- FindStat

Identifier

St000882: Permutations ⟶ ℤ

Values

=>
                            
                            
                            
                            

                        [1]=>1
[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]=>1
[2,3,1,4]=>1
[2,3,4,1]=>1
[2,4,1,3]=>1
[2,4,3,1]=>2
[3,1,2,4]=>1
[3,1,4,2]=>1
[3,2,1,4]=>2
[3,2,4,1]=>2
[3,4,1,2]=>1
[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]=>8
[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]=>1
[1,3,4,2,5]=>1
[1,3,4,5,2]=>1
[1,3,5,2,4]=>1
[1,3,5,4,2]=>2
[1,4,2,3,5]=>1
[1,4,2,5,3]=>1
[1,4,3,2,5]=>2
[1,4,3,5,2]=>2
[1,4,5,2,3]=>1
[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]=>8
[2,1,3,4,5]=>1
[2,1,3,5,4]=>1
[2,1,4,3,5]=>1
[2,1,4,5,3]=>1
[2,1,5,3,4]=>1
[2,1,5,4,3]=>2
[2,3,1,4,5]=>1
[2,3,1,5,4]=>1
[2,3,4,1,5]=>1
[2,3,4,5,1]=>1
[2,3,5,1,4]=>1
[2,3,5,4,1]=>2
[2,4,1,3,5]=>1
[2,4,1,5,3]=>1
[2,4,3,1,5]=>2
[2,4,3,5,1]=>2
[2,4,5,1,3]=>1
[2,4,5,3,1]=>3
[2,5,1,3,4]=>1
[2,5,1,4,3]=>2
[2,5,3,1,4]=>2
[2,5,3,4,1]=>3
[2,5,4,1,3]=>3
[2,5,4,3,1]=>8
[3,1,2,4,5]=>1
[3,1,2,5,4]=>1
[3,1,4,2,5]=>1
[3,1,4,5,2]=>1
[3,1,5,2,4]=>1
[3,1,5,4,2]=>2
[3,2,1,4,5]=>2
[3,2,1,5,4]=>2
[3,2,4,1,5]=>2
[3,2,4,5,1]=>2
[3,2,5,1,4]=>2
[3,2,5,4,1]=>4
[3,4,1,2,5]=>1
[3,4,1,5,2]=>1
[3,4,2,1,5]=>3
[3,4,2,5,1]=>3
[3,4,5,1,2]=>1
[3,4,5,2,1]=>4
[3,5,1,2,4]=>1
[3,5,1,4,2]=>2
[3,5,2,1,4]=>3
[3,5,2,4,1]=>5
[3,5,4,1,2]=>3
[3,5,4,2,1]=>11
[4,1,2,3,5]=>1
[4,1,2,5,3]=>1
[4,1,3,2,5]=>2
[4,1,3,5,2]=>2
[4,1,5,2,3]=>1
[4,1,5,3,2]=>3
[4,2,1,3,5]=>2
[4,2,1,5,3]=>2
[4,2,3,1,5]=>3
[4,2,3,5,1]=>3
[4,2,5,1,3]=>2
[4,2,5,3,1]=>5
[4,3,1,2,5]=>3
[4,3,1,5,2]=>3
[4,3,2,1,5]=>8
[4,3,2,5,1]=>8
[4,3,5,1,2]=>3
[4,3,5,2,1]=>11
[4,5,1,2,3]=>1
[4,5,1,3,2]=>3
[4,5,2,1,3]=>3
[4,5,2,3,1]=>6
[4,5,3,1,2]=>6
[4,5,3,2,1]=>20
[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]=>8
[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]=>11
[5,3,1,2,4]=>3
[5,3,1,4,2]=>5
[5,3,2,1,4]=>8
[5,3,2,4,1]=>11
[5,3,4,1,2]=>6
[5,3,4,2,1]=>20
