- FindStat

edit this statistic or download as text // json

Identifier

St001735: Permutations ⟶ ℤ

Values

=>
                            
                            
                            
                            

                        [1]=>1
[1,2]=>1
[2,1]=>1
[1,2,3]=>1
[1,3,2]=>2
[2,1,3]=>2
[2,3,1]=>1
[3,1,2]=>1
[3,2,1]=>1
[1,2,3,4]=>1
[1,2,4,3]=>2
[1,3,2,4]=>2
[1,3,4,2]=>2
[1,4,2,3]=>2
[1,4,3,2]=>4
[2,1,3,4]=>2
[2,1,4,3]=>4
[2,3,1,4]=>2
[2,3,4,1]=>1
[2,4,1,3]=>2
[2,4,3,1]=>2
[3,1,2,4]=>2
[3,1,4,2]=>4
[3,2,1,4]=>4
[3,2,4,1]=>2
[3,4,1,2]=>1
[3,4,2,1]=>1
[4,1,2,3]=>1
[4,1,3,2]=>2
[4,2,1,3]=>2
[4,2,3,1]=>1
[4,3,1,2]=>1
[4,3,2,1]=>1
[1,2,3,4,5]=>1
[1,2,3,5,4]=>2
[1,2,4,3,5]=>2
[1,2,4,5,3]=>2
[1,2,5,3,4]=>2
[1,2,5,4,3]=>4
[1,3,2,4,5]=>2
[1,3,2,5,4]=>4
[1,3,4,2,5]=>2
[1,3,4,5,2]=>2
[1,3,5,2,4]=>2
[1,3,5,4,2]=>4
[1,4,2,3,5]=>2
[1,4,2,5,3]=>6
[1,4,3,2,5]=>6
[1,4,3,5,2]=>4
[1,4,5,2,3]=>2
[1,4,5,3,2]=>4
[1,5,2,3,4]=>2
[1,5,2,4,3]=>6
[1,5,3,2,4]=>6
[1,5,3,4,2]=>4
[1,5,4,2,3]=>4
[1,5,4,3,2]=>8
[2,1,3,4,5]=>2
[2,1,3,5,4]=>4
[2,1,4,3,5]=>4
[2,1,4,5,3]=>4
[2,1,5,3,4]=>4
[2,1,5,4,3]=>8
[2,3,1,4,5]=>2
[2,3,1,5,4]=>4
[2,3,4,1,5]=>2
[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]=>6
[2,4,3,1,5]=>6
[2,4,3,5,1]=>2
[2,4,5,1,3]=>2
[2,4,5,3,1]=>2
[2,5,1,3,4]=>2
[2,5,1,4,3]=>6
[2,5,3,1,4]=>6
[2,5,3,4,1]=>2
[2,5,4,1,3]=>4
[2,5,4,3,1]=>4
[3,1,2,4,5]=>2
[3,1,2,5,4]=>4
[3,1,4,2,5]=>6
[3,1,4,5,2]=>4
[3,1,5,2,4]=>6
[3,1,5,4,2]=>8
[3,2,1,4,5]=>4
[3,2,1,5,4]=>8
[3,2,4,1,5]=>6
[3,2,4,5,1]=>2
[3,2,5,1,4]=>6
[3,2,5,4,1]=>4
[3,4,1,2,5]=>2
[3,4,1,5,2]=>4
[3,4,2,1,5]=>4
[3,4,2,5,1]=>2
[3,4,5,1,2]=>1
[3,4,5,2,1]=>1
[3,5,1,2,4]=>2
[3,5,1,4,2]=>4
[3,5,2,1,4]=>4
[3,5,2,4,1]=>2
[3,5,4,1,2]=>2
[3,5,4,2,1]=>2
[4,1,2,3,5]=>2
[4,1,2,5,3]=>4
[4,1,3,2,5]=>4
[4,1,3,5,2]=>4
[4,1,5,2,3]=>4
[4,1,5,3,2]=>8
[4,2,1,3,5]=>4
[4,2,1,5,3]=>8
[4,2,3,1,5]=>4
[4,2,3,5,1]=>2
[4,2,5,1,3]=>4
[4,2,5,3,1]=>4
[4,3,1,2,5]=>4
[4,3,1,5,2]=>8
[4,3,2,1,5]=>8
[4,3,2,5,1]=>4
[4,3,5,1,2]=>2
[4,3,5,2,1]=>2
[4,5,1,2,3]=>1
[4,5,1,3,2]=>2
[4,5,2,1,3]=>2
[4,5,2,3,1]=>1
[4,5,3,1,2]=>1
[4,5,3,2,1]=>1
[5,1,2,3,4]=>1
[5,1,2,4,3]=>2
[5,1,3,2,4]=>2
[5,1,3,4,2]=>2
[5,1,4,2,3]=>2
[5,1,4,3,2]=>4
[5,2,1,3,4]=>2
[5,2,1,4,3]=>4
[5,2,3,1,4]=>2
[5,2,3,4,1]=>1
[5,2,4,1,3]=>2
[5,2,4,3,1]=>2
[5,3,1,2,4]=>2
[5,3,1,4,2]=>4
[5,3,2,1,4]=>4
[5,3,2,4,1]=>2
[5,3,4,1,2]=>1
[5,3,4,2,1]=>1
[5,4,1,2,3]=>1
[5,4,1,3,2]=>2
[5,4,2,1,3]=>2
[5,4,2,3,1]=>1
[5,4,3,1,2]=>1
[5,4,3,2,1]=>1
[1,2,3,4,5,6]=>1
[1,2,3,4,6,5]=>2
[1,2,3,5,4,6]=>2
[1,2,3,5,6,4]=>2
[1,2,3,6,4,5]=>2
[1,2,3,6,5,4]=>4
[1,2,4,3,5,6]=>2
[1,2,4,3,6,5]=>4
[1,2,4,5,3,6]=>2
[1,2,4,5,6,3]=>2
[1,2,4,6,3,5]=>2
[1,2,4,6,5,3]=>4
[1,2,5,3,4,6]=>2
[1,2,5,3,6,4]=>6
[1,2,5,4,3,6]=>6
