- FindStat

Identifier

St000769: Integer compositions ⟶ ℤ

Values

=>
                            
                            
                            
                            

                        []=>0
[1]=>0
[1,1]=>0
[2]=>0
[1,1,1]=>0
[1,2]=>0
[2,1]=>1
[3]=>0
[1,1,1,1]=>0
[1,1,2]=>0
[1,2,1]=>2
[1,3]=>0
[2,1,1]=>1
[2,2]=>0
[3,1]=>1
[4]=>0
[1,1,1,1,1]=>0
[1,1,1,2]=>0
[1,1,2,1]=>3
[1,1,3]=>0
[1,2,1,1]=>2
[1,2,2]=>0
[1,3,1]=>2
[1,4]=>0
[2,1,1,1]=>1
[2,1,2]=>1
[2,2,1]=>2
[2,3]=>0
[3,1,1]=>1
[3,2]=>1
[4,1]=>1
[5]=>0
[1,1,1,1,1,1]=>0
[1,1,1,1,2]=>0
[1,1,1,2,1]=>4
[1,1,1,3]=>0
[1,1,2,1,1]=>3
[1,1,2,2]=>0
[1,1,3,1]=>3
[1,1,4]=>0
[1,2,1,1,1]=>2
[1,2,1,2]=>2
[1,2,2,1]=>3
[1,2,3]=>0
[1,3,1,1]=>2
[1,3,2]=>2
[1,4,1]=>2
[1,5]=>0
[2,1,1,1,1]=>1
[2,1,1,2]=>1
[2,1,2,1]=>4
[2,1,3]=>1
[2,2,1,1]=>2
[2,2,2]=>0
[2,3,1]=>2
[2,4]=>0
[3,1,1,1]=>1
[3,1,2]=>1
[3,2,1]=>3
[3,3]=>0
[4,1,1]=>1
[4,2]=>1
[5,1]=>1
[6]=>0
[1,1,1,1,1,1,1]=>0
[1,1,1,1,1,2]=>0
[1,1,1,1,2,1]=>5
[1,1,1,1,3]=>0
[1,1,1,2,1,1]=>4
[1,1,1,2,2]=>0
[1,1,1,3,1]=>4
[1,1,1,4]=>0
[1,1,2,1,1,1]=>3
[1,1,2,1,2]=>3
[1,1,2,2,1]=>4
[1,1,2,3]=>0
[1,1,3,1,1]=>3
[1,1,3,2]=>3
[1,1,4,1]=>3
[1,1,5]=>0
[1,2,1,1,1,1]=>2
[1,2,1,1,2]=>2
[1,2,1,2,1]=>6
[1,2,1,3]=>2
[1,2,2,1,1]=>3
[1,2,2,2]=>0
[1,2,3,1]=>3
[1,2,4]=>0
[1,3,1,1,1]=>2
[1,3,1,2]=>2
[1,3,2,1]=>5
[1,3,3]=>0
[1,4,1,1]=>2
[1,4,2]=>2
[1,5,1]=>2
[1,6]=>0
[2,1,1,1,1,1]=>1
[2,1,1,1,2]=>1
[2,1,1,2,1]=>5
[2,1,1,3]=>1
[2,1,2,1,1]=>4
[2,1,2,2]=>1
[2,1,3,1]=>4
[2,1,4]=>1
[2,2,1,1,1]=>2
[2,2,1,2]=>2
[2,2,2,1]=>3
[2,2,3]=>0
[2,3,1,1]=>2
[2,3,2]=>2
[2,4,1]=>2
[2,5]=>0
[3,1,1,1,1]=>1
[3,1,1,2]=>1
[3,1,2,1]=>4
[3,1,3]=>1
[3,2,1,1]=>3
[3,2,2]=>1
[3,3,1]=>2
[3,4]=>0
[4,1,1,1]=>1
[4,1,2]=>1
[4,2,1]=>3
[4,3]=>1
[5,1,1]=>1
[5,2]=>1
[6,1]=>1
[7]=>0
[1,1,1,1,1,1,1,1]=>0
[1,1,1,1,1,1,2]=>0
[1,1,1,1,1,2,1]=>6
[1,1,1,1,1,3]=>0
[1,1,1,1,2,1,1]=>5
[1,1,1,1,2,2]=>0
[1,1,1,1,3,1]=>5
[1,1,1,1,4]=>0
[1,1,1,2,1,1,1]=>4
[1,1,1,2,1,2]=>4
[1,1,1,2,2,1]=>5
[1,1,1,2,3]=>0
[1,1,1,3,1,1]=>4
[1,1,1,3,2]=>4
[1,1,1,4,1]=>4
[1,1,1,5]=>0
[1,1,2,1,1,1,1]=>3
