1,2,4,5,3]=>4
[1,2,5,3,4]=>9
[1,2,5,4,3]=>6
[1,3,2,4,5]=>9
[1,3,2,5,4]=>16
[1,3,4,2,5]=>9
[1,3,4,5,2]=>4
[1,3,5,2,4]=>9
[1,3,5,4,2]=>6
[1,4,2,3,5]=>9
[1,4,2,5,3]=>16
[1,4,3,2,5]=>11
[1,4,3,5,2]=>16
[1,4,5,2,3]=>9
[1,4,5,3,2]=>6
[1,5,2,3,4]=>9
[1,5,2,4,3]=>16
[1,5,3,2,4]=>11
[1,5,3,4,2]=>16
[1,5,4,2,3]=>11
[1,5,4,3,2]=>4
[2,1,3,4,5]=>4
[2,1,3,5,4]=>11
[2,1,4,3,5]=>16
[2,1,4,5,3]=>11
[2,1,5,3,4]=>16
[2,1,5,4,3]=>9
[2,3,1,4,5]=>9
[2,3,1,5,4]=>16
[2,3,4,1,5]=>9
[2,3,4,5,1]=>4
[2,3,5,1,4]=>9
[2,3,5,4,1]=>6
[2,4,1,3,5]=>9
[2,4,1,5,3]=>16
[2,4,3,1,5]=>11
[2,4,3,5,1]=>16
[2,4,5,1,3]=>9
[2,4,5,3,1]=>6
[2,5,1,3,4]=>9
[2,5,1,4,3]=>16
[2,5,3,1,4]=>11
[2,5,3,4,1]=>16
[2,5,4,1,3]=>11
[2,5,4,3,1]=>4
[3,1,2,4,5]=>4
[3,1,2,5,4]=>11
[3,1,4,2,5]=>16
[3,1,4,5,2]=>11
[3,1,5,2,4]=>16
[3,1,5,4,2]=>9
[3,2,1,4,5]=>6
[3,2,1,5,4]=>9
[3,2,4,1,5]=>16
[3,2,4,5,1]=>11
[3,2,5,1,4]=>16
[3,2,5,4,1]=>9
[3,4,1,2,5]=>9
[3,4,1,5,2]=>16
[3,4,2,1,5]=>11
[3,4,2,5,1]=>16
[3,4,5,1,2]=>9
[3,4,5,2,1]=>6
[3,5,1,2,4]=>9
[3,5,1,4,2]=>16
[3,5,2,1,4]=>11
[3,5,2,4,1]=>16
[3,5,4,1,2]=>11
[3,5,4,2,1]=>4
[4,1,2,3,5]=>4
[4,1,2,5,3]=>11
[4,1,3,2,5]=>16
[4,1,3,5,2]=>11
[4,1,5,2,3]=>16
[4,1,5,3,2]=>9
[4,2,1,3,5]=>6
[4,2,1,5,3]=>9
[4,2,3,1,5]=>16
[4,2,3,5,1]=>11
[4,2,5,1,3]=>16
[4,2,5,3,1]=>9
[4,3,1,2,5]=>6
[4,3,1,5,2]=>9
[4,3,2,1,5]=>4
[4,3,2,5,1]=>9
[4,3,5,1,2]=>16
[4,3,5,2,1]=>9
[4,5,1,2,3]=>9
[4,5,1,3,2]=>16
[4,5,2,1,3]=>11
[4,5,2,3,1]=>16
[4,5,3,1,2]=>11
[4,5,3,2,1]=>4
[5,1,2,3,4]=>4
[5,1,2,4,3]=>11
[5,1,3,2,4]=>16
[5,1,3,4,2]=>11
[5,1,4,2,3]=>16
[5,1,4,3,2]=>9
[5,2,1,3,4]=>6
[5,2,1,4,3]=>9
[5,2,3,1,4]=>16
[5,2,3,4,1]=>11
[5,2,4,1,3]=>16
[5,2,4,3,1]=>9
[5,3,1,2,4]=>6
[5,3,1,4,2]=>9
[5,3,2,1,4]=>4
[5,3,2,4,1]=>9
[5,3,4,1,2]=>16
[5,3,4,2,1]=>9
[5,4,1,2,3]=>6
[5,4,1,3,2]=>9
[5,4,2,1,3]=>4
[5,4,2,3,1]=>9
[5,4,3,1,2]=>4
[5,4,3,2,1]=>1
[1,2,3,4,5,6]=>1
[1,2,3,4,6,5]=>5
[1,2,3,5,4,6]=>14
[1,2,3,5,6,4]=>5
[1,2,3,6,4,5]=>14
[1,2,3,6,5,4]=>10
[1,2,4,3,5,6]=>19
[1,2,4,3,6,5]=>35
[1,2,4,5,3,6]=>14
[1,2,4,5,6,3]=>5
[1,2,4,6,3,5]=>14
[1,2,4,6,5,3]=>10
[1,2,5,3,4,6]=>19
[1,2,5,3,6,4]=>35
[1,2,5,4,3,6]=>26
[1,2,5,4,6,3]=>35
[1,2,5,6,3,4]=>14
[1,2,5,6,4,3]=>10
[1,2,6,3,4,5]=>19
[1,2,6,3,5,4]=>35
[1,2,6,4,3,5]=>26
[1,2,6,4,5,3]=>35
[1,2,6,5,3,4]=>26
[1,2,6,5,4,3]=>10
[1,3,2,4,5,6]=>14
[1,3,2,4,6,5]=>40
[1,3,2,5,4,6]=>61
[1,3,2,5,6,4]=>40
[1,3,2,6,4,5]=>61
[1,3,2,6,5,4]=>35
[1,3,4,2,5,6]=>19
[1,3,4,2,6,5]=>35
[1,3,4,5,2,6]=>14
[1,3,4,5,6,2]=>5
[1,3,4,6,2,5]=>14
[1,3,4,6,5,2]=>10
[1,3,5,2,4,6]=>19
[1,3,5,2,6,4]=>35
[1,3,5,4,2,6]=>26
[1,3,5,4,6,2]=>35
[1,3,5,6,2,4]=>14
[1,3,5,6,4,2]=>10
[1,3,6,2,4,5]=>19
[1,3,6,2,5,4]=>35
[1,3,6,4,2,5]=>26
[1,3,6,4,5,2]=>35
[1,3,6,5,2,4]=>26
[1,3,6,5,4,2]=>10
[1,4,2,3,5,6]=>14
[1,4,2,3,6,5]=>40
[1,4,2,5,3,6]=>61
[1,4,2,5,6,3]=>40
[1,4,2,6,3,5]=>61
[1,4,2,6,5,3]=>35
[1,4,3,2,5,6]=>26
[1,4,3,2,6,5]=>40
[1,4,3,5,2,6]=>61