[5,4,1,2,3]=>4
[5,4,1,3,2]=>11
[5,4,2,1,3]=>11
[5,4,2,3,1]=>20
[5,4,3,1,2]=>20
[5,4,3,2,1]=>62
[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]=>1
[1,2,4,5,3,6]=>1
[1,2,4,5,6,3]=>1
[1,2,4,6,3,5]=>1
[1,2,4,6,5,3]=>2
[1,2,5,3,4,6]=>1
[1,2,5,3,6,4]=>1
[1,2,5,4,3,6]=>2
[1,2,5,4,6,3]=>2
[1,2,5,6,3,4]=>1
[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]=>8
[1,3,2,4,5,6]=>1
[1,3,2,4,6,5]=>1
[1,3,2,5,4,6]=>1
[1,3,2,5,6,4]=>1
[1,3,2,6,4,5]=>1
[1,3,2,6,5,4]=>2
[1,3,4,2,5,6]=>1
[1,3,4,2,6,5]=>1
[1,3,4,5,2,6]=>1
[1,3,4,5,6,2]=>1
[1,3,4,6,2,5]=>1
[1,3,4,6,5,2]=>2
[1,3,5,2,4,6]=>1
[1,3,5,2,6,4]=>1
[1,3,5,4,2,6]=>2
[1,3,5,4,6,2]=>2
[1,3,5,6,2,4]=>1
[1,3,5,6,4,2]=>3
[1,3,6,2,4,5]=>1
[1,3,6,2,5,4]=>2
[1,3,6,4,2,5]=>2
[1,3,6,4,5,2]=>3
[1,3,6,5,2,4]=>3
[1,3,6,5,4,2]=>8
[1,4,2,3,5,6]=>1
[1,4,2,3,6,5]=>1
[1,4,2,5,3,6]=>1
[1,4,2,5,6,3]=>1
[1,4,2,6,3,5]=>1
[1,4,2,6,5,3]=>2
[1,4,3,2,5,6]=>2
[1,4,3,2,6,5]=>2
[1,4,3,5,2,6]=>2
[1,4,3,5,6,2]=>2
[1,4,3,6,2,5]=>2
[1,4,3,6,5,2]=>4
[1,4,5,2,3,6]=>1
[1,4,5,2,6,3]=>1
[1,4,5,3,2,6]=>3
[1,4,5,3,6,2]=>3
[1,4,5,6,2,3]=>1
[1,4,5,6,3,2]=>4
[1,4,6,2,3,5]=>1
[1,4,6,2,5,3]=>2
[1,4,6,3,2,5]=>3
[1,4,6,3,5,2]=>5
[1,4,6,5,2,3]=>3
[1,4,6,5,3,2]=>11
[1,5,2,3,4,6]=>1
[1,5,2,3,6,4]=>1
[1,5,2,4,3,6]=>2
[1,5,2,4,6,3]=>2
[1,5,2,6,3,4]=>1
[1,5,2,6,4,3]=>3
[1,5,3,2,4,6]=>2
[1,5,3,2,6,4]=>2
[1,5,3,4,2,6]=>3
[1,5,3,4,6,2]=>3
[1,5,3,6,2,4]=>2
[1,5,3,6,4,2]=>5
[1,5,4,2,3,6]=>3
[1,5,4,2,6,3]=>3
[1,5,4,3,2,6]=>8
[1,5,4,3,6,2]=>8
[1,5,4,6,2,3]=>3
[1,5,4,6,3,2]=>11
[1,5,6,2,3,4]=>1
[1,5,6,2,4,3]=>3
[1,5,6,3,2,4]=>3
[1,5,6,3,4,2]=>6
[1,5,6,4,2,3]=>6
[1,5,6,4,3,2]=>20
[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]=>8
[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]=>11
[1,6,4,2,3,5]=>3
[1,6,4,2,5,3]=>5
[1,6,4,3,2,5]=>8
[1,6,4,3,5,2]=>11
[1,6,4,5,2,3]=>6
[1,6,4,5,3,2]=>20
[1,6,5,2,3,4]=>4
[1,6,5,2,4,3]=>11
[1,6,5,3,2,4]=>11
[1,6,5,3,4,2]=>20
[1,6,5,4,2,3]=>20
[1,6,5,4,3,2]=>62
[2,1,3,4,5,6]=>1
[2,1,3,4,6,5]=>1
[2,1,3,5,4,6]=>1
[2,1,3,5,6,4]=>1
[2,1,3,6,4,5]=>1