[1,2,5,4,6,3]=>4
[1,2,5,6,3,4]=>2
[1,2,5,6,4,3]=>4
[1,2,6,3,4,5]=>2
[1,2,6,3,5,4]=>6
[1,2,6,4,3,5]=>6
[1,2,6,4,5,3]=>4
[1,2,6,5,3,4]=>4
[1,2,6,5,4,3]=>8
[1,3,2,4,5,6]=>2
[1,3,2,4,6,5]=>4
[1,3,2,5,4,6]=>4
[1,3,2,5,6,4]=>4
[1,3,2,6,4,5]=>4
[1,3,2,6,5,4]=>8
[1,3,4,2,5,6]=>2
[1,3,4,2,6,5]=>4
[1,3,4,5,2,6]=>2
[1,3,4,5,6,2]=>2
[1,3,4,6,2,5]=>2
[1,3,4,6,5,2]=>4
[1,3,5,2,4,6]=>2
[1,3,5,2,6,4]=>6
[1,3,5,4,2,6]=>6
[1,3,5,4,6,2]=>4
[1,3,5,6,2,4]=>2
[1,3,5,6,4,2]=>4
[1,3,6,2,4,5]=>2
[1,3,6,2,5,4]=>6
[1,3,6,4,2,5]=>6
[1,3,6,4,5,2]=>4
[1,3,6,5,2,4]=>4
[1,3,6,5,4,2]=>8
[1,4,2,3,5,6]=>2
[1,4,2,3,6,5]=>4
[1,4,2,5,3,6]=>6
[1,4,2,5,6,3]=>6
[1,4,2,6,3,5]=>6
[1,4,2,6,5,3]=>12
[1,4,3,2,5,6]=>6
[1,4,3,2,6,5]=>12
[1,4,3,5,2,6]=>6
[1,4,3,5,6,2]=>4
[1,4,3,6,2,5]=>6
[1,4,3,6,5,2]=>8
[1,4,5,2,3,6]=>2
[1,4,5,2,6,3]=>6
[1,4,5,3,2,6]=>6
[1,4,5,3,6,2]=>4
[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]=>6
[1,4,6,3,2,5]=>6
[1,4,6,3,5,2]=>4
[1,4,6,5,2,3]=>4
[1,4,6,5,3,2]=>8
[1,5,2,3,4,6]=>2
[1,5,2,3,6,4]=>6
[1,5,2,4,3,6]=>6
[1,5,2,4,6,3]=>6
[1,5,2,6,3,4]=>6
[1,5,2,6,4,3]=>18
[1,5,3,2,4,6]=>6
[1,5,3,2,6,4]=>18
[1,5,3,4,2,6]=>6
[1,5,3,4,6,2]=>4
[1,5,3,6,2,4]=>6
[1,5,3,6,4,2]=>12
[1,5,4,2,3,6]=>6
[1,5,4,2,6,3]=>18
[1,5,4,3,2,6]=>18
[1,5,4,3,6,2]=>12
[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]=>6
[1,5,6,3,2,4]=>6
[1,5,6,3,4,2]=>4
[1,5,6,4,2,3]=>4
[1,5,6,4,3,2]=>8
[1,6,2,3,4,5]=>2
[1,6,2,3,5,4]=>6
[1,6,2,4,3,5]=>6
[1,6,2,4,5,3]=>6
[1,6,2,5,3,4]=>6
[1,6,2,5,4,3]=>18
[1,6,3,2,4,5]=>6
[1,6,3,2,5,4]=>18
[1,6,3,4,2,5]=>6
[1,6,3,4,5,2]=>4
[1,6,3,5,2,4]=>6
[1,6,3,5,4,2]=>12
[1,6,4,2,3,5]=>6
[1,6,4,2,5,3]=>18
[1,6,4,3,2,5]=>18
[1,6,4,3,5,2]=>12
[1,6,4,5,2,3]=>4
[1,6,4,5,3,2]=>8
[1,6,5,2,3,4]=>4
[1,6,5,2,4,3]=>12
[1,6,5,3,2,4]=>12
[1,6,5,3,4,2]=>8
[1,6,5,4,2,3]=>8
[1,6,5,4,3,2]=>16
[2,1,3,4,5,6]=>2
[2,1,3,4,6,5]=>4
[2,1,3,5,4,6]=>4
[2,1,3,5,6,4]=>4
[2,1,3,6,4,5]=>4
[2,1,3,6,5,4]=>8
[2,1,4,3,5,6]=>4
[2,1,4,3,6,5]=>8
[2,1,4,5,3,6]=>4
[2,1,4,5,6,3]=>4
[2,1,4,6,3,5]=>4
[2,1,4,6,5,3]=>8
[2,1,5,3,4,6]=>4
[2,1,5,3,6,4]=>12
[2,1,5,4,3,6]=>12
[2,1,5,4,6,3]=>8
[2,1,5,6,3,4]=>4
[2,1,5,6,4,3]=>8
[2,1,6,3,4,5]=>4
[2,1,6,3,5,4]=>12
[2,1,6,4,3,5]=>12
[2,1,6,4,5,3]=>8
[2,1,6,5,3,4]=>8
[2,1,6,5,4,3]=>16
[2,3,1,4,5,6]=>2
[2,3,1,4,6,5]=>4
[2,3,1,5,4,6]=>4
[2,3,1,5,6,4]=>4
[2,3,1,6,4,5]=>4
[2,3,1,6,5,4]=>8
[2,3,4,1,5,6]=>2
[2,3,4,1,6,5]=>4
[2,3,4,5,1,6]=>2
[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]=>6
[2,3,5,4,1,6]=>6
[2,3,5,4,6,1]=>2
[2,3,5,6,1,4]=>2
[2,3,5,6,4,1]=>2
[2,3,6,1,4,5]=>2
[2,3,6,1,5,4]=>6
[2,3,6,4,1,5]=>6
[2,3,6,4,5,1]=>2
[2,3,6,5,1,4]=>4
[2,3,6,5,4,1]=>4
[2,4,1,3,5,6]=>2
[2,4,1,3,6,5]=>4
[2,4,1,5,3,6]=>6
[2,4,1,5,6,3]=>6
[2,4,1,6,3,5]=>6
[2,4,1,6,5,3]=>12
[2,4,3,1,5,6]=>6