[1,4,3,5,6,2]=>40
[1,4,3,6,2,5]=>61
[1,4,3,6,5,2]=>35
[1,4,5,2,3,6]=>19
[1,4,5,2,6,3]=>35
[1,4,5,3,2,6]=>26
[1,4,5,3,6,2]=>35
[1,4,5,6,2,3]=>14
[1,4,5,6,3,2]=>10
[1,4,6,2,3,5]=>19
[1,4,6,2,5,3]=>35
[1,4,6,3,2,5]=>26
[1,4,6,3,5,2]=>35
[1,4,6,5,2,3]=>26
[1,4,6,5,3,2]=>10
[1,5,2,3,4,6]=>14
[1,5,2,3,6,4]=>40
[1,5,2,4,3,6]=>61
[1,5,2,4,6,3]=>40
[1,5,2,6,3,4]=>61
[1,5,2,6,4,3]=>35
[1,5,3,2,4,6]=>26
[1,5,3,2,6,4]=>40
[1,5,3,4,2,6]=>61
[1,5,3,4,6,2]=>40
[1,5,3,6,2,4]=>61
[1,5,3,6,4,2]=>35
[1,5,4,2,3,6]=>26
[1,5,4,2,6,3]=>40
[1,5,4,3,2,6]=>19
[1,5,4,3,6,2]=>40
[1,5,4,6,2,3]=>61
[1,5,4,6,3,2]=>35
[1,5,6,2,3,4]=>19
[1,5,6,2,4,3]=>35
[1,5,6,3,2,4]=>26
[1,5,6,3,4,2]=>35
[1,5,6,4,2,3]=>26
[1,5,6,4,3,2]=>10
[1,6,2,3,4,5]=>14
[1,6,2,3,5,4]=>40
[1,6,2,4,3,5]=>61
[1,6,2,4,5,3]=>40
[1,6,2,5,3,4]=>61
[1,6,2,5,4,3]=>35
[1,6,3,2,4,5]=>26
[1,6,3,2,5,4]=>40
[1,6,3,4,2,5]=>61
[1,6,3,4,5,2]=>40
[1,6,3,5,2,4]=>61
[1,6,3,5,4,2]=>35
[1,6,4,2,3,5]=>26
[1,6,4,2,5,3]=>40
[1,6,4,3,2,5]=>19
[1,6,4,3,5,2]=>40
[1,6,4,5,2,3]=>61
[1,6,4,5,3,2]=>35
[1,6,5,2,3,4]=>26
[1,6,5,2,4,3]=>40
[1,6,5,3,2,4]=>19
[1,6,5,3,4,2]=>40
[1,6,5,4,2,3]=>19
[1,6,5,4,3,2]=>5
[2,1,3,4,5,6]=>5
[2,1,3,4,6,5]=>19
[2,1,3,5,4,6]=>40
[2,1,3,5,6,4]=>19
[2,1,3,6,4,5]=>40
[2,1,3,6,5,4]=>26
[2,1,4,3,5,6]=>35
[2,1,4,3,6,5]=>61
[2,1,4,5,3,6]=>40
[2,1,4,5,6,3]=>19
[2,1,4,6,3,5]=>40
[2,1,4,6,5,3]=>26
[2,1,5,3,4,6]=>35
[2,1,5,3,6,4]=>61
[2,1,5,4,3,6]=>40
[2,1,5,4,6,3]=>61
[2,1,5,6,3,4]=>40
[2,1,5,6,4,3]=>26
[2,1,6,3,4,5]=>35
[2,1,6,3,5,4]=>61
[2,1,6,4,3,5]=>40
[2,1,6,4,5,3]=>61
[2,1,6,5,3,4]=>40
[2,1,6,5,4,3]=>14
[2,3,1,4,5,6]=>14
[2,3,1,4,6,5]=>40
[2,3,1,5,4,6]=>61
[2,3,1,5,6,4]=>40
[2,3,1,6,4,5]=>61
[2,3,1,6,5,4]=>35
[2,3,4,1,5,6]=>19
[2,3,4,1,6,5]=>35
[2,3,4,5,1,6]=>14
[2,3,4,5,6,1]=>5
[2,3,4,6,1,5]=>14
[2,3,4,6,5,1]=>10
[2,3,5,1,4,6]=>19
[2,3,5,1,6,4]=>35
[2,3,5,4,1,6]=>26
[2,3,5,4,6,1]=>35
[2,3,5,6,1,4]=>14
[2,3,5,6,4,1]=>10
[2,3,6,1,4,5]=>19
[2,3,6,1,5,4]=>35
[2,3,6,4,1,5]=>26
[2,3,6,4,5,1]=>35
[2,3,6,5,1,4]=>26
[2,3,6,5,4,1]=>10
[2,4,1,3,5,6]=>14
[2,4,1,3,6,5]=>40
[2,4,1,5,3,6]=>61
[2,4,1,5,6,3]=>40
[2,4,1,6,3,5]=>61
[2,4,1,6,5,3]=>35
[2,4,3,1,5,6]=>26
[2,4,3,1,6,5]=>40
[2,4,3,5,1,6]=>61
[2,4,3,5,6,1]=>40
[2,4,3,6,1,5]=>61
[2,4,3,6,5,1]=>35
[2,4,5,1,3,6]=>19
[2,4,5,1,6,3]=>35
[2,4,5,3,1,6]=>26
[2,4,5,3,6,1]=>35
[2,4,5,6,1,3]=>14
[2,4,5,6,3,1]=>10
[2,4,6,1,3,5]=>19
[2,4,6,1,5,3]=>35
[2,4,6,3,1,5]=>26
[2,4,6,3,5,1]=>35
[2,4,6,5,1,3]=>26
[2,4,6,5,3,1]=>10
[2,5,1,3,4,6]=>14
[2,5,1,3,6,4]=>40
[2,5,1,4,3,6]=>61
[2,5,1,4,6,3]=>40
[2,5,1,6,3,4]=>61
[2,5,1,6,4,3]=>35
[2,5,3,1,4,6]=>26
[2,5,3,1,6,4]=>40
[2,5,3,4,1,6]=>61
[2,5,3,4,6,1]=>40
[2,5,3,6,1,4]=>61
[2,5,3,6,4,1]=>35
[2,5,4,1,3,6]=>26
[2,5,4,1,6,3]=>40
[2,5,4,3,1,6]=>19
[2,5,4,3,6,1]=>40
[2,5,4,6,1,3]=>61
[2,5,4,6,3,1]=>35
[2,5,6,1,3,4]=>19
[2,5,6,1,4,3]=>35
[2,5,6,3,1,4]=>26
[2,5,6,3,4,1]=>35
