- FindStat

Identifier

St001486: Integer compositions ⟶ ℤ

Values

=>
                            
                            
                            
                            

                        [1]=>1
[1,1]=>2
[2]=>2
[1,1,1]=>2
[1,2]=>3
[2,1]=>3
[3]=>2
[1,1,1,1]=>2
[1,1,2]=>3
[1,2,1]=>4
[1,3]=>3
[2,1,1]=>3
[2,2]=>4
[3,1]=>3
[4]=>2
[1,1,1,1,1]=>2
[1,1,1,2]=>3
[1,1,2,1]=>4
[1,1,3]=>3
[1,2,1,1]=>4
[1,2,2]=>5
[1,3,1]=>4
[1,4]=>3
[2,1,1,1]=>3
[2,1,2]=>4
[2,2,1]=>5
[2,3]=>4
[3,1,1]=>3
[3,2]=>4
[4,1]=>3
[5]=>2
[1,1,1,1,1,1]=>2
[1,1,1,1,2]=>3
[1,1,1,2,1]=>4
[1,1,1,3]=>3
[1,1,2,1,1]=>4
[1,1,2,2]=>5
[1,1,3,1]=>4
[1,1,4]=>3
[1,2,1,1,1]=>4
[1,2,1,2]=>5
[1,2,2,1]=>6
[1,2,3]=>5
[1,3,1,1]=>4
[1,3,2]=>5
[1,4,1]=>4
[1,5]=>3
[2,1,1,1,1]=>3
[2,1,1,2]=>4
[2,1,2,1]=>5
[2,1,3]=>4
[2,2,1,1]=>5
[2,2,2]=>6
[2,3,1]=>5
[2,4]=>4
[3,1,1,1]=>3
[3,1,2]=>4
[3,2,1]=>5
[3,3]=>4
[4,1,1]=>3
[4,2]=>4
[5,1]=>3
[6]=>2
[1,1,1,1,1,1,1]=>2
[1,1,1,1,1,2]=>3
[1,1,1,1,2,1]=>4
[1,1,1,1,3]=>3
[1,1,1,2,1,1]=>4
[1,1,1,2,2]=>5
[1,1,1,3,1]=>4
[1,1,1,4]=>3
[1,1,2,1,1,1]=>4
[1,1,2,1,2]=>5
[1,1,2,2,1]=>6
[1,1,2,3]=>5
[1,1,3,1,1]=>4
[1,1,3,2]=>5
[1,1,4,1]=>4
[1,1,5]=>3
[1,2,1,1,1,1]=>4
[1,2,1,1,2]=>5
[1,2,1,2,1]=>6
[1,2,1,3]=>5
[1,2,2,1,1]=>6
[1,2,2,2]=>7
[1,2,3,1]=>6
[1,2,4]=>5
[1,3,1,1,1]=>4
[1,3,1,2]=>5
[1,3,2,1]=>6
[1,3,3]=>5
[1,4,1,1]=>4
[1,4,2]=>5
[1,5,1]=>4
[1,6]=>3
[2,1,1,1,1,1]=>3
[2,1,1,1,2]=>4
[2,1,1,2,1]=>5
[2,1,1,3]=>4
[2,1,2,1,1]=>5
[2,1,2,2]=>6
[2,1,3,1]=>5
[2,1,4]=>4
[2,2,1,1,1]=>5
[2,2,1,2]=>6
[2,2,2,1]=>7
[2,2,3]=>6
[2,3,1,1]=>5
[2,3,2]=>6
[2,4,1]=>5
[2,5]=>4
[3,1,1,1,1]=>3
[3,1,1,2]=>4
[3,1,2,1]=>5
[3,1,3]=>4
[3,2,1,1]=>5
[3,2,2]=>6
[3,3,1]=>5
[3,4]=>4
[4,1,1,1]=>3
[4,1,2]=>4
[4,2,1]=>5
[4,3]=>4
[5,1,1]=>3
[5,2]=>4
[6,1]=>3
[7]=>2
[1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,2]=>3
[1,1,1,1,1,2,1]=>4
[1,1,1,1,1,3]=>3
[1,1,1,1,2,1,1]=>4
[1,1,1,1,2,2]=>5
[1,1,1,1,3,1]=>4
[1,1,1,1,4]=>3
[1,1,1,2,1,1,1]=>4
[1,1,1,2,1,2]=>5
[1,1,1,2,2,1]=>6
[1,1,1,2,3]=>5
[1,1,1,3,1,1]=>4
[1,1,1,3,2]=>5
[1,1,1,4,1]=>4
[1,1,1,5]=>3