[2,1,3,6,5,4]=>2
[2,1,4,3,5,6]=>1
[2,1,4,3,6,5]=>1
[2,1,4,5,3,6]=>1
[2,1,4,5,6,3]=>1
[2,1,4,6,3,5]=>1
[2,1,4,6,5,3]=>2
[2,1,5,3,4,6]=>1
[2,1,5,3,6,4]=>1
[2,1,5,4,3,6]=>2
[2,1,5,4,6,3]=>2
[2,1,5,6,3,4]=>1
[2,1,5,6,4,3]=>3
[2,1,6,3,4,5]=>1
[2,1,6,3,5,4]=>2
[2,1,6,4,3,5]=>2
[2,1,6,4,5,3]=>3
[2,1,6,5,3,4]=>3
[2,1,6,5,4,3]=>8
[2,3,1,4,5,6]=>1
[2,3,1,4,6,5]=>1
[2,3,1,5,4,6]=>1
[2,3,1,5,6,4]=>1
[2,3,1,6,4,5]=>1
[2,3,1,6,5,4]=>2
[2,3,4,1,5,6]=>1
[2,3,4,1,6,5]=>1
[2,3,4,5,1,6]=>1
[2,3,4,5,6,1]=>1
[2,3,4,6,1,5]=>1
[2,3,4,6,5,1]=>2
[2,3,5,1,4,6]=>1
[2,3,5,1,6,4]=>1
[2,3,5,4,1,6]=>2
[2,3,5,4,6,1]=>2
[2,3,5,6,1,4]=>1
[2,3,5,6,4,1]=>3
[2,3,6,1,4,5]=>1
[2,3,6,1,5,4]=>2
[2,3,6,4,1,5]=>2
[2,3,6,4,5,1]=>3
[2,3,6,5,1,4]=>3
[2,3,6,5,4,1]=>8
[2,4,1,3,5,6]=>1
[2,4,1,3,6,5]=>1
[2,4,1,5,3,6]=>1
[2,4,1,5,6,3]=>1
[2,4,1,6,3,5]=>1
[2,4,1,6,5,3]=>2
[2,4,3,1,5,6]=>2
[2,4,3,1,6,5]=>2
[2,4,3,5,1,6]=>2
[2,4,3,5,6,1]=>2
[2,4,3,6,1,5]=>2
[2,4,3,6,5,1]=>4
[2,4,5,1,3,6]=>1
[2,4,5,1,6,3]=>1
[2,4,5,3,1,6]=>3
[2,4,5,3,6,1]=>3
[2,4,5,6,1,3]=>1
[2,4,5,6,3,1]=>4
[2,4,6,1,3,5]=>1
[2,4,6,1,5,3]=>2
[2,4,6,3,1,5]=>3
[2,4,6,3,5,1]=>5
[2,4,6,5,1,3]=>3
[2,4,6,5,3,1]=>11
[2,5,1,3,4,6]=>1
[2,5,1,3,6,4]=>1
[2,5,1,4,3,6]=>2
[2,5,1,4,6,3]=>2
[2,5,1,6,3,4]=>1
[2,5,1,6,4,3]=>3
[2,5,3,1,4,6]=>2
[2,5,3,1,6,4]=>2
[2,5,3,4,1,6]=>3
[2,5,3,4,6,1]=>3
[2,5,3,6,1,4]=>2
[2,5,3,6,4,1]=>5
[2,5,4,1,3,6]=>3
[2,5,4,1,6,3]=>3
[2,5,4,3,1,6]=>8
[2,5,4,3,6,1]=>8
[2,5,4,6,1,3]=>3
[2,5,4,6,3,1]=>11
[2,5,6,1,3,4]=>1
[2,5,6,1,4,3]=>3
[2,5,6,3,1,4]=>3
[2,5,6,3,4,1]=>6
[2,5,6,4,1,3]=>6
[2,5,6,4,3,1]=>20
[2,6,1,3,4,5]=>1
[2,6,1,3,5,4]=>2
[2,6,1,4,3,5]=>2
[2,6,1,4,5,3]=>3
[2,6,1,5,3,4]=>3
[2,6,1,5,4,3]=>8
[2,6,3,1,4,5]=>2
[2,6,3,1,5,4]=>4
[2,6,3,4,1,5]=>3
[2,6,3,4,5,1]=>4
[2,6,3,5,1,4]=>5
[2,6,3,5,4,1]=>11
[2,6,4,1,3,5]=>3
[2,6,4,1,5,3]=>5
[2,6,4,3,1,5]=>8
[2,6,4,3,5,1]=>11
[2,6,4,5,1,3]=>6
[2,6,4,5,3,1]=>20
[2,6,5,1,3,4]=>4
[2,6,5,1,4,3]=>11
[2,6,5,3,1,4]=>11
[2,6,5,3,4,1]=>20
[2,6,5,4,1,3]=>20
[2,6,5,4,3,1]=>62
[3,1,2,4,5,6]=>1