[2,5,6,4,1,3]=>26
[2,5,6,4,3,1]=>10
[2,6,1,3,4,5]=>14
[2,6,1,3,5,4]=>40
[2,6,1,4,3,5]=>61
[2,6,1,4,5,3]=>40
[2,6,1,5,3,4]=>61
[2,6,1,5,4,3]=>35
[2,6,3,1,4,5]=>26
[2,6,3,1,5,4]=>40
[2,6,3,4,1,5]=>61
[2,6,3,4,5,1]=>40
[2,6,3,5,1,4]=>61
[2,6,3,5,4,1]=>35
[2,6,4,1,3,5]=>26
[2,6,4,1,5,3]=>40
[2,6,4,3,1,5]=>19
[2,6,4,3,5,1]=>40
[2,6,4,5,1,3]=>61
[2,6,4,5,3,1]=>35
[2,6,5,1,3,4]=>26
[2,6,5,1,4,3]=>40
[2,6,5,3,1,4]=>19
[2,6,5,3,4,1]=>40
[2,6,5,4,1,3]=>19
[2,6,5,4,3,1]=>5
[3,1,2,4,5,6]=>5
[3,1,2,4,6,5]=>19
[3,1,2,5,4,6]=>40
[3,1,2,5,6,4]=>19
[3,1,2,6,4,5]=>40
[3,1,2,6,5,4]=>26
[3,1,4,2,5,6]=>35
[3,1,4,2,6,5]=>61
[3,1,4,5,2,6]=>40
[3,1,4,5,6,2]=>19
[3,1,4,6,2,5]=>40
[3,1,4,6,5,2]=>26
[3,1,5,2,4,6]=>35
[3,1,5,2,6,4]=>61
[3,1,5,4,2,6]=>40
[3,1,5,4,6,2]=>61
[3,1,5,6,2,4]=>40
[3,1,5,6,4,2]=>26
[3,1,6,2,4,5]=>35
[3,1,6,2,5,4]=>61
[3,1,6,4,2,5]=>40
[3,1,6,4,5,2]=>61
[3,1,6,5,2,4]=>40
[3,1,6,5,4,2]=>14
[3,2,1,4,5,6]=>10
[3,2,1,4,6,5]=>26
[3,2,1,5,4,6]=>35
[3,2,1,5,6,4]=>26
[3,2,1,6,4,5]=>35
[3,2,1,6,5,4]=>19
[3,2,4,1,5,6]=>35
[3,2,4,1,6,5]=>61
[3,2,4,5,1,6]=>40
[3,2,4,5,6,1]=>19
[3,2,4,6,1,5]=>40
[3,2,4,6,5,1]=>26
[3,2,5,1,4,6]=>35
[3,2,5,1,6,4]=>61
[3,2,5,4,1,6]=>40
[3,2,5,4,6,1]=>61
[3,2,5,6,1,4]=>40
[3,2,5,6,4,1]=>26
[3,2,6,1,4,5]=>35
[3,2,6,1,5,4]=>61
[3,2,6,4,1,5]=>40
[3,2,6,4,5,1]=>61
[3,2,6,5,1,4]=>40
[3,2,6,5,4,1]=>14
[3,4,1,2,5,6]=>14
[3,4,1,2,6,5]=>40
[3,4,1,5,2,6]=>61
[3,4,1,5,6,2]=>40
[3,4,1,6,2,5]=>61
[3,4,1,6,5,2]=>35
[3,4,2,1,5,6]=>26
[3,4,2,1,6,5]=>40
[3,4,2,5,1,6]=>61
[3,4,2,5,6,1]=>40
[3,4,2,6,1,5]=>61
[3,4,2,6,5,1]=>35
[3,4,5,1,2,6]=>19
[3,4,5,1,6,2]=>35
[3,4,5,2,1,6]=>26
[3,4,5,2,6,1]=>35
[3,4,5,6,1,2]=>14
[3,4,5,6,2,1]=>10
[3,4,6,1,2,5]=>19
[3,4,6,1,5,2]=>35
[3,4,6,2,1,5]=>26
[3,4,6,2,5,1]=>35
[3,4,6,5,1,2]=>26
[3,4,6,5,2,1]=>10
[3,5,1,2,4,6]=>14
[3,5,1,2,6,4]=>40
[3,5,1,4,2,6]=>61
[3,5,1,4,6,2]=>40
[3,5,1,6,2,4]=>61
[3,5,1,6,4,2]=>35
[3,5,2,1,4,6]=>26
[3,5,2,1,6,4]=>40
[3,5,2,4,1,6]=>61
[3,5,2,4,6,1]=>40
[3,5,2,6,1,4]=>61
[3,5,2,6,4,1]=>35
[3,5,4,1,2,6]=>26
[3,5,4,1,6,2]=>40
[3,5,4,2,1,6]=>19
[3,5,4,2,6,1]=>40
[3,5,4,6,1,2]=>61
[3,5,4,6,2,1]=>35
[3,5,6,1,2,4]=>19
[3,5,6,1,4,2]=>35
[3,5,6,2,1,4]=>26
[3,5,6,2,4,1]=>35
[3,5,6,4,1,2]=>26
[3,5,6,4,2,1]=>10
[3,6,1,2,4,5]=>14
[3,6,1,2,5,4]=>40
[3,6,1,4,2,5]=>61
[3,6,1,4,5,2]=>40
[3,6,1,5,2,4]=>61
[3,6,1,5,4,2]=>35
[3,6,2,1,4,5]=>26
[3,6,2,1,5,4]=>40
[3,6,2,4,1,5]=>61
[3,6,2,4,5,1]=>40
[3,6,2,5,1,4]=>61
[3,6,2,5,4,1]=>35
[3,6,4,1,2,5]=>26
[3,6,4,1,5,2]=>40
[3,6,4,2,1,5]=>19
[3,6,4,2,5,1]=>40
[3,6,4,5,1,2]=>61
[3,6,4,5,2,1]=>35
[3,6,5,1,2,4]=>26
[3,6,5,1,4,2]=>40
[3,6,5,2,1,4]=>19
[3,6,5,2,4,1]=>40
[3,6,5,4,1,2]=>19
[3,6,5,4,2,1]=>5
[4,1,2,3,5,6]=>5
[4,1,2,3,6,5]=>19
[4,1,2,5,3,6]=>40
[4,1,2,5,6,3]=>19
[4,1,2,6,3,5]=>40
[4,1,2,6,5,3]=>26
[4,1,3,2,5,6]=>35
[4,1,3,2,6,5]=>61
[4,1,3,5,2,6]=>40
[4,1,3,5,6,2]=>19
[4,1,3,6,2,5]=>40