[1,1,2,1,1,1,1]=>4
[1,1,2,1,1,2]=>5
[1,1,2,1,2,1]=>6
[1,1,2,1,3]=>5
[1,1,2,2,1,1]=>6
[1,1,2,2,2]=>7
[1,1,2,3,1]=>6
[1,1,2,4]=>5
[1,1,3,1,1,1]=>4
[1,1,3,1,2]=>5
[1,1,3,2,1]=>6
[1,1,3,3]=>5
[1,1,4,1,1]=>4
[1,1,4,2]=>5
[1,1,5,1]=>4
[1,1,6]=>3
[1,2,1,1,1,1,1]=>4
[1,2,1,1,1,2]=>5
[1,2,1,1,2,1]=>6
[1,2,1,1,3]=>5
[1,2,1,2,1,1]=>6
[1,2,1,2,2]=>7
[1,2,1,3,1]=>6
[1,2,1,4]=>5
[1,2,2,1,1,1]=>6
[1,2,2,1,2]=>7
[1,2,2,2,1]=>8
[1,2,2,3]=>7
[1,2,3,1,1]=>6
[1,2,3,2]=>7
[1,2,4,1]=>6
[1,2,5]=>5
[1,3,1,1,1,1]=>4
[1,3,1,1,2]=>5
[1,3,1,2,1]=>6
[1,3,1,3]=>5
[1,3,2,1,1]=>6
[1,3,2,2]=>7
[1,3,3,1]=>6
[1,3,4]=>5
[1,4,1,1,1]=>4
[1,4,1,2]=>5
[1,4,2,1]=>6
[1,4,3]=>5
[1,5,1,1]=>4
[1,5,2]=>5
[1,6,1]=>4
[1,7]=>3
[2,1,1,1,1,1,1]=>3
[2,1,1,1,1,2]=>4
[2,1,1,1,2,1]=>5
[2,1,1,1,3]=>4
[2,1,1,2,1,1]=>5
[2,1,1,2,2]=>6
[2,1,1,3,1]=>5
[2,1,1,4]=>4
[2,1,2,1,1,1]=>5
[2,1,2,1,2]=>6
[2,1,2,2,1]=>7
[2,1,2,3]=>6
[2,1,3,1,1]=>5
[2,1,3,2]=>6
[2,1,4,1]=>5
[2,1,5]=>4
[2,2,1,1,1,1]=>5
[2,2,1,1,2]=>6
[2,2,1,2,1]=>7
[2,2,1,3]=>6
[2,2,2,1,1]=>7
[2,2,2,2]=>8
[2,2,3,1]=>7
[2,2,4]=>6
[2,3,1,1,1]=>5
[2,3,1,2]=>6
[2,3,2,1]=>7
[2,3,3]=>6
[2,4,1,1]=>5
[2,4,2]=>6
[2,5,1]=>5
[2,6]=>4
[3,1,1,1,1,1]=>3
[3,1,1,1,2]=>4
[3,1,1,2,1]=>5
[3,1,1,3]=>4
[3,1,2,1,1]=>5
[3,1,2,2]=>6
[3,1,3,1]=>5
[3,1,4]=>4
[3,2,1,1,1]=>5
[3,2,1,2]=>6
[3,2,2,1]=>7
[3,2,3]=>6
[3,3,1,1]=>5
[3,3,2]=>6
[3,4,1]=>5
[3,5]=>4
[4,1,1,1,1]=>3
[4,1,1,2]=>4
[4,1,2,1]=>5
[4,1,3]=>4
[4,2,1,1]=>5
[4,2,2]=>6
[4,3,1]=>5
[4,4]=>4
[5,1,1,1]=>3
[5,1,2]=>4
[5,2,1]=>5
[5,3]=>4
[6,1,1]=>3
[6,2]=>4
[7,1]=>3
[8]=>2
[1,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,1,2]=>3
[1,1,1,1,1,1,2,1]=>4
[1,1,1,1,1,1,3]=>3
[1,1,1,1,1,2,1,1]=>4
[1,1,1,1,1,2,2]=>5
[1,1,1,1,1,3,1]=>4
[1,1,1,1,1,4]=>3
[1,1,1,1,2,1,1,1]=>4
[1,1,1,1,2,1,2]=>5
[1,1,1,1,2,2,1]=>6
[1,1,1,1,2,3]=>5
[1,1,1,1,3,1,1]=>4
[1,1,1,1,3,2]=>5
[1,1,1,1,4,1]=>4
[1,1,1,1,5]=>3
[1,1,1,2,1,1,1,1]=>4
[1,1,1,2,1,1,2]=>5
[1,1,1,2,1,2,1]=>6
[1,1,1,2,1,3]=>5
[1,1,1,2,2,1,1]=>6
[1,1,1,2,2,2]=>7
[1,1,1,2,3,1]=>6
[1,1,1,2,4]=>5
[1,1,1,3,1,1,1]=>4
[1,1,1,3,1,2]=>5