[2,4,3,1,6,5]=>12
[2,4,3,5,1,6]=>6
[2,4,3,5,6,1]=>2
[2,4,3,6,1,5]=>6
[2,4,3,6,5,1]=>4
[2,4,5,1,3,6]=>2
[2,4,5,1,6,3]=>6
[2,4,5,3,1,6]=>6
[2,4,5,3,6,1]=>2
[2,4,5,6,1,3]=>2
[2,4,5,6,3,1]=>2
[2,4,6,1,3,5]=>2
[2,4,6,1,5,3]=>6
[2,4,6,3,1,5]=>6
[2,4,6,3,5,1]=>2
[2,4,6,5,1,3]=>4
[2,4,6,5,3,1]=>4
[2,5,1,3,4,6]=>2
[2,5,1,3,6,4]=>6
[2,5,1,4,3,6]=>6
[2,5,1,4,6,3]=>6
[2,5,1,6,3,4]=>6
[2,5,1,6,4,3]=>18
[2,5,3,1,4,6]=>6
[2,5,3,1,6,4]=>18
[2,5,3,4,1,6]=>6
[2,5,3,4,6,1]=>2
[2,5,3,6,1,4]=>6
[2,5,3,6,4,1]=>6
[2,5,4,1,3,6]=>6
[2,5,4,1,6,3]=>18
[2,5,4,3,1,6]=>18
[2,5,4,3,6,1]=>6
[2,5,4,6,1,3]=>4
[2,5,4,6,3,1]=>4
[2,5,6,1,3,4]=>2
[2,5,6,1,4,3]=>6
[2,5,6,3,1,4]=>6
[2,5,6,3,4,1]=>2
[2,5,6,4,1,3]=>4
[2,5,6,4,3,1]=>4
[2,6,1,3,4,5]=>2
[2,6,1,3,5,4]=>6
[2,6,1,4,3,5]=>6
[2,6,1,4,5,3]=>6
[2,6,1,5,3,4]=>6
[2,6,1,5,4,3]=>18
[2,6,3,1,4,5]=>6
[2,6,3,1,5,4]=>18
[2,6,3,4,1,5]=>6
[2,6,3,4,5,1]=>2
[2,6,3,5,1,4]=>6
[2,6,3,5,4,1]=>6
[2,6,4,1,3,5]=>6
[2,6,4,1,5,3]=>18
[2,6,4,3,1,5]=>18
[2,6,4,3,5,1]=>6
[2,6,4,5,1,3]=>4
[2,6,4,5,3,1]=>4
[2,6,5,1,3,4]=>4
[2,6,5,1,4,3]=>12
[2,6,5,3,1,4]=>12
[2,6,5,3,4,1]=>4
[2,6,5,4,1,3]=>8
[2,6,5,4,3,1]=>8
[3,1,2,4,5,6]=>2
[3,1,2,4,6,5]=>4
[3,1,2,5,4,6]=>4
[3,1,2,5,6,4]=>4
[3,1,2,6,4,5]=>4
[3,1,2,6,5,4]=>8
[3,1,4,2,5,6]=>6
[3,1,4,2,6,5]=>12
[3,1,4,5,2,6]=>6
[3,1,4,5,6,2]=>4
[3,1,4,6,2,5]=>6
[3,1,4,6,5,2]=>8
[3,1,5,2,4,6]=>6
[3,1,5,2,6,4]=>18
[3,1,5,4,2,6]=>18
[3,1,5,4,6,2]=>8
[3,1,5,6,2,4]=>6
[3,1,5,6,4,2]=>8
[3,1,6,2,4,5]=>6
[3,1,6,2,5,4]=>18
[3,1,6,4,2,5]=>18
[3,1,6,4,5,2]=>8
[3,1,6,5,2,4]=>12
[3,1,6,5,4,2]=>16
[3,2,1,4,5,6]=>4
[3,2,1,4,6,5]=>8
[3,2,1,5,4,6]=>8
[3,2,1,5,6,4]=>8
[3,2,1,6,4,5]=>8
[3,2,1,6,5,4]=>16
[3,2,4,1,5,6]=>6
[3,2,4,1,6,5]=>12
[3,2,4,5,1,6]=>6
[3,2,4,5,6,1]=>2
[3,2,4,6,1,5]=>6
[3,2,4,6,5,1]=>4
[3,2,5,1,4,6]=>6
[3,2,5,1,6,4]=>18
[3,2,5,4,1,6]=>18
[3,2,5,4,6,1]=>4
[3,2,5,6,1,4]=>6
[3,2,5,6,4,1]=>4
[3,2,6,1,4,5]=>6
[3,2,6,1,5,4]=>18
[3,2,6,4,1,5]=>18
[3,2,6,4,5,1]=>4
[3,2,6,5,1,4]=>12
[3,2,6,5,4,1]=>8
[3,4,1,2,5,6]=>2
[3,4,1,2,6,5]=>4
[3,4,1,5,2,6]=>6
[3,4,1,5,6,2]=>4
[3,4,1,6,2,5]=>6
[3,4,1,6,5,2]=>8
[3,4,2,1,5,6]=>4
[3,4,2,1,6,5]=>8
[3,4,2,5,1,6]=>6
[3,4,2,5,6,1]=>2
[3,4,2,6,1,5]=>6
[3,4,2,6,5,1]=>4
[3,4,5,1,2,6]=>2
[3,4,5,1,6,2]=>4
[3,4,5,2,1,6]=>4
[3,4,5,2,6,1]=>2
[3,4,5,6,1,2]=>1
[3,4,5,6,2,1]=>1
[3,4,6,1,2,5]=>2
[3,4,6,1,5,2]=>4
[3,4,6,2,1,5]=>4
[3,4,6,2,5,1]=>2
[3,4,6,5,1,2]=>2
[3,4,6,5,2,1]=>2
[3,5,1,2,4,6]=>2
[3,5,1,2,6,4]=>6
[3,5,1,4,2,6]=>6
[3,5,1,4,6,2]=>4
[3,5,1,6,2,4]=>6
[3,5,1,6,4,2]=>12
[3,5,2,1,4,6]=>4
[3,5,2,1,6,4]=>12
[3,5,2,4,1,6]=>6
[3,5,2,4,6,1]=>2
[3,5,2,6,1,4]=>6
[3,5,2,6,4,1]=>6
[3,5,4,1,2,6]=>6
[3,5,4,1,6,2]=>12
[3,5,4,2,1,6]=>12
[3,5,4,2,6,1]=>6
[3,5,4,6,1,2]=>2
[3,5,4,6,2,1]=>2
[3,5,6,1,2,4]=>2
[3,5,6,1,4,2]=>4