[4,1,3,6,5,2]=>26
[4,1,5,2,3,6]=>35
[4,1,5,2,6,3]=>61
[4,1,5,3,2,6]=>40
[4,1,5,3,6,2]=>61
[4,1,5,6,2,3]=>40
[4,1,5,6,3,2]=>26
[4,1,6,2,3,5]=>35
[4,1,6,2,5,3]=>61
[4,1,6,3,2,5]=>40
[4,1,6,3,5,2]=>61
[4,1,6,5,2,3]=>40
[4,1,6,5,3,2]=>14
[4,2,1,3,5,6]=>10
[4,2,1,3,6,5]=>26
[4,2,1,5,3,6]=>35
[4,2,1,5,6,3]=>26
[4,2,1,6,3,5]=>35
[4,2,1,6,5,3]=>19
[4,2,3,1,5,6]=>35
[4,2,3,1,6,5]=>61
[4,2,3,5,1,6]=>40
[4,2,3,5,6,1]=>19
[4,2,3,6,1,5]=>40
[4,2,3,6,5,1]=>26
[4,2,5,1,3,6]=>35
[4,2,5,1,6,3]=>61
[4,2,5,3,1,6]=>40
[4,2,5,3,6,1]=>61
[4,2,5,6,1,3]=>40
[4,2,5,6,3,1]=>26
[4,2,6,1,3,5]=>35
[4,2,6,1,5,3]=>61
[4,2,6,3,1,5]=>40
[4,2,6,3,5,1]=>61
[4,2,6,5,1,3]=>40
[4,2,6,5,3,1]=>14
[4,3,1,2,5,6]=>10
[4,3,1,2,6,5]=>26
[4,3,1,5,2,6]=>35
[4,3,1,5,6,2]=>26
[4,3,1,6,2,5]=>35
[4,3,1,6,5,2]=>19
[4,3,2,1,5,6]=>10
[4,3,2,1,6,5]=>14
[4,3,2,5,1,6]=>35
[4,3,2,5,6,1]=>26
[4,3,2,6,1,5]=>35
[4,3,2,6,5,1]=>19
[4,3,5,1,2,6]=>35
[4,3,5,1,6,2]=>61
[4,3,5,2,1,6]=>40
[4,3,5,2,6,1]=>61
[4,3,5,6,1,2]=>40
[4,3,5,6,2,1]=>26
[4,3,6,1,2,5]=>35
[4,3,6,1,5,2]=>61
[4,3,6,2,1,5]=>40
[4,3,6,2,5,1]=>61
[4,3,6,5,1,2]=>40
[4,3,6,5,2,1]=>14
[4,5,1,2,3,6]=>14
[4,5,1,2,6,3]=>40
[4,5,1,3,2,6]=>61
[4,5,1,3,6,2]=>40
[4,5,1,6,2,3]=>61
[4,5,1,6,3,2]=>35
[4,5,2,1,3,6]=>26
[4,5,2,1,6,3]=>40
[4,5,2,3,1,6]=>61
[4,5,2,3,6,1]=>40
[4,5,2,6,1,3]=>61
[4,5,2,6,3,1]=>35
[4,5,3,1,2,6]=>26
[4,5,3,1,6,2]=>40
[4,5,3,2,1,6]=>19
[4,5,3,2,6,1]=>40
[4,5,3,6,1,2]=>61
[4,5,3,6,2,1]=>35
[4,5,6,1,2,3]=>19
[4,5,6,1,3,2]=>35
[4,5,6,2,1,3]=>26
[4,5,6,2,3,1]=>35
[4,5,6,3,1,2]=>26
[4,5,6,3,2,1]=>10
[4,6,1,2,3,5]=>14
[4,6,1,2,5,3]=>40
[4,6,1,3,2,5]=>61
[4,6,1,3,5,2]=>40
[4,6,1,5,2,3]=>61
[4,6,1,5,3,2]=>35
[4,6,2,1,3,5]=>26
[4,6,2,1,5,3]=>40
[4,6,2,3,1,5]=>61
[4,6,2,3,5,1]=>40
[4,6,2,5,1,3]=>61
[4,6,2,5,3,1]=>35
[4,6,3,1,2,5]=>26
[4,6,3,1,5,2]=>40
[4,6,3,2,1,5]=>19
[4,6,3,2,5,1]=>40
[4,6,3,5,1,2]=>61
[4,6,3,5,2,1]=>35
[4,6,5,1,2,3]=>26
[4,6,5,1,3,2]=>40
[4,6,5,2,1,3]=>19
[4,6,5,2,3,1]=>40
[4,6,5,3,1,2]=>19
[4,6,5,3,2,1]=>5
[5,1,2,3,4,6]=>5
[5,1,2,3,6,4]=>19
[5,1,2,4,3,6]=>40
[5,1,2,4,6,3]=>19
[5,1,2,6,3,4]=>40
[5,1,2,6,4,3]=>26
[5,1,3,2,4,6]=>35
[5,1,3,2,6,4]=>61
[5,1,3,4,2,6]=>40
[5,1,3,4,6,2]=>19
[5,1,3,6,2,4]=>40
[5,1,3,6,4,2]=>26
[5,1,4,2,3,6]=>35
[5,1,4,2,6,3]=>61
[5,1,4,3,2,6]=>40
[5,1,4,3,6,2]=>61
[5,1,4,6,2,3]=>40
[5,1,4,6,3,2]=>26
[5,1,6,2,3,4]=>35
[5,1,6,2,4,3]=>61
[5,1,6,3,2,4]=>40
[5,1,6,3,4,2]=>61
[5,1,6,4,2,3]=>40
[5,1,6,4,3,2]=>14
[5,2,1,3,4,6]=>10
[5,2,1,3,6,4]=>26
[5,2,1,4,3,6]=>35
[5,2,1,4,6,3]=>26
[5,2,1,6,3,4]=>35
[5,2,1,6,4,3]=>19
[5,2,3,1,4,6]=>35
[5,2,3,1,6,4]=>61
[5,2,3,4,1,6]=>40
[5,2,3,4,6,1]=>19
[5,2,3,6,1,4]=>40
[5,2,3,6,4,1]=>26
[5,2,4,1,3,6]=>35
[5,2,4,1,6,3]=>61
[5,2,4,3,1,6]=>40
[5,2,4,3,6,1]=>61
[5,2,4,6,1,3]=>40
[5,2,4,6,3,1]=>26
[5,2,6,1,3,4]=>35
[5,2,6,1,4,3]=>61
[5,2,6,3,1,4]=>40
[5,2,6,3,4,1]=>61
[5,2,6,4,1,3]=>40
[5,2,6,4,3,1]=>14