[1,1,2,1,1,2]=>3
[1,1,2,1,2,1]=>8
[1,1,2,1,3]=>3
[1,1,2,2,1,1]=>4
[1,1,2,2,2]=>0
[1,1,2,3,1]=>4
[1,1,2,4]=>0
[1,1,3,1,1,1]=>3
[1,1,3,1,2]=>3
[1,1,3,2,1]=>7
[1,1,3,3]=>0
[1,1,4,1,1]=>3
[1,1,4,2]=>3
[1,1,5,1]=>3
[1,1,6]=>0
[1,2,1,1,1,1,1]=>2
[1,2,1,1,1,2]=>2
[1,2,1,1,2,1]=>7
[1,2,1,1,3]=>2
[1,2,1,2,1,1]=>6
[1,2,1,2,2]=>2
[1,2,1,3,1]=>6
[1,2,1,4]=>2
[1,2,2,1,1,1]=>3
[1,2,2,1,2]=>3
[1,2,2,2,1]=>4
[1,2,2,3]=>0
[1,2,3,1,1]=>3
[1,2,3,2]=>3
[1,2,4,1]=>3
[1,2,5]=>0
[1,3,1,1,1,1]=>2
[1,3,1,1,2]=>2
[1,3,1,2,1]=>6
[1,3,1,3]=>2
[1,3,2,1,1]=>5
[1,3,2,2]=>2
[1,3,3,1]=>3
[1,3,4]=>0
[1,4,1,1,1]=>2
[1,4,1,2]=>2
[1,4,2,1]=>5
[1,4,3]=>2
[1,5,1,1]=>2
[1,5,2]=>2
[1,6,1]=>2
[1,7]=>0
[2,1,1,1,1,1,1]=>1
[2,1,1,1,1,2]=>1
[2,1,1,1,2,1]=>6
[2,1,1,1,3]=>1
[2,1,1,2,1,1]=>5
[2,1,1,2,2]=>1
[2,1,1,3,1]=>5
[2,1,1,4]=>1
[2,1,2,1,1,1]=>4
[2,1,2,1,2]=>4
[2,1,2,2,1]=>5
[2,1,2,3]=>1
[2,1,3,1,1]=>4
[2,1,3,2]=>4
[2,1,4,1]=>4
[2,1,5]=>1
[2,2,1,1,1,1]=>2
[2,2,1,1,2]=>2
[2,2,1,2,1]=>6
[2,2,1,3]=>2
[2,2,2,1,1]=>3
[2,2,2,2]=>0
[2,2,3,1]=>3
[2,2,4]=>0
[2,3,1,1,1]=>2
[2,3,1,2]=>2
[2,3,2,1]=>5
[2,3,3]=>0
[2,4,1,1]=>2
[2,4,2]=>2
[2,5,1]=>2
[2,6]=>0
[3,1,1,1,1,1]=>1
[3,1,1,1,2]=>1
[3,1,1,2,1]=>5
[3,1,1,3]=>1
[3,1,2,1,1]=>4
[3,1,2,2]=>1
[3,1,3,1]=>4
[3,1,4]=>1
[3,2,1,1,1]=>3
[3,2,1,2]=>3
[3,2,2,1]=>4
[3,2,3]=>1
[3,3,1,1]=>2
[3,3,2]=>2
[3,4,1]=>2
[3,5]=>0
[4,1,1,1,1]=>1
[4,1,1,2]=>1
[4,1,2,1]=>4
[4,1,3]=>1
[4,2,1,1]=>3
[4,2,2]=>1
[4,3,1]=>3
[4,4]=>0
[5,1,1,1]=>1
[5,1,2]=>1
[5,2,1]=>3
[5,3]=>1
[6,1,1]=>1
[6,2]=>1
[7,1]=>1
[8]=>0
[1,1,1,1,1,1,1,1,1]=>0
[1,1,1,1,1,1,1,2]=>0
[1,1,1,1,1,1,2,1]=>7
[1,1,1,1,1,1,3]=>0
[1,1,1,1,1,2,1,1]=>6
[1,1,1,1,1,2,2]=>0
[1,1,1,1,1,3,1]=>6
[1,1,1,1,1,4]=>0
[1,1,1,1,2,1,1,1]=>5
[1,1,1,1,2,1,2]=>5
[1,1,1,1,2,2,1]=>6
[1,1,1,1,2,3]=>0
[1,1,1,1,3,1,1]=>5
[1,1,1,1,3,2]=>5
[1,1,1,1,4,1]=>5
[1,1,1,1,5]=>0
[1,1,1,2,1,1,1,1]=>4
[1,1,1,2,1,1,2]=>4
[1,1,1,2,1,2,1]=>10
[1,1,1,2,1,3]=>4
[1,1,1,2,2,1,1]=>5
[1,1,1,2,2,2]=>0
[1,1,1,2,3,1]=>5
[1,1,1,2,4]=>0
[1,1,1,3,1,1,1]=>4
[1,1,1,3,1,2]=>4
[1,1,1,3,2,1]=>9
[1,1,1,3,3]=>0
[1,1,1,4,1,1]=>4
[1,1,1,4,2]=>4