[3,5,6,2,1,4]=>4
[3,5,6,2,4,1]=>2
[3,5,6,4,1,2]=>2
[3,5,6,4,2,1]=>2
[3,6,1,2,4,5]=>2
[3,6,1,2,5,4]=>6
[3,6,1,4,2,5]=>6
[3,6,1,4,5,2]=>4
[3,6,1,5,2,4]=>6
[3,6,1,5,4,2]=>12
[3,6,2,1,4,5]=>4
[3,6,2,1,5,4]=>12
[3,6,2,4,1,5]=>6
[3,6,2,4,5,1]=>2
[3,6,2,5,1,4]=>6
[3,6,2,5,4,1]=>6
[3,6,4,1,2,5]=>6
[3,6,4,1,5,2]=>12
[3,6,4,2,1,5]=>12
[3,6,4,2,5,1]=>6
[3,6,4,5,1,2]=>2
[3,6,4,5,2,1]=>2
[3,6,5,1,2,4]=>4
[3,6,5,1,4,2]=>8
[3,6,5,2,1,4]=>8
[3,6,5,2,4,1]=>4
[3,6,5,4,1,2]=>4
[3,6,5,4,2,1]=>4
[4,1,2,3,5,6]=>2
[4,1,2,3,6,5]=>4
[4,1,2,5,3,6]=>6
[4,1,2,5,6,3]=>4
[4,1,2,6,3,5]=>6
[4,1,2,6,5,3]=>8
[4,1,3,2,5,6]=>4
[4,1,3,2,6,5]=>8
[4,1,3,5,2,6]=>6
[4,1,3,5,6,2]=>4
[4,1,3,6,2,5]=>6
[4,1,3,6,5,2]=>8
[4,1,5,2,3,6]=>6
[4,1,5,2,6,3]=>18
[4,1,5,3,2,6]=>18
[4,1,5,3,6,2]=>12
[4,1,5,6,2,3]=>4
[4,1,5,6,3,2]=>8
[4,1,6,2,3,5]=>6
[4,1,6,2,5,3]=>18
[4,1,6,3,2,5]=>18
[4,1,6,3,5,2]=>12
[4,1,6,5,2,3]=>8
[4,1,6,5,3,2]=>16
[4,2,1,3,5,6]=>4
[4,2,1,3,6,5]=>8
[4,2,1,5,3,6]=>12
[4,2,1,5,6,3]=>8
[4,2,1,6,3,5]=>12
[4,2,1,6,5,3]=>16
[4,2,3,1,5,6]=>4
[4,2,3,1,6,5]=>8
[4,2,3,5,1,6]=>6
[4,2,3,5,6,1]=>2
[4,2,3,6,1,5]=>6
[4,2,3,6,5,1]=>4
[4,2,5,1,3,6]=>6
[4,2,5,1,6,3]=>18
[4,2,5,3,1,6]=>18
[4,2,5,3,6,1]=>6
[4,2,5,6,1,3]=>4
[4,2,5,6,3,1]=>4
[4,2,6,1,3,5]=>6
[4,2,6,1,5,3]=>18
[4,2,6,3,1,5]=>18
[4,2,6,3,5,1]=>6
[4,2,6,5,1,3]=>8
[4,2,6,5,3,1]=>8
[4,3,1,2,5,6]=>4
[4,3,1,2,6,5]=>8
[4,3,1,5,2,6]=>18
[4,3,1,5,6,2]=>8
[4,3,1,6,2,5]=>18
[4,3,1,6,5,2]=>16
[4,3,2,1,5,6]=>8
[4,3,2,1,6,5]=>16
[4,3,2,5,1,6]=>18
[4,3,2,5,6,1]=>4
[4,3,2,6,1,5]=>18
[4,3,2,6,5,1]=>8
[4,3,5,1,2,6]=>6
[4,3,5,1,6,2]=>12
[4,3,5,2,1,6]=>12
[4,3,5,2,6,1]=>6
[4,3,5,6,1,2]=>2
[4,3,5,6,2,1]=>2
[4,3,6,1,2,5]=>6
[4,3,6,1,5,2]=>12
[4,3,6,2,1,5]=>12
[4,3,6,2,5,1]=>6
[4,3,6,5,1,2]=>4
[4,3,6,5,2,1]=>4
[4,5,1,2,3,6]=>2
[4,5,1,2,6,3]=>4
[4,5,1,3,2,6]=>4
[4,5,1,3,6,2]=>4
[4,5,1,6,2,3]=>4
[4,5,1,6,3,2]=>8
[4,5,2,1,3,6]=>4
[4,5,2,1,6,3]=>8
[4,5,2,3,1,6]=>4
[4,5,2,3,6,1]=>2
[4,5,2,6,1,3]=>4
[4,5,2,6,3,1]=>4
[4,5,3,1,2,6]=>4
[4,5,3,1,6,2]=>8
[4,5,3,2,1,6]=>8
[4,5,3,2,6,1]=>4
[4,5,3,6,1,2]=>2
[4,5,3,6,2,1]=>2
[4,5,6,1,2,3]=>1
[4,5,6,1,3,2]=>2
[4,5,6,2,1,3]=>2
[4,5,6,2,3,1]=>1
[4,5,6,3,1,2]=>1
[4,5,6,3,2,1]=>1
[4,6,1,2,3,5]=>2
[4,6,1,2,5,3]=>4
[4,6,1,3,2,5]=>4
[4,6,1,3,5,2]=>4
[4,6,1,5,2,3]=>4
[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]=>4
[4,6,2,3,5,1]=>2
[4,6,2,5,1,3]=>4
[4,6,2,5,3,1]=>4
[4,6,3,1,2,5]=>4
[4,6,3,1,5,2]=>8
[4,6,3,2,1,5]=>8
[4,6,3,2,5,1]=>4
[4,6,3,5,1,2]=>2
[4,6,3,5,2,1]=>2
[4,6,5,1,2,3]=>2
[4,6,5,1,3,2]=>4
[4,6,5,2,1,3]=>4
[4,6,5,2,3,1]=>2
[4,6,5,3,1,2]=>2
[4,6,5,3,2,1]=>2
[5,1,2,3,4,6]=>2
[5,1,2,3,6,4]=>4
[5,1,2,4,3,6]=>4
[5,1,2,4,6,3]=>4
[5,1,2,6,3,4]=>4
[5,1,2,6,4,3]=>8
[5,1,3,2,4,6]=>4
[5,1,3,2,6,4]=>8
[5,1,3,4,2,6]=>4