[5,3,1,2,4,6]=>10
[5,3,1,2,6,4]=>26
[5,3,1,4,2,6]=>35
[5,3,1,4,6,2]=>26
[5,3,1,6,2,4]=>35
[5,3,1,6,4,2]=>19
[5,3,2,1,4,6]=>10
[5,3,2,1,6,4]=>14
[5,3,2,4,1,6]=>35
[5,3,2,4,6,1]=>26
[5,3,2,6,1,4]=>35
[5,3,2,6,4,1]=>19
[5,3,4,1,2,6]=>35
[5,3,4,1,6,2]=>61
[5,3,4,2,1,6]=>40
[5,3,4,2,6,1]=>61
[5,3,4,6,1,2]=>40
[5,3,4,6,2,1]=>26
[5,3,6,1,2,4]=>35
[5,3,6,1,4,2]=>61
[5,3,6,2,1,4]=>40
[5,3,6,2,4,1]=>61
[5,3,6,4,1,2]=>40
[5,3,6,4,2,1]=>14
[5,4,1,2,3,6]=>10
[5,4,1,2,6,3]=>26
[5,4,1,3,2,6]=>35
[5,4,1,3,6,2]=>26
[5,4,1,6,2,3]=>35
[5,4,1,6,3,2]=>19
[5,4,2,1,3,6]=>10
[5,4,2,1,6,3]=>14
[5,4,2,3,1,6]=>35
[5,4,2,3,6,1]=>26
[5,4,2,6,1,3]=>35
[5,4,2,6,3,1]=>19
[5,4,3,1,2,6]=>10
[5,4,3,1,6,2]=>14
[5,4,3,2,1,6]=>5
[5,4,3,2,6,1]=>14
[5,4,3,6,1,2]=>35
[5,4,3,6,2,1]=>19
[5,4,6,1,2,3]=>35
[5,4,6,1,3,2]=>61
[5,4,6,2,1,3]=>40
[5,4,6,2,3,1]=>61
[5,4,6,3,1,2]=>40
[5,4,6,3,2,1]=>14
[5,6,1,2,3,4]=>14
[5,6,1,2,4,3]=>40
[5,6,1,3,2,4]=>61
[5,6,1,3,4,2]=>40
[5,6,1,4,2,3]=>61
[5,6,1,4,3,2]=>35
[5,6,2,1,3,4]=>26
[5,6,2,1,4,3]=>40
[5,6,2,3,1,4]=>61
[5,6,2,3,4,1]=>40
[5,6,2,4,1,3]=>61
[5,6,2,4,3,1]=>35
[5,6,3,1,2,4]=>26
[5,6,3,1,4,2]=>40
[5,6,3,2,1,4]=>19
[5,6,3,2,4,1]=>40
[5,6,3,4,1,2]=>61
[5,6,3,4,2,1]=>35
[5,6,4,1,2,3]=>26
[5,6,4,1,3,2]=>40
[5,6,4,2,1,3]=>19
[5,6,4,2,3,1]=>40
[5,6,4,3,1,2]=>19
[5,6,4,3,2,1]=>5
[6,1,2,3,4,5]=>5
[6,1,2,3,5,4]=>19
[6,1,2,4,3,5]=>40
[6,1,2,4,5,3]=>19
[6,1,2,5,3,4]=>40
[6,1,2,5,4,3]=>26
[6,1,3,2,4,5]=>35
[6,1,3,2,5,4]=>61
[6,1,3,4,2,5]=>40
[6,1,3,4,5,2]=>19
[6,1,3,5,2,4]=>40
[6,1,3,5,4,2]=>26
[6,1,4,2,3,5]=>35
[6,1,4,2,5,3]=>61
[6,1,4,3,2,5]=>40
[6,1,4,3,5,2]=>61
[6,1,4,5,2,3]=>40
[6,1,4,5,3,2]=>26
[6,1,5,2,3,4]=>35
[6,1,5,2,4,3]=>61
[6,1,5,3,2,4]=>40
[6,1,5,3,4,2]=>61
[6,1,5,4,2,3]=>40
[6,1,5,4,3,2]=>14
[6,2,1,3,4,5]=>10
[6,2,1,3,5,4]=>26
[6,2,1,4,3,5]=>35
[6,2,1,4,5,3]=>26
[6,2,1,5,3,4]=>35
[6,2,1,5,4,3]=>19
[6,2,3,1,4,5]=>35
[6,2,3,1,5,4]=>61
[6,2,3,4,1,5]=>40
[6,2,3,4,5,1]=>19
[6,2,3,5,1,4]=>40
[6,2,3,5,4,1]=>26
[6,2,4,1,3,5]=>35
[6,2,4,1,5,3]=>61
[6,2,4,3,1,5]=>40
[6,2,4,3,5,1]=>61
[6,2,4,5,1,3]=>40
[6,2,4,5,3,1]=>26
[6,2,5,1,3,4]=>35
[6,2,5,1,4,3]=>61
[6,2,5,3,1,4]=>40
[6,2,5,3,4,1]=>61
[6,2,5,4,1,3]=>40
[6,2,5,4,3,1]=>14
[6,3,1,2,4,5]=>10
[6,3,1,2,5,4]=>26
[6,3,1,4,2,5]=>35
[6,3,1,4,5,2]=>26
[6,3,1,5,2,4]=>35
[6,3,1,5,4,2]=>19
[6,3,2,1,4,5]=>10
[6,3,2,1,5,4]=>14
[6,3,2,4,1,5]=>35
[6,3,2,4,5,1]=>26
[6,3,2,5,1,4]=>35
[6,3,2,5,4,1]=>19
[6,3,4,1,2,5]=>35
[6,3,4,1,5,2]=>61
[6,3,4,2,1,5]=>40
[6,3,4,2,5,1]=>61
[6,3,4,5,1,2]=>40
[6,3,4,5,2,1]=>26
[6,3,5,1,2,4]=>35
[6,3,5,1,4,2]=>61
[6,3,5,2,1,4]=>40
[6,3,5,2,4,1]=>61
[6,3,5,4,1,2]=>40
[6,3,5,4,2,1]=>14
[6,4,1,2,3,5]=>10
[6,4,1,2,5,3]=>26
[6,4,1,3,2,5]=>35
[6,4,1,3,5,2]=>26
[6,4,1,5,2,3]=>35
[6,4,1,5,3,2]=>19
[6,4,2,1,3,5]=>10
[6,4,2,1,5,3]=>14
[6,4,2,3,1,5]=>35
[6,4,2,3,5,1]=>26
[6,4,2,5,1,3]=>35
[6,4,2,5,3,1]=>19
[6,4,3,1,2,5]=>10