[1,1,1,3,2,1]=>6
[1,1,1,3,3]=>5
[1,1,1,4,1,1]=>4
[1,1,1,4,2]=>5
[1,1,1,5,1]=>4
[1,1,1,6]=>3
[1,1,2,1,1,1,1,1]=>4
[1,1,2,1,1,1,2]=>5
[1,1,2,1,1,2,1]=>6
[1,1,2,1,1,3]=>5
[1,1,2,1,2,1,1]=>6
[1,1,2,1,2,2]=>7
[1,1,2,1,3,1]=>6
[1,1,2,1,4]=>5
[1,1,2,2,1,1,1]=>6
[1,1,2,2,1,2]=>7
[1,1,2,2,2,1]=>8
[1,1,2,2,3]=>7
[1,1,2,3,1,1]=>6
[1,1,2,3,2]=>7
[1,1,2,4,1]=>6
[1,1,2,5]=>5
[1,1,3,1,1,1,1]=>4
[1,1,3,1,1,2]=>5
[1,1,3,1,2,1]=>6
[1,1,3,1,3]=>5
[1,1,3,2,1,1]=>6
[1,1,3,2,2]=>7
[1,1,3,3,1]=>6
[1,1,3,4]=>5
[1,1,4,1,1,1]=>4
[1,1,4,1,2]=>5
[1,1,4,2,1]=>6
[1,1,4,3]=>5
[1,1,5,1,1]=>4
[1,1,5,2]=>5
[1,1,6,1]=>4
[1,1,7]=>3
[1,2,1,1,1,1,1,1]=>4
[1,2,1,1,1,1,2]=>5
[1,2,1,1,1,2,1]=>6
[1,2,1,1,1,3]=>5
[1,2,1,1,2,1,1]=>6
[1,2,1,1,2,2]=>7
[1,2,1,1,3,1]=>6
[1,2,1,1,4]=>5
[1,2,1,2,1,1,1]=>6
[1,2,1,2,1,2]=>7
[1,2,1,2,2,1]=>8
[1,2,1,2,3]=>7
[1,2,1,3,1,1]=>6
[1,2,1,3,2]=>7
[1,2,1,4,1]=>6
[1,2,1,5]=>5
[1,2,2,1,1,1,1]=>6
[1,2,2,1,1,2]=>7
[1,2,2,1,2,1]=>8
[1,2,2,1,3]=>7
[1,2,2,2,1,1]=>8
[1,2,2,2,2]=>9
[1,2,2,3,1]=>8
[1,2,2,4]=>7
[1,2,3,1,1,1]=>6
[1,2,3,1,2]=>7
[1,2,3,2,1]=>8
[1,2,3,3]=>7
[1,2,4,1,1]=>6
[1,2,4,2]=>7
[1,2,5,1]=>6
[1,2,6]=>5
[1,3,1,1,1,1,1]=>4
[1,3,1,1,1,2]=>5
[1,3,1,1,2,1]=>6
[1,3,1,1,3]=>5
[1,3,1,2,1,1]=>6
[1,3,1,2,2]=>7
[1,3,1,3,1]=>6
[1,3,1,4]=>5
[1,3,2,1,1,1]=>6
[1,3,2,1,2]=>7
[1,3,2,2,1]=>8
[1,3,2,3]=>7
[1,3,3,1,1]=>6
[1,3,3,2]=>7
[1,3,4,1]=>6
[1,3,5]=>5
[1,4,1,1,1,1]=>4
[1,4,1,1,2]=>5
[1,4,1,2,1]=>6
[1,4,1,3]=>5
[1,4,2,1,1]=>6
[1,4,2,2]=>7
[1,4,3,1]=>6
[1,4,4]=>5
[1,5,1,1,1]=>4
[1,5,1,2]=>5
[1,5,2,1]=>6
[1,5,3]=>5
[1,6,1,1]=>4
[1,6,2]=>5
[1,7,1]=>4
[1,8]=>3
[2,1,1,1,1,1,1,1]=>3
[2,1,1,1,1,1,2]=>4
[2,1,1,1,1,2,1]=>5
[2,1,1,1,1,3]=>4
[2,1,1,1,2,1,1]=>5
[2,1,1,1,2,2]=>6
[2,1,1,1,3,1]=>5
[2,1,1,1,4]=>4
[2,1,1,2,1,1,1]=>5
[2,1,1,2,1,2]=>6
[2,1,1,2,2,1]=>7
[2,1,1,2,3]=>6
[2,1,1,3,1,1]=>5
[2,1,1,3,2]=>6
[2,1,1,4,1]=>5
[2,1,1,5]=>4
[2,1,2,1,1,1,1]=>5
[2,1,2,1,1,2]=>6
[2,1,2,1,2,1]=>7
[2,1,2,1,3]=>6
[2,1,2,2,1,1]=>7
[2,1,2,2,2]=>8
[2,1,2,3,1]=>7
[2,1,2,4]=>6
[2,1,3,1,1,1]=>5
[2,1,3,1,2]=>6
[2,1,3,2,1]=>7
[2,1,3,3]=>6
[2,1,4,1,1]=>5