[1,1,1,5,1]=>4
[1,1,1,6]=>0
[1,1,2,1,1,1,1,1]=>3
[1,1,2,1,1,1,2]=>3
[1,1,2,1,1,2,1]=>9
[1,1,2,1,1,3]=>3
[1,1,2,1,2,1,1]=>8
[1,1,2,1,2,2]=>3
[1,1,2,1,3,1]=>8
[1,1,2,1,4]=>3
[1,1,2,2,1,1,1]=>4
[1,1,2,2,1,2]=>4
[1,1,2,2,2,1]=>5
[1,1,2,2,3]=>0
[1,1,2,3,1,1]=>4
[1,1,2,3,2]=>4
[1,1,2,4,1]=>4
[1,1,2,5]=>0
[1,1,3,1,1,1,1]=>3
[1,1,3,1,1,2]=>3
[1,1,3,1,2,1]=>8
[1,1,3,1,3]=>3
[1,1,3,2,1,1]=>7
[1,1,3,2,2]=>3
[1,1,3,3,1]=>4
[1,1,3,4]=>0
[1,1,4,1,1,1]=>3
[1,1,4,1,2]=>3
[1,1,4,2,1]=>7
[1,1,4,3]=>3
[1,1,5,1,1]=>3
[1,1,5,2]=>3
[1,1,6,1]=>3
[1,1,7]=>0
[1,2,1,1,1,1,1,1]=>2
[1,2,1,1,1,1,2]=>2
[1,2,1,1,1,2,1]=>8
[1,2,1,1,1,3]=>2
[1,2,1,1,2,1,1]=>7
[1,2,1,1,2,2]=>2
[1,2,1,1,3,1]=>7
[1,2,1,1,4]=>2
[1,2,1,2,1,1,1]=>6
[1,2,1,2,1,2]=>6
[1,2,1,2,2,1]=>7
[1,2,1,2,3]=>2
[1,2,1,3,1,1]=>6
[1,2,1,3,2]=>6
[1,2,1,4,1]=>6
[1,2,1,5]=>2
[1,2,2,1,1,1,1]=>3
[1,2,2,1,1,2]=>3
[1,2,2,1,2,1]=>8
[1,2,2,1,3]=>3
[1,2,2,2,1,1]=>4
[1,2,2,2,2]=>0
[1,2,2,3,1]=>4
[1,2,2,4]=>0
[1,2,3,1,1,1]=>3
[1,2,3,1,2]=>3
[1,2,3,2,1]=>7
[1,2,3,3]=>0
[1,2,4,1,1]=>3
[1,2,4,2]=>3
[1,2,5,1]=>3
[1,2,6]=>0
[1,3,1,1,1,1,1]=>2
[1,3,1,1,1,2]=>2
[1,3,1,1,2,1]=>7
[1,3,1,1,3]=>2
[1,3,1,2,1,1]=>6
[1,3,1,2,2]=>2
[1,3,1,3,1]=>6
[1,3,1,4]=>2
[1,3,2,1,1,1]=>5
[1,3,2,1,2]=>5
[1,3,2,2,1]=>6
[1,3,2,3]=>2
[1,3,3,1,1]=>3
[1,3,3,2]=>3
[1,3,4,1]=>3
[1,3,5]=>0
[1,4,1,1,1,1]=>2
[1,4,1,1,2]=>2
[1,4,1,2,1]=>6
[1,4,1,3]=>2
[1,4,2,1,1]=>5
[1,4,2,2]=>2
[1,4,3,1]=>5
[1,4,4]=>0
[1,5,1,1,1]=>2
[1,5,1,2]=>2
[1,5,2,1]=>5
[1,5,3]=>2
[1,6,1,1]=>2
[1,6,2]=>2
[1,7,1]=>2
[1,8]=>0
[2,1,1,1,1,1,1,1]=>1
[2,1,1,1,1,1,2]=>1
[2,1,1,1,1,2,1]=>7
[2,1,1,1,1,3]=>1
[2,1,1,1,2,1,1]=>6
[2,1,1,1,2,2]=>1
[2,1,1,1,3,1]=>6
[2,1,1,1,4]=>1
[2,1,1,2,1,1,1]=>5
[2,1,1,2,1,2]=>5
[2,1,1,2,2,1]=>6
[2,1,1,2,3]=>1
[2,1,1,3,1,1]=>5
[2,1,1,3,2]=>5
[2,1,1,4,1]=>5
[2,1,1,5]=>1
[2,1,2,1,1,1,1]=>4
[2,1,2,1,1,2]=>4
[2,1,2,1,2,1]=>9
[2,1,2,1,3]=>4
[2,1,2,2,1,1]=>5
[2,1,2,2,2]=>1
[2,1,2,3,1]=>5
[2,1,2,4]=>1
[2,1,3,1,1,1]=>4
[2,1,3,1,2]=>4
[2,1,3,2,1]=>8
[2,1,3,3]=>1
[2,1,4,1,1]=>4
[2,1,4,2]=>4
[2,1,5,1]=>4
[2,1,6]=>1
[2,2,1,1,1,1,1]=>2
[2,2,1,1,1,2]=>2