[6,4,3,1,5,2]=>14
[6,4,3,2,1,5]=>5
[6,4,3,2,5,1]=>14
[6,4,3,5,1,2]=>35
[6,4,3,5,2,1]=>19
[6,4,5,1,2,3]=>35
[6,4,5,1,3,2]=>61
[6,4,5,2,1,3]=>40
[6,4,5,2,3,1]=>61
[6,4,5,3,1,2]=>40
[6,4,5,3,2,1]=>14
[6,5,1,2,3,4]=>10
[6,5,1,2,4,3]=>26
[6,5,1,3,2,4]=>35
[6,5,1,3,4,2]=>26
[6,5,1,4,2,3]=>35
[6,5,1,4,3,2]=>19
[6,5,2,1,3,4]=>10
[6,5,2,1,4,3]=>14
[6,5,2,3,1,4]=>35
[6,5,2,3,4,1]=>26
[6,5,2,4,1,3]=>35
[6,5,2,4,3,1]=>19
[6,5,3,1,2,4]=>10
[6,5,3,1,4,2]=>14
[6,5,3,2,1,4]=>5
[6,5,3,2,4,1]=>14
[6,5,3,4,1,2]=>35
[6,5,3,4,2,1]=>19
[6,5,4,1,2,3]=>10
[6,5,4,1,3,2]=>14
[6,5,4,2,1,3]=>5
[6,5,4,2,3,1]=>14
[6,5,4,3,1,2]=>5
[6,5,4,3,2,1]=>1
[1,2,3,4,5,6,7]=>1
[1,2,3,4,5,7,6]=>6
[1,2,3,4,6,5,7]=>20
[1,2,3,4,6,7,5]=>6
[1,2,3,4,7,5,6]=>20
[1,2,3,4,7,6,5]=>15
[1,2,3,5,4,6,7]=>34
[1,2,3,5,4,7,6]=>64
[1,2,3,5,6,4,7]=>20
[1,2,3,5,6,7,4]=>6
[1,2,3,5,7,4,6]=>20
[1,2,3,5,7,6,4]=>15
[1,2,3,6,4,5,7]=>34
[1,2,3,6,4,7,5]=>64
[1,2,3,6,5,4,7]=>50
[1,2,3,6,5,7,4]=>64
[1,2,3,6,7,4,5]=>20
[1,2,3,6,7,5,4]=>15
[1,2,3,7,4,5,6]=>34
[1,2,3,7,4,6,5]=>64
[1,2,3,7,5,4,6]=>50
[1,2,3,7,5,6,4]=>64
[1,2,3,7,6,4,5]=>50
[1,2,3,7,6,5,4]=>20
[1,2,4,3,5,6,7]=>34
[1,2,4,3,5,7,6]=>99
[1,2,4,3,6,5,7]=>155
[1,2,4,3,6,7,5]=>99
[1,2,4,3,7,5,6]=>155
[1,2,4,3,7,6,5]=>90
[1,2,4,5,3,6,7]=>34
[1,2,4,5,3,7,6]=>64
[1,2,4,5,6,3,7]=>20
[1,2,4,5,6,7,3]=>6
[1,2,4,5,7,3,6]=>20
[1,2,4,5,7,6,3]=>15
[1,2,4,6,3,5,7]=>34
[1,2,4,6,3,7,5]=>64
[1,2,4,6,5,3,7]=>50
[1,2,4,6,5,7,3]=>64
[1,2,4,6,7,3,5]=>20
[1,2,4,6,7,5,3]=>15
[1,2,4,7,3,5,6]=>34
[1,2,4,7,3,6,5]=>64
[1,2,4,7,5,3,6]=>50
[1,2,4,7,5,6,3]=>64
[1,2,4,7,6,3,5]=>50
[1,2,4,7,6,5,3]=>20
[1,2,5,3,4,6,7]=>34
[1,2,5,3,4,7,6]=>99
[1,2,5,3,6,4,7]=>155
[1,2,5,3,6,7,4]=>99
[1,2,5,3,7,4,6]=>155
[1,2,5,3,7,6,4]=>90
[1,2,5,4,3,6,7]=>71
[1,2,5,4,3,7,6]=>111
[1,2,5,4,6,3,7]=>155
[1,2,5,4,6,7,3]=>99
[1,2,5,4,7,3,6]=>155
[1,2,5,4,7,6,3]=>90
[1,2,5,6,3,4,7]=>34
[1,2,5,6,3,7,4]=>64
[1,2,5,6,4,3,7]=>50
[1,2,5,6,4,7,3]=>64
[1,2,5,6,7,3,4]=>20
[1,2,5,6,7,4,3]=>15
[1,2,5,7,3,4,6]=>34
[1,2,5,7,3,6,4]=>64
[1,2,5,7,4,3,6]=>50
[1,2,5,7,4,6,3]=>64
[1,2,5,7,6,3,4]=>50
[1,2,5,7,6,4,3]=>20
[1,2,6,3,4,5,7]=>34
[1,2,6,3,4,7,5]=>99
[1,2,6,3,5,4,7]=>155
[1,2,6,3,5,7,4]=>99
[1,2,6,3,7,4,5]=>155
[1,2,6,3,7,5,4]=>90
[1,2,6,4,3,5,7]=>71
[1,2,6,4,3,7,5]=>111
[1,2,6,4,5,3,7]=>155
[1,2,6,4,5,7,3]=>99
[1,2,6,4,7,3,5]=>155
[1,2,6,4,7,5,3]=>90
[1,2,6,5,3,4,7]=>71
[1,2,6,5,3,7,4]=>111
[1,2,6,5,4,3,7]=>55
[1,2,6,5,4,7,3]=>111
[1,2,6,5,7,3,4]=>155
[1,2,6,5,7,4,3]=>90
[1,2,6,7,3,4,5]=>34
[1,2,6,7,3,5,4]=>64
[1,2,6,7,4,3,5]=>50
[1,2,6,7,4,5,3]=>64
[1,2,6,7,5,3,4]=>50
[1,2,6,7,5,4,3]=>20
[1,2,7,3,4,5,6]=>34
[1,2,7,3,4,6,5]=>99
[1,2,7,3,5,4,6]=>155
[1,2,7,3,5,6,4]=>99
[1,2,7,3,6,4,5]=>155
[1,2,7,3,6,5,4]=>90
[1,2,7,4,3,5,6]=>71
[1,2,7,4,3,6,5]=>111
[1,2,7,4,5,3,6]=>155
[1,2,7,4,5,6,3]=>99
[1,2,7,4,6,3,5]=>155
[1,2,7,4,6,5,3]=>90
[1,2,7,5,3,4,6]=>71