[2,1,4,2]=>6
[2,1,5,1]=>5
[2,1,6]=>4
[2,2,1,1,1,1,1]=>5
[2,2,1,1,1,2]=>6
[2,2,1,1,2,1]=>7
[2,2,1,1,3]=>6
[2,2,1,2,1,1]=>7
[2,2,1,2,2]=>8
[2,2,1,3,1]=>7
[2,2,1,4]=>6
[2,2,2,1,1,1]=>7
[2,2,2,1,2]=>8
[2,2,2,2,1]=>9
[2,2,2,3]=>8
[2,2,3,1,1]=>7
[2,2,3,2]=>8
[2,2,4,1]=>7
[2,2,5]=>6
[2,3,1,1,1,1]=>5
[2,3,1,1,2]=>6
[2,3,1,2,1]=>7
[2,3,1,3]=>6
[2,3,2,1,1]=>7
[2,3,2,2]=>8
[2,3,3,1]=>7
[2,3,4]=>6
[2,4,1,1,1]=>5
[2,4,1,2]=>6
[2,4,2,1]=>7
[2,4,3]=>6
[2,5,1,1]=>5
[2,5,2]=>6
[2,6,1]=>5
[2,7]=>4
[3,1,1,1,1,1,1]=>3
[3,1,1,1,1,2]=>4
[3,1,1,1,2,1]=>5
[3,1,1,1,3]=>4
[3,1,1,2,1,1]=>5
[3,1,1,2,2]=>6
[3,1,1,3,1]=>5
[3,1,1,4]=>4
[3,1,2,1,1,1]=>5
[3,1,2,1,2]=>6
[3,1,2,2,1]=>7
[3,1,2,3]=>6
[3,1,3,1,1]=>5
[3,1,3,2]=>6
[3,1,4,1]=>5
[3,1,5]=>4
[3,2,1,1,1,1]=>5
[3,2,1,1,2]=>6
[3,2,1,2,1]=>7
[3,2,1,3]=>6
[3,2,2,1,1]=>7
[3,2,2,2]=>8
[3,2,3,1]=>7
[3,2,4]=>6
[3,3,1,1,1]=>5
[3,3,1,2]=>6
[3,3,2,1]=>7
[3,3,3]=>6
[3,4,1,1]=>5
[3,4,2]=>6
[3,5,1]=>5
[3,6]=>4
[4,1,1,1,1,1]=>3
[4,1,1,1,2]=>4
[4,1,1,2,1]=>5
[4,1,1,3]=>4
[4,1,2,1,1]=>5
[4,1,2,2]=>6
[4,1,3,1]=>5
[4,1,4]=>4
[4,2,1,1,1]=>5
[4,2,1,2]=>6
[4,2,2,1]=>7
[4,2,3]=>6
[4,3,1,1]=>5
[4,3,2]=>6
[4,4,1]=>5
[4,5]=>4
[5,1,1,1,1]=>3
[5,1,1,2]=>4
[5,1,2,1]=>5
[5,1,3]=>4
[5,2,1,1]=>5
[5,2,2]=>6
[5,3,1]=>5
[5,4]=>4
[6,1,1,1]=>3
[6,1,2]=>4
[6,2,1]=>5
[6,3]=>4
[7,1,1]=>3
[7,2]=>4
[8,1]=>3
[9]=>2
[1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,1,1,2]=>3
[1,1,1,1,1,1,1,2,1]=>4
[1,1,1,1,1,1,1,3]=>3
[1,1,1,1,1,1,2,1,1]=>4
[1,1,1,1,1,1,2,2]=>5
[1,1,1,1,1,1,3,1]=>4
[1,1,1,1,1,1,4]=>3
[1,1,1,1,1,2,1,1,1]=>4
[1,1,1,1,1,2,1,2]=>5
[1,1,1,1,1,2,2,1]=>6
[1,1,1,1,1,2,3]=>5
[1,1,1,1,1,3,1,1]=>4
[1,1,1,1,1,3,2]=>5
[1,1,1,1,1,4,1]=>4
[1,1,1,1,1,5]=>3
[1,1,1,1,2,1,1,1,1]=>4
[1,1,1,1,2,1,1,2]=>5
[1,1,1,1,2,1,2,1]=>6
[1,1,1,1,2,1,3]=>5
[1,1,1,1,2,2,1,1]=>6
[1,1,1,1,2,2,2]=>7
[1,1,1,1,2,3,1]=>6
[1,1,1,1,2,4]=>5
[1,1,1,1,3,1,1,1]=>4
[1,1,1,1,3,1,2]=>5
[1,1,1,1,3,2,1]=>6
[1,1,1,1,3,3]=>5
[1,1,1,1,4,1,1]=>4
[1,1,1,1,4,2]=>5
[1,1,1,1,5,1]=>4
[1,1,1,1,6]=>3
[1,1,1,2,1,1,1,1,1]=>4
[1,1,1,2,1,1,1,2]=>5
[1,1,1,2,1,1,2,1]=>6