[2,2,1,1,2,1]=>7
[2,2,1,1,3]=>2
[2,2,1,2,1,1]=>6
[2,2,1,2,2]=>2
[2,2,1,3,1]=>6
[2,2,1,4]=>2
[2,2,2,1,1,1]=>3
[2,2,2,1,2]=>3
[2,2,2,2,1]=>4
[2,2,2,3]=>0
[2,2,3,1,1]=>3
[2,2,3,2]=>3
[2,2,4,1]=>3
[2,2,5]=>0
[2,3,1,1,1,1]=>2
[2,3,1,1,2]=>2
[2,3,1,2,1]=>6
[2,3,1,3]=>2
[2,3,2,1,1]=>5
[2,3,2,2]=>2
[2,3,3,1]=>3
[2,3,4]=>0
[2,4,1,1,1]=>2
[2,4,1,2]=>2
[2,4,2,1]=>5
[2,4,3]=>2
[2,5,1,1]=>2
[2,5,2]=>2
[2,6,1]=>2
[2,7]=>0
[3,1,1,1,1,1,1]=>1
[3,1,1,1,1,2]=>1
[3,1,1,1,2,1]=>6
[3,1,1,1,3]=>1
[3,1,1,2,1,1]=>5
[3,1,1,2,2]=>1
[3,1,1,3,1]=>5
[3,1,1,4]=>1
[3,1,2,1,1,1]=>4
[3,1,2,1,2]=>4
[3,1,2,2,1]=>5
[3,1,2,3]=>1
[3,1,3,1,1]=>4
[3,1,3,2]=>4
[3,1,4,1]=>4
[3,1,5]=>1
[3,2,1,1,1,1]=>3
[3,2,1,1,2]=>3
[3,2,1,2,1]=>7
[3,2,1,3]=>3
[3,2,2,1,1]=>4
[3,2,2,2]=>1
[3,2,3,1]=>4
[3,2,4]=>1
[3,3,1,1,1]=>2
[3,3,1,2]=>2
[3,3,2,1]=>5
[3,3,3]=>0
[3,4,1,1]=>2
[3,4,2]=>2
[3,5,1]=>2
[3,6]=>0
[4,1,1,1,1,1]=>1
[4,1,1,1,2]=>1
[4,1,1,2,1]=>5
[4,1,1,3]=>1
[4,1,2,1,1]=>4
[4,1,2,2]=>1
[4,1,3,1]=>4
[4,1,4]=>1
[4,2,1,1,1]=>3
[4,2,1,2]=>3
[4,2,2,1]=>4
[4,2,3]=>1
[4,3,1,1]=>3
[4,3,2]=>3
[4,4,1]=>2
[4,5]=>0
[5,1,1,1,1]=>1
[5,1,1,2]=>1
[5,1,2,1]=>4
[5,1,3]=>1
[5,2,1,1]=>3
[5,2,2]=>1
[5,3,1]=>3
[5,4]=>1
[6,1,1,1]=>1
[6,1,2]=>1
[6,2,1]=>3
[6,3]=>1
[7,1,1]=>1
[7,2]=>1
[8,1]=>1
[9]=>0
[1,1,1,1,1,1,1,1,1,1]=>0
[1,1,1,1,1,1,1,1,2]=>0
[1,1,1,1,1,1,2,2]=>0
[1,1,1,1,2,1,1,2]=>5
[1,1,1,1,2,2,1,1]=>6
[1,1,1,1,3,3]=>0
[1,1,1,1,5,1]=>5
[1,1,1,2,1,1,1,2]=>4
[1,1,2,1,1,1,1,2]=>3
[1,1,2,1,1,2,1,1]=>9
[1,1,2,1,2,3]=>3
[1,1,2,2,1,1,1,1]=>4
[1,1,2,2,2,2]=>0
[1,1,3,1,1,1,2]=>3
[1,1,3,1,1,3]=>3
[1,1,3,2,1,2]=>7
[1,1,3,3,1,1]=>4
[1,1,4,4]=>0
[1,1,7,1]=>3
[1,2,1,1,1,1,1,1,1]=>2
[1,2,1,1,1,1,1,2]=>2
[1,2,1,1,4,1]=>7
[1,2,1,2,1,1,2]=>6
[1,2,2,1,1,1,2]=>3
[1,2,2,1,2,1,1]=>8
[1,2,3,1,1,2]=>3
[1,2,6,1]=>3
[1,3,1,1,1,1,2]=>2
[1,3,1,1,3,1]=>7
[1,3,1,2,1,2]=>6
[1,3,2,1,1,2]=>5
[1,3,3,1,2]=>3
[1,3,5,1]=>3
[1,4,1,1,1,2]=>2
[1,4,1,1,2,1]=>7
[1,4,1,2,2]=>2
[1,4,2,1,2]=>5
[1,4,3,2]=>5
[1,4,4,1]=>3
[1,5,1,1,1,1]=>2
[1,5,1,1,2]=>2
[1,5,1,3]=>2
[1,5,2,2]=>2
[1,5,3,1]=>5
[1,5,4]=>2
[1,6,1,2]=>2
[1,6,2,1]=>5