[1,2,7,5,3,6,4]=>111
[1,2,7,5,4,3,6]=>55
[1,2,7,5,4,6,3]=>111
[1,2,7,5,6,3,4]=>155
[1,2,7,5,6,4,3]=>90
[1,2,7,6,3,4,5]=>71
[1,2,7,6,3,5,4]=>111
[1,2,7,6,4,3,5]=>55
[1,2,7,6,4,5,3]=>111
[1,2,7,6,5,3,4]=>55
[1,2,7,6,5,4,3]=>15
[1,3,2,4,5,6,7]=>20
[1,3,2,4,5,7,6]=>78
[1,3,2,4,6,5,7]=>169
[1,3,2,4,6,7,5]=>78
[1,3,2,4,7,5,6]=>169
[1,3,2,4,7,6,5]=>111
[1,3,2,5,4,6,7]=>155
[1,3,2,5,4,7,6]=>272
[1,3,2,5,6,4,7]=>169
[1,3,2,5,6,7,4]=>78
[1,3,2,5,7,4,6]=>169
[1,3,2,5,7,6,4]=>111
[1,3,2,6,4,5,7]=>155
[1,3,2,6,4,7,5]=>272
[1,3,2,6,5,4,7]=>181
[1,3,2,6,5,7,4]=>272
[1,3,2,6,7,4,5]=>169
[1,3,2,6,7,5,4]=>111
[1,3,2,7,4,5,6]=>155
[1,3,2,7,4,6,5]=>272
[1,3,2,7,5,4,6]=>181
[1,3,2,7,5,6,4]=>272
[1,3,2,7,6,4,5]=>181
[1,3,2,7,6,5,4]=>64
[1,3,4,2,5,6,7]=>34
[1,3,4,2,5,7,6]=>99
[1,3,4,2,6,5,7]=>155
[1,3,4,2,6,7,5]=>99
[1,3,4,2,7,5,6]=>155
[1,3,4,2,7,6,5]=>90
[1,3,4,5,2,6,7]=>34
[1,3,4,5,2,7,6]=>64
[1,3,4,5,6,2,7]=>20
[1,3,4,5,6,7,2]=>6
[1,3,4,5,7,2,6]=>20
[1,3,4,5,7,6,2]=>15
[1,3,4,6,2,5,7]=>34
[1,3,4,6,2,7,5]=>64
[1,3,4,6,5,2,7]=>50
[1,3,4,6,5,7,2]=>64
[1,3,4,6,7,2,5]=>20
[1,3,4,6,7,5,2]=>15
[1,3,4,7,2,5,6]=>34
[1,3,4,7,2,6,5]=>64
[1,3,4,7,5,2,6]=>50
[1,3,4,7,5,6,2]=>64
[1,3,4,7,6,2,5]=>50
[1,3,4,7,6,5,2]=>20
[1,3,5,2,4,6,7]=>34
[1,3,5,2,4,7,6]=>99
[1,3,5,2,6,4,7]=>155
[1,3,5,2,6,7,4]=>99
[1,3,5,2,7,4,6]=>155
[1,3,5,2,7,6,4]=>90
[1,3,5,4,2,6,7]=>71
[1,3,5,4,2,7,6]=>111
[1,3,5,4,6,2,7]=>155
[1,3,5,4,6,7,2]=>99
[1,3,5,4,7,2,6]=>155
[1,3,5,4,7,6,2]=>90
[1,3,5,6,2,4,7]=>34
[1,3,5,6,2,7,4]=>64
[1,3,5,6,4,2,7]=>50
[1,3,5,6,4,7,2]=>64
[1,3,5,6,7,2,4]=>20
[1,3,5,6,7,4,2]=>15
[1,3,5,7,2,4,6]=>34
[1,3,5,7,2,6,4]=>64
[1,3,5,7,4,2,6]=>50
[1,3,5,7,4,6,2]=>64
[1,3,5,7,6,2,4]=>50
[1,3,5,7,6,4,2]=>20
[1,3,6,2,4,5,7]=>34
[1,3,6,2,4,7,5]=>99
[1,3,6,2,5,4,7]=>155
[1,3,6,2,5,7,4]=>99
[1,3,6,2,7,4,5]=>155
[1,3,6,2,7,5,4]=>90
[1,3,6,4,2,5,7]=>71
[1,3,6,4,2,7,5]=>111
[1,3,6,4,5,2,7]=>155
[1,3,6,4,5,7,2]=>99
[1,3,6,4,7,2,5]=>155
[1,3,6,4,7,5,2]=>90
[1,3,6,5,2,4,7]=>71
[1,3,6,5,2,7,4]=>111
[1,3,6,5,4,2,7]=>55
[1,3,6,5,4,7,2]=>111
[1,3,6,5,7,2,4]=>155
[1,3,6,5,7,4,2]=>90
[1,3,6,7,2,4,5]=>34
[1,3,6,7,2,5,4]=>64
[1,3,6,7,4,2,5]=>50
[1,3,6,7,4,5,2]=>64
[1,3,6,7,5,2,4]=>50
[1,3,6,7,5,4,2]=>20
[1,3,7,2,4,5,6]=>34
[1,3,7,2,4,6,5]=>99
[1,3,7,2,5,4,6]=>155
[1,3,7,2,5,6,4]=>99
[1,3,7,2,6,4,5]=>155
[1,3,7,2,6,5,4]=>90
[1,3,7,4,2,5,6]=>71
[1,3,7,4,2,6,5]=>111
[1,3,7,4,5,2,6]=>155
[1,3,7,4,5,6,2]=>99
[1,3,7,4,6,2,5]=>155
[1,3,7,4,6,5,2]=>90
[1,3,7,5,2,4,6]=>71
[1,3,7,5,2,6,4]=>111
[1,3,7,5,4,2,6]=>55
[1,3,7,5,4,6,2]=>111
[1,3,7,5,6,2,4]=>155
[1,3,7,5,6,4,2]=>90
[1,3,7,6,2,4,5]=>71
[1,3,7,6,2,5,4]=>111
[1,3,7,6,4,2,5]=>55
[1,3,7,6,4,5,2]=>111
[1,3,7,6,5,2,4]=>55
[1,3,7,6,5,4,2]=>15
[1,4,2,3,5,6,7]=>20
[1,4,2,3,5,7,6]=>78
[1,4,2,3,6,5,7]=>169
[1,4,2,3,6,7,5]=>78
[1,4,2,3,7,5,6]=>169
[1,4,2,3,7,6,5]=>111
[1,4,2,5,3,6,7]=>155