[5,1,3,4,6,2]=>4
[5,1,3,6,2,4]=>4
[5,1,3,6,4,2]=>8
[5,1,4,2,3,6]=>4
[5,1,4,2,6,3]=>12
[5,1,4,3,2,6]=>12
[5,1,4,3,6,2]=>8
[5,1,4,6,2,3]=>4
[5,1,4,6,3,2]=>8
[5,1,6,2,3,4]=>4
[5,1,6,2,4,3]=>12
[5,1,6,3,2,4]=>12
[5,1,6,3,4,2]=>8
[5,1,6,4,2,3]=>8
[5,1,6,4,3,2]=>16
[5,2,1,3,4,6]=>4
[5,2,1,3,6,4]=>8
[5,2,1,4,3,6]=>8
[5,2,1,4,6,3]=>8
[5,2,1,6,3,4]=>8
[5,2,1,6,4,3]=>16
[5,2,3,1,4,6]=>4
[5,2,3,1,6,4]=>8
[5,2,3,4,1,6]=>4
[5,2,3,4,6,1]=>2
[5,2,3,6,1,4]=>4
[5,2,3,6,4,1]=>4
[5,2,4,1,3,6]=>4
[5,2,4,1,6,3]=>12
[5,2,4,3,1,6]=>12
[5,2,4,3,6,1]=>4
[5,2,4,6,1,3]=>4
[5,2,4,6,3,1]=>4
[5,2,6,1,3,4]=>4
[5,2,6,1,4,3]=>12
[5,2,6,3,1,4]=>12
[5,2,6,3,4,1]=>4
[5,2,6,4,1,3]=>8
[5,2,6,4,3,1]=>8
[5,3,1,2,4,6]=>4
[5,3,1,2,6,4]=>8
[5,3,1,4,2,6]=>12
[5,3,1,4,6,2]=>8
[5,3,1,6,2,4]=>12
[5,3,1,6,4,2]=>16
[5,3,2,1,4,6]=>8
[5,3,2,1,6,4]=>16
[5,3,2,4,1,6]=>12
[5,3,2,4,6,1]=>4
[5,3,2,6,1,4]=>12
[5,3,2,6,4,1]=>8
[5,3,4,1,2,6]=>4
[5,3,4,1,6,2]=>8
[5,3,4,2,1,6]=>8
[5,3,4,2,6,1]=>4
[5,3,4,6,1,2]=>2
[5,3,4,6,2,1]=>2
[5,3,6,1,2,4]=>4
[5,3,6,1,4,2]=>8
[5,3,6,2,1,4]=>8
[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]=>4
[5,4,1,2,6,3]=>8
[5,4,1,3,2,6]=>8
[5,4,1,3,6,2]=>8
[5,4,1,6,2,3]=>8
[5,4,1,6,3,2]=>16
[5,4,2,1,3,6]=>8
[5,4,2,1,6,3]=>16
[5,4,2,3,1,6]=>8
[5,4,2,3,6,1]=>4
[5,4,2,6,1,3]=>8
[5,4,2,6,3,1]=>8
[5,4,3,1,2,6]=>8
[5,4,3,1,6,2]=>16
[5,4,3,2,1,6]=>16
[5,4,3,2,6,1]=>8
[5,4,3,6,1,2]=>4
[5,4,3,6,2,1]=>4
[5,4,6,1,2,3]=>2
[5,4,6,1,3,2]=>4
[5,4,6,2,1,3]=>4
[5,4,6,2,3,1]=>2
[5,4,6,3,1,2]=>2
[5,4,6,3,2,1]=>2
[5,6,1,2,3,4]=>1
[5,6,1,2,4,3]=>2
[5,6,1,3,2,4]=>2
[5,6,1,3,4,2]=>2
[5,6,1,4,2,3]=>2
[5,6,1,4,3,2]=>4
[5,6,2,1,3,4]=>2
[5,6,2,1,4,3]=>4
[5,6,2,3,1,4]=>2
[5,6,2,3,4,1]=>1
[5,6,2,4,1,3]=>2
[5,6,2,4,3,1]=>2
[5,6,3,1,2,4]=>2
[5,6,3,1,4,2]=>4
[5,6,3,2,1,4]=>4
[5,6,3,2,4,1]=>2
[5,6,3,4,1,2]=>1
[5,6,3,4,2,1]=>1
[5,6,4,1,2,3]=>1
[5,6,4,1,3,2]=>2
[5,6,4,2,1,3]=>2
[5,6,4,2,3,1]=>1
[5,6,4,3,1,2]=>1
[5,6,4,3,2,1]=>1
[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]=>2
[6,1,2,5,3,4]=>2
[6,1,2,5,4,3]=>4
[6,1,3,2,4,5]=>2
[6,1,3,2,5,4]=>4
[6,1,3,4,2,5]=>2
[6,1,3,4,5,2]=>2
[6,1,3,5,2,4]=>2
[6,1,3,5,4,2]=>4
[6,1,4,2,3,5]=>2
[6,1,4,2,5,3]=>6
[6,1,4,3,2,5]=>6
[6,1,4,3,5,2]=>4
[6,1,4,5,2,3]=>2
[6,1,4,5,3,2]=>4
[6,1,5,2,3,4]=>2
[6,1,5,2,4,3]=>6
[6,1,5,3,2,4]=>6
[6,1,5,3,4,2]=>4
[6,1,5,4,2,3]=>4
[6,1,5,4,3,2]=>8
[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]=>4
[6,2,1,5,3,4]=>4
[6,2,1,5,4,3]=>8
[6,2,3,1,4,5]=>2
[6,2,3,1,5,4]=>4
[6,2,3,4,1,5]=>2
[6,2,3,4,5,1]=>1
[6,2,3,5,1,4]=>2
[6,2,3,5,4,1]=>2
[6,2,4,1,3,5]=>2
[6,2,4,1,5,3]=>6
[6,2,4,3,1,5]=>6
[6,2,4,3,5,1]=>2
[6,2,4,5,1,3]=>2
[6,2,4,5,3,1]=>2
[6,2,5,1,3,4]=>2
[6,2,5,1,4,3]=>6
[6,2,5,3,1,4]=>6
[6,2,5,3,4,1]=>2
[6,2,5,4,1,3]=>4
[6,2,5,4,3,1]=>4