[1,6,3]=>2
[1,7,1,1]=>2
[1,7,2]=>2
[1,8,1]=>2
[1,9]=>0
[2,1,1,1,1,1,1,1,1]=>1
[2,1,1,1,1,1,1,2]=>1
[2,1,1,1,1,2,1,1]=>7
[2,1,1,1,2,3]=>1
[2,1,1,2,1,1,1,1]=>5
[2,1,1,2,2,2]=>1
[2,1,2,1,1,3]=>4
[2,1,2,2,1,2]=>5
[2,1,2,3,1,1]=>5
[2,1,3,4]=>1
[2,1,6,1]=>4
[2,2,1,1,1,1,1,1]=>2
[2,2,1,1,2,1,1]=>7
[2,2,1,1,2,2]=>2
[2,2,2,1,1,1,1]=>3
[2,2,2,1,1,2]=>3
[2,2,2,1,2,1]=>8
[2,2,2,2,1,1]=>4
[2,2,2,2,2]=>0
[2,2,3,3]=>0
[3,1,1,1,1,1,1,1]=>1
[3,1,1,1,1,3]=>1
[3,1,1,2,1,2]=>5
[3,1,1,3,1,1]=>5
[3,1,2,4]=>1
[3,1,3,1,1,1]=>4
[3,2,1,1,1,1,1]=>3
[3,2,1,1,1,2]=>3
[3,2,1,2,1,1]=>7
[3,2,2,1,1,1]=>4
[3,2,2,2,1]=>5
[3,2,2,3]=>1
[3,3,1,1,1,1]=>2
[3,3,2,1,1]=>5
[3,3,2,2]=>2
[3,3,3,1]=>3
[4,1,1,1,1,1,1]=>1
[4,1,1,4]=>1
[4,2,1,1,1,1]=>3
[4,2,1,3]=>3
[4,2,2,1,1]=>4
[4,2,2,2]=>1
[4,3,1,1,1]=>3
[4,3,1,2]=>3
[4,3,2,1]=>6
[4,3,3]=>1
[4,4,1,1]=>2
[4,4,2]=>2
[5,1,1,1,1,1]=>1
[5,2,1,1,1]=>3
[5,2,2,1]=>4
[5,3,1,1]=>3
[5,3,2]=>3
[5,4,1]=>3
[5,5]=>0
[6,1,1,1,1]=>1
[6,2,1,1]=>3
[6,2,2]=>1
[6,3,1]=>3
[6,4]=>1
[7,1,1,1]=>1
[7,2,1]=>3
[7,3]=>1
[8,1,1]=>1
[8,2]=>1
[9,1]=>1
[10]=>0
[1,10]=>0
[1,8,1,1]=>2
[1,7,2,1]=>5
[1,6,3,1]=>5
[1,5,4,1]=>5
[1,4,5,1]=>3
[1,3,6,1]=>3
[1,2,7,1]=>3
[1,1,8,1]=>3
[10,1]=>1
[1,8,2]=>2
[1,7,1,2]=>2
[1,6,1,1,2]=>2
[1,5,1,1,1,2]=>2
[1,4,1,1,1,1,2]=>2
[1,3,1,1,1,1,1,2]=>2
[1,2,1,1,1,1,1,1,2]=>2
[1,1,1,1,1,1,1,1,1,2]=>0
[1,7,3]=>2
[1,6,2,2]=>2
[1,5,2,1,2]=>5
[1,4,2,1,1,2]=>5
[1,3,2,1,1,1,2]=>5
[1,2,2,1,1,1,1,2]=>3
[1,1,2,1,1,1,1,1,2]=>3
[1,2,2,2,2,2]=>0
[1,2,2,2,1,3]=>4
[1,2,2,1,3,2]=>8
[1,2,2,1,2,3]=>3
[1,2,2,1,1,4]=>3
[1,2,1,3,2,2]=>6
[1,2,1,3,1,3]=>6
[1,2,1,2,3,2]=>7
[1,2,1,2,2,3]=>2
[1,2,1,2,1,4]=>6
[1,2,1,1,4,2]=>7
[1,2,1,1,3,3]=>2
[1,2,1,1,2,4]=>2
[1,2,1,1,1,5]=>2
[1,1,3,2,2,2]=>3
[1,1,3,2,1,3]=>7
[1,1,3,1,3,2]=>8
[1,1,3,1,2,3]=>3
[1,1,3,1,1,4]=>3
[1,1,2,3,2,2]=>4
[1,1,2,3,1,3]=>4
[1,1,2,2,3,2]=>5
[1,1,2,2,2,3]=>0
[1,1,2,2,1,4]=>4
[1,1,2,1,4,2]=>8
[1,1,2,1,3,3]=>3
[1,1,2,1,2,4]=>3
[1,1,2,1,1,5]=>3
[1,1,1,4,2,2]=>4
[1,1,1,4,1,3]=>4
[1,1,1,3,3,2]=>5
[1,1,1,3,2,3]=>4
[1,1,1,3,1,4]=>4
[1,1,1,2,4,2]=>5
[1,1,1,2,3,3]=>0
[1,1,1,2,2,4]=>0