[3,1,2,4,6,5]=>1
[3,1,2,5,4,6]=>1
[3,1,2,5,6,4]=>1
[3,1,2,6,4,5]=>1
[3,1,2,6,5,4]=>2
[3,1,4,2,5,6]=>1
[3,1,4,2,6,5]=>1
[3,1,4,5,2,6]=>1
[3,1,4,5,6,2]=>1
[3,1,4,6,2,5]=>1
[3,1,4,6,5,2]=>2
[3,1,5,2,4,6]=>1
[3,1,5,2,6,4]=>1
[3,1,5,4,2,6]=>2
[3,1,5,4,6,2]=>2
[3,1,5,6,2,4]=>1
[3,1,5,6,4,2]=>3
[3,1,6,2,4,5]=>1
[3,1,6,2,5,4]=>2
[3,1,6,4,2,5]=>2
[3,1,6,4,5,2]=>3
[3,1,6,5,2,4]=>3
[3,1,6,5,4,2]=>8
[3,2,1,4,5,6]=>2
[3,2,1,4,6,5]=>2
[3,2,1,5,4,6]=>2
[3,2,1,5,6,4]=>2
[3,2,1,6,4,5]=>2
[3,2,1,6,5,4]=>4
[3,2,4,1,5,6]=>2
[3,2,4,1,6,5]=>2
[3,2,4,5,1,6]=>2
[3,2,4,5,6,1]=>2
[3,2,4,6,1,5]=>2
[3,2,4,6,5,1]=>4
[3,2,5,1,4,6]=>2
[3,2,5,1,6,4]=>2
[3,2,5,4,1,6]=>4
[3,2,5,4,6,1]=>4
[3,2,5,6,1,4]=>2
[3,2,5,6,4,1]=>6
[3,2,6,1,4,5]=>2
[3,2,6,1,5,4]=>4
[3,2,6,4,1,5]=>4
[3,2,6,4,5,1]=>6
[3,2,6,5,1,4]=>6
[3,2,6,5,4,1]=>16
[3,4,1,2,5,6]=>1
[3,4,1,2,6,5]=>1
[3,4,1,5,2,6]=>1
[3,4,1,5,6,2]=>1
[3,4,1,6,2,5]=>1
[3,4,1,6,5,2]=>2
[3,4,2,1,5,6]=>3
[3,4,2,1,6,5]=>3
[3,4,2,5,1,6]=>3
[3,4,2,5,6,1]=>3
[3,4,2,6,1,5]=>3
[3,4,2,6,5,1]=>6
[3,4,5,1,2,6]=>1
[3,4,5,1,6,2]=>1
[3,4,5,2,1,6]=>4
[3,4,5,2,6,1]=>4
[3,4,5,6,1,2]=>1
[3,4,5,6,2,1]=>5
[3,4,6,1,2,5]=>1
[3,4,6,1,5,2]=>2
[3,4,6,2,1,5]=>4
[3,4,6,2,5,1]=>7
[3,4,6,5,1,2]=>3
[3,4,6,5,2,1]=>14
[3,5,1,2,4,6]=>1
[3,5,1,2,6,4]=>1
[3,5,1,4,2,6]=>2
[3,5,1,4,6,2]=>2
[3,5,1,6,2,4]=>1
[3,5,1,6,4,2]=>3
[3,5,2,1,4,6]=>3
[3,5,2,1,6,4]=>3
[3,5,2,4,1,6]=>5
[3,5,2,4,6,1]=>5
[3,5,2,6,1,4]=>3
[3,5,2,6,4,1]=>8
[3,5,4,1,2,6]=>3
[3,5,4,1,6,2]=>3
[3,5,4,2,1,6]=>11
[3,5,4,2,6,1]=>11
[3,5,4,6,1,2]=>3
[3,5,4,6,2,1]=>14
[3,5,6,1,2,4]=>1
[3,5,6,1,4,2]=>3
[3,5,6,2,1,4]=>4
[3,5,6,2,4,1]=>9
[3,5,6,4,1,2]=>6
[3,5,6,4,2,1]=>26
[3,6,1,2,4,5]=>1
[3,6,1,2,5,4]=>2
[3,6,1,4,2,5]=>2
[3,6,1,4,5,2]=>3
[3,6,1,5,2,4]=>3
[3,6,1,5,4,2]=>8
[3,6,2,1,4,5]=>3
[3,6,2,1,5,4]=>6
[3,6,2,4,1,5]=>5
[3,6,2,4,5,1]=>7
[3,6,2,5,1,4]=>8
[3,6,2,5,4,1]=>19
[3,6,4,1,2,5]=>3
[3,6,4,1,5,2]=>5
[3,6,4,2,1,5]=>11
[3,6,4,2,5,1]=>16
[3,6,4,5,1,2]=>6
[3,6,4,5,2,1]=>26
[3,6,5,1,2,4]=>4
[3,6,5,1,4,2]=>11
[3,6,5,2,1,4]=>15
[3,6,5,2,4,1]=>31