[6,3,1,2,4,5]=>2
[6,3,1,2,5,4]=>4
[6,3,1,4,2,5]=>6
[6,3,1,4,5,2]=>4
[6,3,1,5,2,4]=>6
[6,3,1,5,4,2]=>8
[6,3,2,1,4,5]=>4
[6,3,2,1,5,4]=>8
[6,3,2,4,1,5]=>6
[6,3,2,4,5,1]=>2
[6,3,2,5,1,4]=>6
[6,3,2,5,4,1]=>4
[6,3,4,1,2,5]=>2
[6,3,4,1,5,2]=>4
[6,3,4,2,1,5]=>4
[6,3,4,2,5,1]=>2
[6,3,4,5,1,2]=>1
[6,3,4,5,2,1]=>1
[6,3,5,1,2,4]=>2
[6,3,5,1,4,2]=>4
[6,3,5,2,1,4]=>4
[6,3,5,2,4,1]=>2
[6,3,5,4,1,2]=>2
[6,3,5,4,2,1]=>2
[6,4,1,2,3,5]=>2
[6,4,1,2,5,3]=>4
[6,4,1,3,2,5]=>4
[6,4,1,3,5,2]=>4
[6,4,1,5,2,3]=>4
[6,4,1,5,3,2]=>8
[6,4,2,1,3,5]=>4
[6,4,2,1,5,3]=>8
[6,4,2,3,1,5]=>4
[6,4,2,3,5,1]=>2
[6,4,2,5,1,3]=>4
[6,4,2,5,3,1]=>4
[6,4,3,1,2,5]=>4
[6,4,3,1,5,2]=>8
[6,4,3,2,1,5]=>8
[6,4,3,2,5,1]=>4
[6,4,3,5,1,2]=>2
[6,4,3,5,2,1]=>2
[6,4,5,1,2,3]=>1
[6,4,5,1,3,2]=>2
[6,4,5,2,1,3]=>2
[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]=>2
[6,5,1,3,2,4]=>2
[6,5,1,3,4,2]=>2
[6,5,1,4,2,3]=>2
[6,5,1,4,3,2]=>4
[6,5,2,1,3,4]=>2
[6,5,2,1,4,3]=>4
[6,5,2,3,1,4]=>2
[6,5,2,3,4,1]=>1
[6,5,2,4,1,3]=>2
[6,5,2,4,3,1]=>2
[6,5,3,1,2,4]=>2
[6,5,3,1,4,2]=>4
[6,5,3,2,1,4]=>4
[6,5,3,2,4,1]=>2
[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]=>2
[6,5,4,2,1,3]=>2
[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]=>1
[1,2,3,4,5,7,6]=>2
[1,2,3,4,6,5,7]=>2
[1,2,3,4,6,7,5]=>2
[1,2,3,4,7,5,6]=>2
[1,2,3,4,7,6,5]=>4
[1,2,3,5,4,6,7]=>2
[1,2,3,5,4,7,6]=>4
[1,2,3,5,6,4,7]=>2
[1,2,3,5,6,7,4]=>2
[1,2,3,5,7,4,6]=>2
[1,2,3,5,7,6,4]=>4
[1,2,3,6,4,5,7]=>2
[1,2,3,6,4,7,5]=>6
[1,2,3,6,5,4,7]=>6
[1,2,3,6,5,7,4]=>4
[1,2,3,6,7,4,5]=>2
[1,2,3,6,7,5,4]=>4
[1,2,3,7,4,5,6]=>2
[1,2,3,7,4,6,5]=>6
[1,2,3,7,5,4,6]=>6
[1,2,3,7,5,6,4]=>4
[1,2,3,7,6,4,5]=>4
[1,2,3,7,6,5,4]=>8
[1,2,4,3,5,6,7]=>2
[1,2,4,3,5,7,6]=>4
[1,2,4,3,6,5,7]=>4
[1,2,4,3,6,7,5]=>4
[1,2,4,3,7,5,6]=>4
[1,2,4,3,7,6,5]=>8
[1,2,4,5,3,6,7]=>2
[1,2,4,5,3,7,6]=>4
[1,2,4,5,6,3,7]=>2
[1,2,4,5,6,7,3]=>2
[1,2,4,5,7,3,6]=>2
[1,2,4,5,7,6,3]=>4
[1,2,4,6,3,5,7]=>2
[1,2,4,6,3,7,5]=>6
[1,2,4,6,5,3,7]=>6
[1,2,4,6,5,7,3]=>4
[1,2,4,6,7,3,5]=>2
[1,2,4,6,7,5,3]=>4
[1,2,4,7,3,5,6]=>2
[1,2,4,7,3,6,5]=>6
[1,2,4,7,5,3,6]=>6
[1,2,4,7,5,6,3]=>4
[1,2,4,7,6,3,5]=>4
[1,2,4,7,6,5,3]=>8
[1,2,5,3,4,6,7]=>2
[1,2,5,3,4,7,6]=>4
[1,2,5,3,6,4,7]=>6
[1,2,5,3,6,7,4]=>6
[1,2,5,3,7,4,6]=>6
[1,2,5,3,7,6,4]=>12
[1,2,5,4,3,6,7]=>6
[1,2,5,4,3,7,6]=>12
[1,2,5,4,6,3,7]=>6
[1,2,5,4,6,7,3]=>4
[1,2,5,4,7,3,6]=>6
[1,2,5,4,7,6,3]=>8
[1,2,5,6,3,4,7]=>2
[1,2,5,6,3,7,4]=>6
[1,2,5,6,4,3,7]=>6
[1,2,5,6,4,7,3]=>4
[1,2,5,6,7,3,4]=>2
[1,2,5,6,7,4,3]=>4
[1,2,5,7,3,4,6]=>2
[1,2,5,7,3,6,4]=>6
[1,2,5,7,4,3,6]=>6
[1,2,5,7,4,6,3]=>4
[1,2,5,7,6,3,4]=>4
[1,2,5,7,6,4,3]=>8
[1,2,6,3,4,5,7]=>2
[1,2,6,3,4,7,5]=>6
[1,2,6,3,5,4,7]=>6
[1,2,6,3,5,7,4]=>6
[1,2,6,3,7,4,5]=>6
[1,2,6,3,7,5,4]=>18
[1,2,6,4,3,5,7]=>6
[1,2,6,4,3,7,5]=>18