[1,4,2,5,3,7,6]=>272
[1,4,2,5,6,3,7]=>169
[1,4,2,5,6,7,3]=>78
[1,4,2,5,7,3,6]=>169
[1,4,2,5,7,6,3]=>111
[1,4,2,6,3,5,7]=>155
[1,4,2,6,3,7,5]=>272
[1,4,2,6,5,3,7]=>181
[1,4,2,6,5,7,3]=>272
[1,4,2,6,7,3,5]=>169
[1,4,2,6,7,5,3]=>111
[1,4,2,7,3,5,6]=>155
[1,4,2,7,3,6,5]=>272
[1,4,2,7,5,3,6]=>181
[1,4,2,7,5,6,3]=>272
[1,4,2,7,6,3,5]=>181
[1,4,2,7,6,5,3]=>64
[1,4,3,2,5,6,7]=>50
[1,4,3,2,5,7,6]=>132
[1,4,3,2,6,5,7]=>181
[1,4,3,2,6,7,5]=>132
[1,4,3,2,7,5,6]=>181
[1,4,3,2,7,6,5]=>99
[1,4,3,5,2,6,7]=>155
[1,4,3,5,2,7,6]=>272
[1,4,3,5,6,2,7]=>169
[1,4,3,5,6,7,2]=>78
[1,4,3,5,7,2,6]=>169
[1,4,3,5,7,6,2]=>111
[1,4,3,6,2,5,7]=>155
[1,4,3,6,2,7,5]=>272
[1,4,3,6,5,2,7]=>181
[1,4,3,6,5,7,2]=>272
[1,4,3,6,7,2,5]=>169
[1,4,3,6,7,5,2]=>111
[1,4,3,7,2,5,6]=>155
[1,4,3,7,2,6,5]=>272
[1,4,3,7,5,2,6]=>181
[1,4,3,7,5,6,2]=>272
[1,4,3,7,6,2,5]=>181
[1,4,3,7,6,5,2]=>64
[1,4,5,2,3,6,7]=>34
[1,4,5,2,3,7,6]=>99
[1,4,5,2,6,3,7]=>155
[1,4,5,2,6,7,3]=>99
[1,4,5,2,7,3,6]=>155
[1,4,5,2,7,6,3]=>90
[1,4,5,3,2,6,7]=>71
[1,4,5,3,2,7,6]=>111
[1,4,5,3,6,2,7]=>155
[1,4,5,3,6,7,2]=>99
[1,4,5,3,7,2,6]=>155
[1,4,5,3,7,6,2]=>90
[1,4,5,6,2,3,7]=>34
[1,4,5,6,2,7,3]=>64
[1,4,5,6,3,2,7]=>50
[1,4,5,6,3,7,2]=>64
[1,4,5,6,7,2,3]=>20
[1,4,5,6,7,3,2]=>15
[1,4,5,7,2,3,6]=>34
[1,4,5,7,2,6,3]=>64
[1,4,5,7,3,2,6]=>50
[1,4,5,7,3,6,2]=>64
[1,4,5,7,6,2,3]=>50
[1,4,5,7,6,3,2]=>20
[1,4,6,2,3,5,7]=>34
[1,4,6,2,3,7,5]=>99
[1,4,6,2,5,3,7]=>155
[1,4,6,2,5,7,3]=>99
[1,4,6,2,7,3,5]=>155
[1,4,6,2,7,5,3]=>90
[1,4,6,3,2,5,7]=>71
[1,4,6,3,2,7,5]=>111
[1,4,6,3,5,2,7]=>155
[1,4,6,3,5,7,2]=>99
[1,4,6,3,7,2,5]=>155
[1,4,6,3,7,5,2]=>90
[1,4,6,5,2,3,7]=>71
[1,4,6,5,2,7,3]=>111
[1,4,6,5,3,2,7]=>55
[1,4,6,5,3,7,2]=>111
                    

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Description

The number of permutations with the same descent word as the given permutation.
The descent word of a permutation is the binary word given by Mp00109descent word. For a given permutation, this statistic is the number of permutations with the same descent word, so the number of elements in the fiber of the map Mp00109descent word containing a given permutation.
This statistic appears as up-down analysis in statistical applications in genetics, see [1] and the references therein.

References

[1] Morton, J., Pachter, L., Shiu, A., Sturmfels, B., Wienand, O. Convex rank tests and semigraphoids MathSciNet:2538642

Code

from collections import defaultdict

def word(pi):
    w = [0]*(len(pi)-1)
    for i in pi.descents(from_zero=True):
        w[i] = 1
    return Words([0,1])(w)

@cached_function
def preimages(n):
    D = defaultdict(int)
    for pi in Permutations(n):
        D[word(pi)] += 1
    return D


def statistic(pi):
    return preimages(len(pi))[word(pi)]

Created

Jun 10, 2016 at 08:54 by Christian Stump

Updated

Jan 15, 2018 at 08:00 by Martin Rubey