[3,6,5,4,1,2]=>20
[3,6,5,4,2,1]=>82
[4,1,2,3,5,6]=>1
[4,1,2,3,6,5]=>1
[4,1,2,5,3,6]=>1
[4,1,2,5,6,3]=>1
[4,1,2,6,3,5]=>1
[4,1,2,6,5,3]=>2
[4,1,3,2,5,6]=>2
[4,1,3,2,6,5]=>2
[4,1,3,5,2,6]=>2
[4,1,3,5,6,2]=>2
[4,1,3,6,2,5]=>2
[4,1,3,6,5,2]=>4
[4,1,5,2,3,6]=>1
[4,1,5,2,6,3]=>1
[4,1,5,3,2,6]=>3
[4,1,5,3,6,2]=>3
[4,1,5,6,2,3]=>1
[4,1,5,6,3,2]=>4
[4,1,6,2,3,5]=>1
[4,1,6,2,5,3]=>2
[4,1,6,3,2,5]=>3
[4,1,6,3,5,2]=>5
[4,1,6,5,2,3]=>3
[4,1,6,5,3,2]=>11
[4,2,1,3,5,6]=>2
[4,2,1,3,6,5]=>2
[4,2,1,5,3,6]=>2
[4,2,1,5,6,3]=>2
[4,2,1,6,3,5]=>2
[4,2,1,6,5,3]=>4
[4,2,3,1,5,6]=>3
[4,2,3,1,6,5]=>3
[4,2,3,5,1,6]=>3
[4,2,3,5,6,1]=>3
[4,2,3,6,1,5]=>3
[4,2,3,6,5,1]=>6
[4,2,5,1,3,6]=>2
[4,2,5,1,6,3]=>2
[4,2,5,3,1,6]=>5
[4,2,5,3,6,1]=>5
[4,2,5,6,1,3]=>2
[4,2,5,6,3,1]=>7
[4,2,6,1,3,5]=>2
[4,2,6,1,5,3]=>4
[4,2,6,3,1,5]=>5
[4,2,6,3,5,1]=>8
[4,2,6,5,1,3]=>6
[4,2,6,5,3,1]=>19
[4,3,1,2,5,6]=>3
[4,3,1,2,6,5]=>3
[4,3,1,5,2,6]=>3
[4,3,1,5,6,2]=>3
[4,3,1,6,2,5]=>3
[4,3,1,6,5,2]=>6
[4,3,2,1,5,6]=>8
[4,3,2,1,6,5]=>8
[4,3,2,5,1,6]=>8
[4,3,2,5,6,1]=>8
[4,3,2,6,1,5]=>8
[4,3,2,6,5,1]=>16
[4,3,5,1,2,6]=>3
[4,3,5,1,6,2]=>3
[4,3,5,2,1,6]=>11
[4,3,5,2,6,1]=>11
[4,3,5,6,1,2]=>3
[4,3,5,6,2,1]=>14
[4,3,6,1,2,5]=>3
[4,3,6,1,5,2]=>6
[4,3,6,2,1,5]=>11
[4,3,6,2,5,1]=>19
[4,3,6,5,1,2]=>9
[4,3,6,5,2,1]=>39
[4,5,1,2,3,6]=>1
[4,5,1,2,6,3]=>1
[4,5,1,3,2,6]=>3
[4,5,1,3,6,2]=>3
[4,5,1,6,2,3]=>1
[4,5,1,6,3,2]=>4
[4,5,2,1,3,6]=>3
[4,5,2,1,6,3]=>3
[4,5,2,3,1,6]=>6
[4,5,2,3,6,1]=>6
[4,5,2,6,1,3]=>3
[4,5,2,6,3,1]=>9
[4,5,3,1,2,6]=>6
[4,5,3,1,6,2]=>6
[4,5,3,2,1,6]=>20
[4,5,3,2,6,1]=>20
[4,5,3,6,1,2]=>6
[4,5,3,6,2,1]=>26
[4,5,6,1,2,3]=>1
[4,5,6,1,3,2]=>4
[4,5,6,2,1,3]=>4
[4,5,6,2,3,1]=>10
[4,5,6,3,1,2]=>10
[4,5,6,3,2,1]=>40
[4,6,1,2,3,5]=>1
[4,6,1,2,5,3]=>2
[4,6,1,3,5,2]=>5
[4,6,1,5,2,3]=>3
[4,6,1,5,3,2]=>11
[4,6,2,1,3,5]=>3
[4,6,2,1,5,3]=>6
[4,6,2,3,1,5]=>6
[4,6,2,3,5,1]=>9
[4,6,2,5,1,3]=>8
[4,6,2,5,3,1]=>22
[4,6,3,1,2,5]=>6
[4,6,3,1,5,2]=>11
[4,6,3,2,1,5]=>20
[4,6,3,2,5,1]=>31
[6,2,1,4,3,5]=>4
[6,4,2,1,3,5]=>11
                    