[1,1,1,2,1,1,3]=>5
[1,1,1,2,1,2,1,1]=>6
[1,1,1,2,1,2,2]=>7
[1,1,1,2,1,3,1]=>6
[1,1,1,2,1,4]=>5
[1,1,1,2,2,1,1,1]=>6
[1,1,1,2,2,1,2]=>7
[1,1,1,2,2,2,1]=>8
[1,1,1,2,2,3]=>7
[1,1,1,2,3,1,1]=>6
[1,1,1,2,3,2]=>7
[1,1,1,2,4,1]=>6
[1,1,1,2,5]=>5
[1,1,1,3,1,1,1,1]=>4
[1,1,1,3,1,1,2]=>5
[1,1,1,3,1,2,1]=>6
[1,1,1,3,1,3]=>5
[1,1,1,3,2,1,1]=>6
[1,1,1,3,2,2]=>7
[1,1,1,3,3,1]=>6
[1,1,1,3,4]=>5
[1,1,1,4,1,1,1]=>4
[1,1,1,4,1,2]=>5
[1,1,1,4,2,1]=>6
[1,1,1,4,3]=>5
[1,1,1,5,1,1]=>4
[1,1,1,5,2]=>5
[1,1,1,6,1]=>4
[1,1,1,7]=>3
[1,1,2,1,1,1,1,1,1]=>4
[1,1,2,1,1,1,1,2]=>5
[1,1,2,1,1,1,2,1]=>6
[1,1,2,1,1,1,3]=>5
[1,1,2,1,1,2,1,1]=>6
[1,1,2,1,1,2,2]=>7
[1,1,2,1,1,3,1]=>6
[1,1,2,1,1,4]=>5
[1,1,2,1,2,1,1,1]=>6
[1,1,2,1,2,1,2]=>7
[1,1,2,1,2,2,1]=>8
[1,1,2,1,2,3]=>7
[1,1,2,1,3,1,1]=>6
[1,1,2,1,3,2]=>7
[1,1,2,1,4,1]=>6
[1,1,2,1,5]=>5
[1,1,2,2,1,1,1,1]=>6
[1,1,2,2,1,1,2]=>7
[1,1,2,2,1,2,1]=>8
[1,1,2,2,1,3]=>7
[1,1,2,2,2,1,1]=>8
[1,1,2,2,2,2]=>9
[1,1,2,2,3,1]=>8
[1,1,2,2,4]=>7
[1,1,2,3,1,1,1]=>6
[1,1,2,3,1,2]=>7
[1,1,2,3,2,1]=>8
[1,1,2,3,3]=>7
[1,1,2,4,1,1]=>6
[1,1,2,4,2]=>7
[1,1,2,5,1]=>6
[1,1,2,6]=>5
[1,1,3,1,1,1,1,1]=>4
[1,1,3,1,1,1,2]=>5
[1,1,3,1,1,2,1]=>6
[1,1,3,1,1,3]=>5
[1,1,3,1,2,1,1]=>6
[1,1,3,1,2,2]=>7
[1,1,3,1,3,1]=>6
[1,1,3,1,4]=>5
[1,1,3,2,1,1,1]=>6
[1,1,3,2,1,2]=>7
[1,1,3,2,2,1]=>8
[1,1,3,2,3]=>7
[1,1,3,3,1,1]=>6
[1,1,3,3,2]=>7
[1,1,3,4,1]=>6
[1,1,3,5]=>5
[1,1,4,1,1,1,1]=>4
[1,1,4,1,1,2]=>5
[1,1,4,1,2,1]=>6
[1,1,4,1,3]=>5
[1,1,4,2,1,1]=>6
[1,1,4,2,2]=>7
[1,1,4,3,1]=>6
[1,1,4,4]=>5
[1,1,5,1,1,1]=>4
[1,1,5,1,2]=>5
[1,1,5,2,1]=>6
[1,1,5,3]=>5
[1,1,6,1,1]=>4
[1,1,6,2]=>5
[1,1,7,1]=>4
[1,1,8]=>3
[1,2,1,1,1,1,1,1,1]=>4
[1,2,1,1,1,1,1,2]=>5
[1,2,1,1,1,1,2,1]=>6
[1,2,1,1,1,1,3]=>5
[1,2,1,1,1,2,1,1]=>6
[1,2,1,1,1,2,2]=>7
[1,2,1,1,1,3,1]=>6
[1,2,1,1,1,4]=>5
[1,2,1,1,2,1,1,1]=>6
[1,2,1,1,2,1,2]=>7
[1,2,1,1,2,2,1]=>8
[1,2,1,1,2,3]=>7
[1,2,1,1,3,1,1]=>6
[1,2,1,1,3,2]=>7
[1,2,1,1,4,1]=>6
[1,2,1,1,5]=>5
[1,2,1,2,1,1,1,1]=>6
[1,2,1,2,1,1,2]=>7
[1,2,1,2,1,2,1]=>8
[1,2,1,2,1,3]=>7
[1,2,1,2,2,1,1]=>8
[1,2,1,2,2,2]=>9
[1,2,1,2,3,1]=>8