[1,1,1,2,1,5]=>4
[1,1,1,1,5,2]=>5
[1,1,1,1,4,3]=>5
[1,1,1,1,3,4]=>0
[1,1,1,1,2,5]=>0
[1,1,1,1,1,6]=>0
[1,1,1,1,1,1,1,1,1,1,1,1]=>0
[1,1,1,1,1,1,1,1,2,2]=>0
[1,1,1,1,1,1,2,2,1,1]=>8
[1,1,1,1,1,1,2,1,1,2]=>7
[1,1,1,1,1,1,3,3]=>0
[1,1,1,1,2,2,1,1,1,1]=>6
[1,1,1,1,2,2,2,2]=>0
[1,1,1,1,2,1,1,2,1,1]=>13
[1,1,1,1,2,1,1,1,1,2]=>5
[1,1,1,1,2,1,2,3]=>5
[1,1,1,1,3,3,1,1]=>6
[1,1,1,1,3,2,1,2]=>11
[1,1,1,1,3,1,1,3]=>5
[1,1,1,1,4,4]=>0
[1,1,2,2,1,1,1,1,1,1]=>4
[1,1,2,2,1,1,2,2]=>4
[1,1,2,2,2,2,1,1]=>6
[1,1,2,2,2,1,1,2]=>5
[1,1,2,2,3,3]=>0
[1,1,2,1,1,2,1,1,1,1]=>9
[1,1,2,1,1,2,2,2]=>3
[1,1,2,1,1,1,1,2,1,1]=>11
[1,1,2,1,1,1,1,1,1,2]=>3
[1,1,2,1,1,1,2,3]=>3
[1,1,2,1,2,3,1,1]=>9
[1,1,2,1,2,2,1,2]=>9
[1,1,2,1,2,1,1,3]=>8
[1,1,2,1,3,4]=>3
[1,1,3,3,1,1,1,1]=>4
[1,1,3,3,2,2]=>4
[1,1,3,2,1,2,1,1]=>13
[1,1,3,2,1,1,1,2]=>7
[1,1,3,2,2,3]=>3
[1,1,3,1,1,3,1,1]=>9
[1,1,3,1,1,2,1,2]=>9
[1,1,3,1,1,1,1,3]=>3
[1,1,3,1,2,4]=>3
[1,1,4,4,1,1]=>4
[1,1,4,3,1,2]=>7
[1,1,4,2,1,3]=>7
[1,1,4,1,1,4]=>3
[1,1,5,5]=>0
[2,2,1,1,1,1,1,1,1,1]=>2
[2,2,1,1,1,1,2,2]=>2
[2,2,1,1,2,2,1,1]=>8
[2,2,1,1,2,1,1,2]=>7
[2,2,1,1,3,3]=>2
[2,2,2,2,1,1,1,1]=>4
[2,2,2,2,2,2]=>0
[2,2,2,1,1,2,1,1]=>9
[2,2,2,1,1,1,1,2]=>3
[2,2,2,1,2,3]=>3
[2,2,3,3,1,1]=>4
[2,2,3,2,1,2]=>7
[2,2,3,1,1,3]=>3
[2,2,4,4]=>0
[2,1,1,2,1,1,1,1,1,1]=>5
[2,1,1,2,1,1,2,2]=>5
[2,1,1,2,2,2,1,1]=>7
[2,1,1,2,2,1,1,2]=>6
[2,1,1,2,3,3]=>1
[2,1,1,1,1,2,1,1,1,1]=>7
[2,1,1,1,1,2,2,2]=>1
[2,1,1,1,1,1,1,2,1,1]=>9
[2,1,1,1,1,1,1,1,1,2]=>1
[2,1,1,1,1,1,2,3]=>1
[2,1,1,1,2,3,1,1]=>7
[2,1,1,1,2,2,1,2]=>7
[2,1,1,1,2,1,1,3]=>6
[2,1,1,1,3,4]=>1
[2,1,2,3,1,1,1,1]=>5
[2,1,2,3,2,2]=>5
[2,1,2,2,1,2,1,1]=>11
[2,1,2,2,1,1,1,2]=>5
[2,1,2,2,2,3]=>1
[2,1,2,1,1,3,1,1]=>10
[2,1,2,1,1,2,1,2]=>10
[2,1,2,1,1,1,1,3]=>4
[2,1,2,1,2,4]=>4
[2,1,3,4,1,1]=>5
[2,1,3,3,1,2]=>5
[2,1,3,2,1,3]=>8
[2,1,3,1,1,4]=>4
[2,1,4,5]=>1
[3,3,1,1,1,1,1,1]=>2
[3,3,1,1,2,2]=>2
[3,3,2,2,1,1]=>6
[3,3,2,1,1,2]=>5
[3,3,3,3]=>0
[3,2,1,2,1,1,1,1]=>7
[3,2,1,2,2,2]=>3
[3,2,1,1,1,2,1,1]=>9
[3,2,1,1,1,1,1,2]=>3
[3,2,1,1,2,3]=>3
[3,2,2,3,1,1]=>5
[3,2,2,2,1,2]=>5
[3,2,2,1,1,3]=>4