search for individual values

searching the database for the individual values of this statistic

/ search for generating function

searching the database for statistics with the same generating function

click to show known generating functions

Description

The number of connected components of short braid edges in the graph of braid moves of a permutation.
Given a permutation $\pi$, let $\operatorname{Red}(\pi)$ denote the set of reduced words for $\pi$ in terms of simple transpositions $s_i = (i,i+1)$. We now say that two reduced words are connected by a short braid move if they are obtained from each other by a modification of the form $s_i s_j \leftrightarrow s_j s_i$ for $|i-j| > 1$ as a consecutive subword of a reduced word.
For example, the two reduced words $s_1s_3s_2$ and $s_3s_1s_2$ for
$$(1243) = (12)(34)(23) = (34)(12)(23)$$
share an edge because they are obtained from each other by interchanging $s_1s_3 \leftrightarrow s_3s_1$.
This statistic counts the number connected components of such short braid moves among all reduced words.

Code

def short_braid_move_graph(pi):
    V = [ tuple(w) for w in pi.reduced_words() ]
    is_edge = lambda w1,w2: w1 != w2 and any( w1[:i] == w2[:i] and w1[i+2:] == w2[i+2:] for i in range(len(w1)-1) )
    return Graph([V,is_edge])

def statistic(pi):
    return len( short_braid_move_graph(pi).connected_components() )

Created

Jul 03, 2017 at 16:58 by Christian Stump

Updated

Dec 25, 2017 at 17:32 by Martin Rubey