[1,2,6,4,5,3,7]=>6
[1,2,6,4,5,7,3]=>4
[1,2,6,4,7,3,5]=>6
[1,2,6,4,7,5,3]=>12
[1,2,6,5,3,4,7]=>6
[1,2,6,5,3,7,4]=>18
[1,2,6,5,4,3,7]=>18
[1,2,6,5,4,7,3]=>12
[1,2,6,5,7,3,4]=>4
[1,2,6,5,7,4,3]=>8
[1,2,6,7,3,4,5]=>2
[1,2,6,7,3,5,4]=>6
[1,2,6,7,4,3,5]=>6
[1,2,6,7,4,5,3]=>4
[1,2,6,7,5,3,4]=>4
[1,2,6,7,5,4,3]=>8
[1,2,7,3,4,5,6]=>2
[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]=>18
[1,2,7,4,3,5,6]=>6
[1,2,7,4,3,6,5]=>18
[1,2,7,4,5,3,6]=>6
[1,2,7,4,5,6,3]=>4
[1,2,7,4,6,3,5]=>6
[1,2,7,4,6,5,3]=>12
[1,2,7,5,3,4,6]=>6
[1,2,7,5,3,6,4]=>18
[1,2,7,5,4,3,6]=>18
[1,2,7,5,4,6,3]=>12
[1,2,7,5,6,3,4]=>4
[1,2,7,5,6,4,3]=>8
[1,2,7,6,3,4,5]=>4
[1,2,7,6,3,5,4]=>12
[1,2,7,6,4,3,5]=>12
[1,2,7,6,4,5,3]=>8
[1,2,7,6,5,3,4]=>8
[1,2,7,6,5,4,3]=>16
[1,3,2,4,5,6,7]=>2
[1,3,2,4,5,7,6]=>4
[1,3,2,4,6,5,7]=>4
[1,3,2,4,6,7,5]=>4
[1,3,2,4,7,5,6]=>4
[1,3,2,4,7,6,5]=>8
[1,3,2,5,4,6,7]=>4
[1,3,2,5,4,7,6]=>8
[1,3,2,5,6,4,7]=>4
[1,3,2,5,6,7,4]=>4
[1,3,2,5,7,4,6]=>4
[1,3,2,5,7,6,4]=>8
[1,3,2,6,4,5,7]=>4
[1,3,2,6,4,7,5]=>12
[1,3,2,6,5,4,7]=>12
[1,3,2,6,5,7,4]=>8
[1,3,2,6,7,4,5]=>4
[1,3,2,6,7,5,4]=>8
[1,3,2,7,4,5,6]=>4
[1,3,2,7,4,6,5]=>12
[1,3,2,7,5,4,6]=>12
[1,3,2,7,5,6,4]=>8
[1,3,2,7,6,4,5]=>8
[1,3,2,7,6,5,4]=>16
[1,3,4,2,5,6,7]=>2
[1,3,4,2,5,7,6]=>4
[1,3,4,2,6,5,7]=>4
[1,3,4,2,6,7,5]=>4
[1,3,4,2,7,5,6]=>4
[1,3,4,2,7,6,5]=>8
[1,3,4,5,2,6,7]=>2
[1,3,4,5,2,7,6]=>4
[1,3,4,5,6,2,7]=>2
[1,3,4,5,6,7,2]=>2
[1,3,4,5,7,2,6]=>2
[1,3,4,5,7,6,2]=>4
[1,3,4,6,2,5,7]=>2
[1,3,4,6,2,7,5]=>6
[1,3,4,6,5,2,7]=>6
[1,3,4,6,5,7,2]=>4
[1,3,4,6,7,2,5]=>2
[1,3,4,6,7,5,2]=>4
[1,3,4,7,2,5,6]=>2
[1,3,4,7,2,6,5]=>6
[1,3,4,7,5,2,6]=>6
[1,3,4,7,5,6,2]=>4
[1,3,4,7,6,2,5]=>4
[1,3,4,7,6,5,2]=>8
[1,3,5,2,4,6,7]=>2
[1,3,5,2,4,7,6]=>4
[1,3,5,2,6,4,7]=>6
[1,3,5,2,6,7,4]=>6
[1,3,5,2,7,4,6]=>6
[1,3,5,2,7,6,4]=>12
[1,3,5,4,2,6,7]=>6
[1,3,5,4,2,7,6]=>12
[1,3,5,4,6,2,7]=>6
[1,3,5,4,6,7,2]=>4
[1,3,5,4,7,2,6]=>6
[1,3,5,4,7,6,2]=>8
[1,3,5,6,2,4,7]=>2
[1,3,5,6,2,7,4]=>6
[1,3,5,6,4,2,7]=>6
[1,3,5,6,4,7,2]=>4
[1,3,5,6,7,2,4]=>2
[1,3,5,6,7,4,2]=>4
[1,3,5,7,2,4,6]=>2
[1,3,5,7,2,6,4]=>6
[1,3,5,7,4,2,6]=>6
[1,3,5,7,4,6,2]=>4
[1,3,5,7,6,2,4]=>4
[1,3,5,7,6,4,2]=>8
[1,3,6,2,4,5,7]=>2
[1,3,6,2,4,7,5]=>6
[1,3,6,2,5,4,7]=>6
[1,3,6,2,5,7,4]=>6
[1,3,6,2,7,4,5]=>6
[1,3,6,2,7,5,4]=>18
[1,3,6,4,2,5,7]=>6
[1,3,6,4,2,7,5]=>18
[1,3,6,4,5,2,7]=>6
[1,3,6,4,5,7,2]=>4
[1,3,6,4,7,2,5]=>6
[1,3,6,4,7,5,2]=>12
[1,3,6,5,2,4,7]=>6
[1,3,6,5,2,7,4]=>18
[1,3,6,5,4,2,7]=>18
[1,3,6,5,4,7,2]=>12
[1,3,6,5,7,2,4]=>4
[1,3,6,5,7,4,2]=>8
[1,3,6,7,2,4,5]=>2
[1,3,6,7,2,5,4]=>6
[1,3,6,7,4,2,5]=>6
[1,3,6,7,4,5,2]=>4
[1,3,6,7,5,2,4]=>4
[1,3,6,7,5,4,2]=>8
[1,3,7,2,4,5,6]=>2
[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]=>18
[1,3,7,4,2,5,6]=>6
[1,3,7,4,2,6,5]=>18