[3,2,3,4]=>1
[3,1,1,3,1,1,1,1]=>5
[3,1,1,3,2,2]=>5
[3,1,1,2,1,2,1,1]=>11
[3,1,1,2,1,1,1,2]=>5
[3,1,1,2,2,3]=>1
[3,1,1,1,1,3,1,1]=>7
[3,1,1,1,1,2,1,2]=>7
[3,1,1,1,1,1,1,3]=>1
[3,1,1,1,2,4]=>1
[3,1,2,4,1,1]=>5
[3,1,2,3,1,2]=>5
[3,1,2,2,1,3]=>5
[3,1,2,1,1,4]=>4
[3,1,3,5]=>1
[4,4,1,1,1,1]=>2
[4,4,2,2]=>2
[4,3,1,2,1,1]=>7
[4,3,1,1,1,2]=>3
[4,3,2,3]=>3
[4,2,1,3,1,1]=>7
[4,2,1,2,1,2]=>7
[4,2,1,1,1,3]=>3
[4,2,2,4]=>1
[4,1,1,4,1,1]=>5
[4,1,1,3,1,2]=>5
[4,1,1,2,1,3]=>5
[4,1,1,1,1,4]=>1
[4,1,2,5]=>1
[5,5,1,1]=>2
[5,4,1,2]=>3
[5,3,1,3]=>3
[5,2,1,4]=>3
[5,1,1,5]=>1
[6,6]=>0
[1,11]=>0
[1,9,2]=>2
[1,8,1,2]=>2
[1,7,1,1,2]=>2
[1,6,1,1,1,2]=>2
[1,5,1,1,1,1,2]=>2
[1,4,1,1,1,1,1,2]=>2
[1,3,1,1,1,1,1,1,2]=>2
[1,2,1,1,1,1,1,1,1,2]=>2
[1,1,1,1,1,1,1,1,1,1,2]=>0
[1,2,2,2,2,2,2]=>0
[1,2,2,2,2,1,3]=>5
[1,2,2,2,1,3,2]=>10
[1,2,2,2,1,2,3]=>4
[1,2,2,2,1,1,4]=>4
[1,2,2,1,3,2,2]=>8
[1,2,2,1,3,1,3]=>8
[1,2,2,1,2,3,2]=>9
[1,2,2,1,2,2,3]=>3
[1,2,2,1,2,1,4]=>8
[1,2,2,1,1,4,2]=>9
[1,2,2,1,1,3,3]=>3
[1,2,2,1,1,2,4]=>3
[1,2,2,1,1,1,5]=>3
[1,2,1,3,2,2,2]=>6
[1,2,1,3,2,1,3]=>11
[1,2,1,3,1,3,2]=>12
[1,2,1,3,1,2,3]=>6
[1,2,1,3,1,1,4]=>6
[1,2,1,2,3,2,2]=>7
[1,2,1,2,3,1,3]=>7
[1,2,1,2,2,3,2]=>8
[1,2,1,2,2,2,3]=>2
[1,2,1,2,2,1,4]=>7
[1,2,1,2,1,4,2]=>12
[1,2,1,2,1,3,3]=>6
[1,2,1,2,1,2,4]=>6
[1,2,1,2,1,1,5]=>6
[1,2,1,1,4,2,2]=>7
[1,2,1,1,4,1,3]=>7
[1,2,1,1,3,3,2]=>8
[1,2,1,1,3,2,3]=>7
[1,2,1,1,3,1,4]=>7
[1,2,1,1,2,4,2]=>8
[1,2,1,1,2,3,3]=>2
[1,2,1,1,2,2,4]=>2
[1,2,1,1,2,1,5]=>7
[1,2,1,1,1,5,2]=>8
[1,2,1,1,1,4,3]=>8
[1,2,1,1,1,3,4]=>2
[1,2,1,1,1,2,5]=>2
[1,2,1,1,1,1,6]=>2
[1,1,3,2,2,2,2]=>3
[1,1,3,2,2,1,3]=>8
[1,1,3,2,1,3,2]=>13
[1,1,3,2,1,2,3]=>7
[1,1,3,2,1,1,4]=>7
[1,1,3,1,3,2,2]=>8
[1,1,3,1,3,1,3]=>8
[1,1,3,1,2,3,2]=>9
[1,1,3,1,2,2,3]=>3
[1,1,3,1,2,1,4]=>8
[1,1,3,1,1,4,2]=>9
[1,1,3,1,1,3,3]=>3
[1,1,3,1,1,2,4]=>3
[1,1,3,1,1,1,5]=>3
[1,1,2,3,2,2,2]=>4
[1,1,2,3,2,1,3]=>9
[1,1,2,3,1,3,2]=>10
[1,1,2,3,1,2,3]=>4
[1,1,2,3,1,1,4]=>4
[1,1,2,2,3,2,2]=>5
[1,1,2,2,3,1,3]=>5
[1,1,2,2,2,3,2]=>6
[1,1,2,2,2,2,3]=>0
[1,1,2,2,2,1,4]=>5
[1,1,2,2,1,4,2]=>10
[1,1,2,2,1,3,3]=>4