[1,2,1,2,4]=>7
[1,2,1,3,1,1,1]=>6
[1,2,1,3,1,2]=>7
[1,2,1,3,2,1]=>8
[1,2,1,3,3]=>7
[1,2,1,4,1,1]=>6
[1,2,1,4,2]=>7
[1,2,1,5,1]=>6
[1,2,1,6]=>5
[1,2,2,1,1,1,1,1]=>6
[1,2,2,1,1,1,2]=>7
[1,2,2,1,1,2,1]=>8
[1,2,2,1,1,3]=>7
[1,2,2,1,2,1,1]=>8
[1,2,2,1,2,2]=>9
[1,2,2,1,3,1]=>8
[1,2,2,1,4]=>7
[1,2,2,2,1,1,1]=>8
[1,2,2,2,1,2]=>9
[1,2,2,2,2,1]=>10
[1,2,2,2,3]=>9
[1,2,2,3,1,1]=>8
[1,2,2,3,2]=>9
[1,2,2,4,1]=>8
[1,2,2,5]=>7
[1,2,3,1,1,1,1]=>6
[1,2,3,1,1,2]=>7
[1,2,3,1,2,1]=>8
[1,2,3,1,3]=>7
[1,2,3,2,1,1]=>8
[1,2,3,2,2]=>9
[1,2,3,3,1]=>8
[1,2,3,4]=>7
[1,2,4,1,1,1]=>6
[1,2,4,1,2]=>7
[1,2,4,2,1]=>8
[1,2,4,3]=>7
[1,2,5,1,1]=>6
[1,2,5,2]=>7
[1,2,6,1]=>6
[1,2,7]=>5
[1,3,1,1,1,1,1,1]=>4
[1,3,1,1,1,1,2]=>5
[1,3,1,1,1,2,1]=>6
[1,3,1,1,1,3]=>5
[1,3,1,1,2,1,1]=>6
[1,3,1,1,2,2]=>7
[1,3,1,1,3,1]=>6
[1,3,1,1,4]=>5
[1,3,1,2,1,1,1]=>6
[1,3,1,2,1,2]=>7
[1,3,1,2,2,1]=>8
[1,3,1,2,3]=>7
[1,3,1,3,1,1]=>6
[1,3,1,3,2]=>7
[1,3,1,4,1]=>6
[1,3,1,5]=>5
[1,3,2,1,1,1,1]=>6
[1,3,2,1,1,2]=>7
[1,3,2,1,2,1]=>8
[1,3,2,1,3]=>7
[1,3,2,2,1,1]=>8
[1,3,2,2,2]=>9
[1,3,2,3,1]=>8
[1,3,2,4]=>7
[1,3,3,1,1,1]=>6
[1,3,3,1,2]=>7
[1,3,3,2,1]=>8
[1,3,3,3]=>7
[1,3,4,1,1]=>6
[1,3,4,2]=>7
[1,3,5,1]=>6
[1,3,6]=>5
[1,4,1,1,1,1,1]=>4
[1,4,1,1,1,2]=>5
[1,4,1,1,2,1]=>6
[1,4,1,1,3]=>5
[1,4,1,2,1,1]=>6
[1,4,1,2,2]=>7
[1,4,1,3,1]=>6
[1,4,1,4]=>5
[1,4,2,1,1,1]=>6
[1,4,2,1,2]=>7
[1,4,2,2,1]=>8
[1,4,2,3]=>7
[1,4,3,1,1]=>6
[1,4,3,2]=>7
[1,4,4,1]=>6
[1,4,5]=>5
[1,5,1,1,1,1]=>4
[1,5,1,1,2]=>5
[1,5,1,2,1]=>6
[1,5,1,3]=>5
[1,5,2,1,1]=>6
[1,5,2,2]=>7
[1,5,3,1]=>6
[1,5,4]=>5
[1,6,1,1,1]=>4
[1,6,1,2]=>5
[1,6,2,1]=>6
[1,6,3]=>5
[1,7,1,1]=>4
[1,7,2]=>5
[1,8,1]=>4
[1,9]=>3
[2,1,1,1,1,1,1,1,1]=>3
[2,1,1,1,1,1,1,2]=>4
[2,1,1,1,1,1,2,1]=>5
[2,1,1,1,1,1,3]=>4
[2,1,1,1,1,2,1,1]=>5
[2,1,1,1,1,2,2]=>6
[2,1,1,1,1,3,1]=>5
[2,1,1,1,1,4]=>4
[2,1,1,1,2,1,1,1]=>5
[2,1,1,1,2,1,2]=>6
[2,1,1,1,2,2,1]=>7
[2,1,1,1,2,3]=>6
[2,1,1,1,3,1,1]=>5
[2,1,1,1,3,2]=>6
[2,1,1,1,4,1]=>5
[2,1,1,1,5]=>4
[2,1,1,2,1,1,1,1]=>5
[2,1,1,2,1,1,2]=>6
[2,1,1,2,1,2,1]=>7
[2,1,1,2,1,3]=>6
[2,1,1,2,2,1,1]=>7
[2,1,1,2,2,2]=>8