[1,3,7,4,5,2,6]=>6
[1,3,7,4,5,6,2]=>4
[1,3,7,4,6,2,5]=>6
[1,3,7,4,6,5,2]=>12
[1,3,7,5,2,4,6]=>6
[1,3,7,5,2,6,4]=>18
[1,3,7,5,4,2,6]=>18
[1,3,7,5,4,6,2]=>12
[1,3,7,5,6,2,4]=>4
[1,3,7,5,6,4,2]=>8
[1,3,7,6,2,4,5]=>4
[1,3,7,6,2,5,4]=>12
[1,3,7,6,4,2,5]=>12
[1,3,7,6,4,5,2]=>8
[1,3,7,6,5,2,4]=>8
[1,3,7,6,5,4,2]=>16
[1,4,2,3,5,6,7]=>2
[1,4,2,3,5,7,6]=>4
[1,4,2,3,6,5,7]=>4
[1,4,2,3,6,7,5]=>4
[1,4,2,3,7,5,6]=>4
[1,4,2,3,7,6,5]=>8
[1,4,2,5,3,6,7]=>6
[1,4,2,5,3,7,6]=>12
[1,4,2,5,6,3,7]=>6
[1,4,2,5,6,7,3]=>6
[1,4,2,5,7,3,6]=>6
[1,4,2,5,7,6,3]=>12
[1,4,2,6,3,5,7]=>6
[1,4,2,6,3,7,5]=>18
[1,4,2,6,5,3,7]=>18
[1,4,2,6,5,7,3]=>12
[1,4,2,6,7,3,5]=>6
[1,4,2,6,7,5,3]=>12
[1,4,2,7,3,5,6]=>6
[1,4,2,7,3,6,5]=>18
[1,4,2,7,5,3,6]=>18
[1,4,2,7,5,6,3]=>12
[1,4,2,7,6,3,5]=>12
[1,4,2,7,6,5,3]=>24
[1,4,3,2,5,6,7]=>6
[1,4,3,2,5,7,6]=>12
[1,4,3,2,6,5,7]=>12
[1,4,3,2,6,7,5]=>12
[1,4,3,2,7,5,6]=>12
[1,4,3,2,7,6,5]=>24
[1,4,3,5,2,6,7]=>6
[1,4,3,5,2,7,6]=>12
[1,4,3,5,6,2,7]=>6
[1,4,3,5,6,7,2]=>4
[1,4,3,5,7,2,6]=>6
[1,4,3,5,7,6,2]=>8
[1,4,3,6,2,5,7]=>6
[1,4,3,6,2,7,5]=>18
[1,4,3,6,5,2,7]=>18
[1,4,3,6,5,7,2]=>8
[1,4,3,6,7,2,5]=>6
[1,4,3,6,7,5,2]=>8
[1,4,3,7,2,5,6]=>6
[1,4,3,7,2,6,5]=>18
[1,4,3,7,5,2,6]=>18
[1,4,3,7,5,6,2]=>8
[1,4,3,7,6,2,5]=>12
[1,4,3,7,6,5,2]=>16
[1,4,5,2,3,6,7]=>2
[1,4,5,2,3,7,6]=>4
[1,4,5,2,6,3,7]=>6
[1,4,5,2,6,7,3]=>6
[1,4,5,2,7,3,6]=>6
[1,4,5,2,7,6,3]=>12
[1,4,5,3,2,6,7]=>6
[1,4,5,3,2,7,6]=>12
[1,4,5,3,6,2,7]=>6
[1,4,5,3,6,7,2]=>4
[1,4,5,3,7,2,6]=>6
[1,4,5,3,7,6,2]=>8
[1,4,5,6,2,3,7]=>2
[1,4,5,6,2,7,3]=>6
[1,4,5,6,3,2,7]=>6
[1,4,5,6,3,7,2]=>4
[1,4,5,6,7,2,3]=>2
[1,4,5,6,7,3,2]=>4
[1,4,5,7,2,3,6]=>2
[1,4,5,7,2,6,3]=>6
[1,4,5,7,3,2,6]=>6
[1,4,5,7,3,6,2]=>4
[1,4,5,7,6,2,3]=>4
[1,4,5,7,6,3,2]=>8
[1,4,6,2,3,5,7]=>2
[1,4,6,2,3,7,5]=>6
[1,4,6,2,5,3,7]=>6
[1,4,6,2,5,7,3]=>6
[1,4,6,2,7,3,5]=>6
[1,4,6,2,7,5,3]=>18
[1,4,6,3,2,5,7]=>6
[1,4,6,3,2,7,5]=>18
[1,4,6,3,5,2,7]=>6
[1,4,6,3,5,7,2]=>4
[1,4,6,3,7,2,5]=>6
[1,4,6,3,7,5,2]=>12
[1,4,6,5,2,3,7]=>6
[1,4,6,5,2,7,3]=>18
[1,4,6,5,3,2,7]=>18
                    

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Description

The number of permutations with the same set of runs.
For example, the set of runs of $4132$ is $\{(13), (2), (4)\}$. The only other permutation with this set of runs is $4213$, so the statistic equals $2$ for these two permutations.

Code

def statistic(pi):
    runs = sorted(tuple(r) for r in pi.runs())
    c = 0
    for permuted_runs in Permutations(runs):
        sigma = Permutation([e for r in permuted_runs for e in r])
        if sorted(tuple(r) for r in sigma.runs()) == runs:
            c += 1
    return c

Created

Aug 23, 2021 at 12:07 by Martin Rubey

Updated

Sep 13, 2021 at 13:43 by Martin Rubey