[1,1,2,2,1,2,4]=>4
[1,1,2,2,1,1,5]=>4
[1,1,2,1,4,2,2]=>8
[1,1,2,1,4,1,3]=>8
[1,1,2,1,3,3,2]=>9
[1,1,2,1,3,2,3]=>8
[1,1,2,1,3,1,4]=>8
[1,1,2,1,2,4,2]=>9
[1,1,2,1,2,3,3]=>3
[1,1,2,1,2,2,4]=>3
[1,1,2,1,2,1,5]=>8
[1,1,2,1,1,5,2]=>9
[1,1,2,1,1,4,3]=>9
[1,1,2,1,1,3,4]=>3
[1,1,2,1,1,2,5]=>3
[1,1,2,1,1,1,6]=>3
[1,1,1,4,2,2,2]=>4
[1,1,1,4,2,1,3]=>9
[1,1,1,4,1,3,2]=>10
[1,1,1,4,1,2,3]=>4
[1,1,1,4,1,1,4]=>4
[1,1,1,3,3,2,2]=>5
[1,1,1,3,3,1,3]=>5
[1,1,1,3,2,3,2]=>10
[1,1,1,3,2,2,3]=>4
[1,1,1,3,2,1,4]=>9
[1,1,1,3,1,4,2]=>10
[1,1,1,3,1,3,3]=>4
[1,1,1,3,1,2,4]=>4
[1,1,1,3,1,1,5]=>4
[1,1,1,2,4,2,2]=>5
[1,1,1,2,4,1,3]=>5
[1,1,1,2,3,3,2]=>6
[1,1,1,2,3,2,3]=>5
[1,1,1,2,3,1,4]=>5
[1,1,1,2,2,4,2]=>6
[1,1,1,2,2,3,3]=>0
[1,1,1,2,2,2,4]=>0
[1,1,1,2,2,1,5]=>5
[1,1,1,2,1,5,2]=>10
[1,1,1,2,1,4,3]=>10
[1,1,1,2,1,3,4]=>4
[1,1,1,2,1,2,5]=>4
[1,1,1,2,1,1,6]=>4
[1,1,1,1,5,2,2]=>5
[1,1,1,1,5,1,3]=>5
[1,1,1,1,4,3,2]=>11
[1,1,1,1,4,2,3]=>5
[1,1,1,1,4,1,4]=>5
[1,1,1,1,3,4,2]=>6
[1,1,1,1,3,3,3]=>0
[1,1,1,1,3,2,4]=>5
[1,1,1,1,3,1,5]=>5
[1,1,1,1,2,5,2]=>6
[1,1,1,1,2,4,3]=>6
[1,1,1,1,2,3,4]=>0
[1,1,1,1,2,2,5]=>0
[1,1,1,1,2,1,6]=>5
[1,1,1,1,1,6,2]=>6
[1,1,1,1,1,5,3]=>6
[1,1,1,1,1,4,4]=>0
[1,1,1,1,1,3,5]=>0
[1,1,1,1,1,2,6]=>0
[1,1,1,1,1,1,7]=>0
                    

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Description

The major index of a composition regarded as a word.
This is the sum of the positions of the descents of the composition.
For the statistic which interprets the composition as a descent set, see St000008The major index of the composition..

References

[1] MacMahon, P. A. Two Applications of General Theorems in Combinatory Analysis: (1) To the Theory of Inversions of Permutations; (2) To the Ascertainment of the Numbers of Terms in the Development of a Determinant which has Amongst its Elements an Arbitrary Number of Zeros MathSciNet:1576566

Code

def statistic(w):
    return sum(i+1 for i in range(len(w)-1) if w[i] > w[i+1])

Created

Apr 10, 2017 at 09:50 by Martin Rubey

Updated

Sep 25, 2020 at 00:22 by Martin Rubey