[2,1,1,2,3,1]=>7
[2,1,1,2,4]=>6
[2,1,1,3,1,1,1]=>5
[2,1,1,3,1,2]=>6
[2,1,1,3,2,1]=>7
[2,1,1,3,3]=>6
[2,1,1,4,1,1]=>5
[2,1,1,4,2]=>6
[2,1,1,5,1]=>5
[2,1,1,6]=>4
[2,1,2,1,1,1,1,1]=>5
[2,1,2,1,1,1,2]=>6
[2,1,2,1,1,2,1]=>7
[2,1,2,1,1,3]=>6
[2,1,2,1,2,1,1]=>7
[2,1,2,1,2,2]=>8
[2,1,2,1,3,1]=>7
[2,1,2,1,4]=>6
[2,1,2,2,1,1,1]=>7
[2,1,2,2,1,2]=>8
[2,1,2,2,2,1]=>9
[2,1,2,2,3]=>8
[2,1,2,3,1,1]=>7
[2,1,2,3,2]=>8
[2,1,2,4,1]=>7
[2,1,2,5]=>6
[2,1,3,1,1,1,1]=>5
[2,1,3,1,1,2]=>6
[2,1,3,1,2,1]=>7
[2,1,3,1,3]=>6
[2,1,3,2,1,1]=>7
[2,1,3,2,2]=>8
[2,1,3,3,1]=>7
[2,1,3,4]=>6
[2,1,4,1,1,1]=>5
[2,1,4,1,2]=>6
[2,1,4,2,1]=>7
[2,1,4,3]=>6
[2,1,5,1,1]=>5
[2,1,5,2]=>6
[2,1,6,1]=>5
[2,1,7]=>4
[2,2,1,1,1,1,1,1]=>5
[2,2,1,1,1,1,2]=>6
[2,2,1,1,1,2,1]=>7
[2,2,1,1,1,3]=>6
[2,2,1,1,2,1,1]=>7
[2,2,1,1,2,2]=>8
[2,2,1,1,3,1]=>7
[2,2,1,1,4]=>6
[2,2,1,2,1,1,1]=>7
[2,2,1,2,1,2]=>8
[2,2,1,2,2,1]=>9
[2,2,1,2,3]=>8
[2,2,1,3,1,1]=>7
[2,2,1,3,2]=>8
[2,2,1,4,1]=>7
[2,2,1,5]=>6
[2,2,2,1,1,1,1]=>7
[2,2,2,1,1,2]=>8
[2,2,2,1,2,1]=>9
[2,2,2,1,3]=>8
[2,2,2,2,1,1]=>9
[2,2,2,2,2]=>10
[2,2,2,3,1]=>9
[2,2,2,4]=>8
[2,2,3,1,1,1]=>7
[2,2,3,1,2]=>8
[2,2,3,2,1]=>9
[2,2,3,3]=>8
[2,2,4,1,1]=>7
[2,2,4,2]=>8
[2,2,5,1]=>7
[2,2,6]=>6
[2,3,1,1,1,1,1]=>5
[2,3,1,1,1,2]=>6
[2,3,1,1,2,1]=>7
[2,3,1,1,3]=>6
[2,3,1,2,1,1]=>7
[2,3,1,2,2]=>8
[2,3,1,3,1]=>7
[2,3,1,4]=>6
[2,3,2,1,1,1]=>7
[2,3,2,1,2]=>8
[2,3,2,2,1]=>9
[2,3,2,3]=>8
[2,3,3,1,1]=>7
[2,3,3,2]=>8
[2,3,4,1]=>7
[2,3,5]=>6
[2,4,1,1,1,1]=>5
[2,4,1,1,2]=>6
[2,4,1,2,1]=>7
[2,4,1,3]=>6
[2,4,2,1,1]=>7
[2,4,2,2]=>8
[2,4,3,1]=>7
[2,4,4]=>6
[2,5,1,1,1]=>5
[2,5,1,2]=>6
[2,5,2,1]=>7
[2,5,3]=>6
[2,6,1,1]=>5
[2,6,2]=>6
[2,7,1]=>5
[2,8]=>4
[3,1,1,1,1,1,1,1]=>3
[3,1,1,1,1,1,2]=>4
[3,1,1,1,1,2,1]=>5
[3,1,1,1,1,3]=>4
[3,1,1,1,2,1,1]=>5
[3,1,1,1,2,2]=>6
[3,1,1,1,3,1]=>5
[3,1,1,1,4]=>4
[3,1,1,2,1,1,1]=>5
[3,1,1,2,1,2]=>6
[3,1,1,2,2,1]=>7
[3,1,1,2,3]=>6
[3,1,1,3,1,1]=>5
[3,1,1,3,2]=>6
[3,1,1,4,1]=>5
[3,1,1,5]=>4
[3,1,2,1,1,1,1]=>5
[3,1,2,1,1,2]=>6
[3,1,2,1,2,1]=>7
[3,1,2,1,3]=>6
[3,1,2,2,1,1]=>7
[3,1,2,2,2]=>8
[3,1,2,3,1]=>7
[3,1,2,4]=>6
[3,1,3,1,1,1]=>5
[3,1,3,1,2]=>6
[3,1,3,2,1]=>7
[3,1,3,3]=>6
[3,1,4,1,1]=>5
[3,1,4,2]=>6
[3,1,5,1]=>5
[3,1,6]=>4
[3,2,1,1,1,1,1]=>5
[3,2,1,1,1,2]=>6
[3,2,1,1,2,1]=>7
[3,2,1,1,3]=>6
[3,2,1,2,1,1]=>7
[3,2,1,2,2]=>8
[3,2,1,3,1]=>7
[3,2,1,4]=>6
[3,2,2,1,1,1]=>7
[3,2,2,1,2]=>8
[3,2,2,2,1]=>9
[3,2,2,3]=>8
[3,2,3,1,1]=>7
[3,2,3,2]=>8
[3,2,4,1]=>7
[3,2,5]=>6
[3,3,1,1,1,1]=>5
[3,3,1,1,2]=>6
[3,3,1,2,1]=>7
[3,3,1,3]=>6
[3,3,2,1,1]=>7
[3,3,2,2]=>8
[3,3,3,1]=>7
[3,3,4]=>6
[3,4,1,1,1]=>5
[3,4,1,2]=>6
[3,4,2,1]=>7
[3,4,3]=>6
[3,5,1,1]=>5
[3,5,2]=>6
[3,6,1]=>5
[3,7]=>4
[4,1,1,1,1,1,1]=>3
[4,1,1,1,1,2]=>4
[4,1,1,1,2,1]=>5
[4,1,1,1,3]=>4
[4,1,1,2,1,1]=>5
[4,1,1,2,2]=>6
[4,1,1,3,1]=>5
[4,1,1,4]=>4
[4,1,2,1,1,1]=>5
[4,1,2,1,2]=>6
[4,1,2,2,1]=>7
[4,1,2,3]=>6
[4,1,3,1,1]=>5
[4,1,3,2]=>6
[4,1,4,1]=>5
[4,1,5]=>4
[4,2,1,1,1,1]=>5
[4,2,1,1,2]=>6
[4,2,1,2,1]=>7
[4,2,1,3]=>6
[4,2,2,1,1]=>7
[4,2,2,2]=>8
[4,2,3,1]=>7
[4,2,4]=>6
[4,3,1,1,1]=>5
[4,3,1,2]=>6
[4,3,2,1]=>7
[4,3,3]=>6
[4,4,1,1]=>5
[4,4,2]=>6
[4,5,1]=>5
[4,6]=>4
[5,1,1,1,1,1]=>3
[5,1,1,1,2]=>4
[5,1,1,2,1]=>5
[5,1,1,3]=>4
[5,1,2,1,1]=>5
[5,1,2,2]=>6
[5,1,3,1]=>5
[5,1,4]=>4
[5,2,1,1,1]=>5
[5,2,1,2]=>6
[5,2,2,1]=>7
[5,2,3]=>6
[5,3,1,1]=>5
[5,3,2]=>6
[5,4,1]=>5
[5,5]=>4
[6,1,1,1,1]=>3
[6,1,1,2]=>4
[6,1,2,1]=>5
[6,1,3]=>4
[6,2,1,1]=>5
[6,2,2]=>6
[6,3,1]=>5
[6,4]=>4
[7,1,1,1]=>3
[7,1,2]=>4
[7,2,1]=>5
[7,3]=>4
[8,1,1]=>3
[8,2]=>4
[9,1]=>3
[10]=>2
                    

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 corners of the ribbon associated with an integer composition.
We associate a ribbon shape to a composition $c=(c_1,\dots,c_n)$ with $c_i$ cells in the $i$-th row from bottom to top, such that the cells in two rows overlap in precisely one cell.
This statistic records the total number of corners of the ribbon shape.

Code

def statistic(c):
    if c.size() == 1:
        return 1
    p = c.to_skew_partition()
    return len(p.inner_corners()) + len(p.outer_corners())

Created

Oct 28, 2019 at 18:32 by Martin Rubey

Updated

Oct 28, 2019 at 18:32 by Martin Rubey