edit this statistic or download as text // json
Identifier
Values
=>
[1]=>0 [1,1]=>0 [2]=>0 [1,1,1]=>0 [1,2]=>0 [2,1]=>0 [3]=>0 [1,1,1,1]=>0 [1,1,2]=>0 [1,2,1]=>0 [1,3]=>0 [2,1,1]=>0 [2,2]=>0 [3,1]=>0 [4]=>0 [1,1,1,1,1]=>0 [1,1,1,2]=>0 [1,1,2,1]=>0 [1,1,3]=>0 [1,2,1,1]=>0 [1,2,2]=>0 [1,3,1]=>0 [1,4]=>0 [2,1,1,1]=>0 [2,1,2]=>1 [2,2,1]=>0 [2,3]=>0 [3,1,1]=>0 [3,2]=>0 [4,1]=>0 [5]=>0 [1,1,1,1,1,1]=>0 [1,1,1,1,2]=>0 [1,1,1,2,1]=>0 [1,1,1,3]=>0 [1,1,2,1,1]=>0 [1,1,2,2]=>0 [1,1,3,1]=>0 [1,1,4]=>0 [1,2,1,1,1]=>0 [1,2,1,2]=>1 [1,2,2,1]=>0 [1,2,3]=>0 [1,3,1,1]=>0 [1,3,2]=>0 [1,4,1]=>0 [1,5]=>0 [2,1,1,1,1]=>0 [2,1,1,2]=>1 [2,1,2,1]=>1 [2,1,3]=>1 [2,2,1,1]=>0 [2,2,2]=>0 [2,3,1]=>0 [2,4]=>0 [3,1,1,1]=>0 [3,1,2]=>1 [3,2,1]=>0 [3,3]=>0 [4,1,1]=>0 [4,2]=>0 [5,1]=>0 [6]=>0 [1,1,1,1,1,1,1]=>0 [1,1,1,1,1,2]=>0 [1,1,1,1,2,1]=>0 [1,1,1,1,3]=>0 [1,1,1,2,1,1]=>0 [1,1,1,2,2]=>0 [1,1,1,3,1]=>0 [1,1,1,4]=>0 [1,1,2,1,1,1]=>0 [1,1,2,1,2]=>1 [1,1,2,2,1]=>0 [1,1,2,3]=>0 [1,1,3,1,1]=>0 [1,1,3,2]=>0 [1,1,4,1]=>0 [1,1,5]=>0 [1,2,1,1,1,1]=>0 [1,2,1,1,2]=>1 [1,2,1,2,1]=>1 [1,2,1,3]=>1 [1,2,2,1,1]=>0 [1,2,2,2]=>0 [1,2,3,1]=>0 [1,2,4]=>0 [1,3,1,1,1]=>0 [1,3,1,2]=>1 [1,3,2,1]=>0 [1,3,3]=>0 [1,4,1,1]=>0 [1,4,2]=>0 [1,5,1]=>0 [1,6]=>0 [2,1,1,1,1,1]=>0 [2,1,1,1,2]=>1 [2,1,1,2,1]=>1 [2,1,1,3]=>1 [2,1,2,1,1]=>1 [2,1,2,2]=>1 [2,1,3,1]=>1 [2,1,4]=>1 [2,2,1,1,1]=>0 [2,2,1,2]=>1 [2,2,2,1]=>0 [2,2,3]=>0 [2,3,1,1]=>0 [2,3,2]=>0 [2,4,1]=>0 [2,5]=>0 [3,1,1,1,1]=>0 [3,1,1,2]=>1 [3,1,2,1]=>1 [3,1,3]=>1 [3,2,1,1]=>0 [3,2,2]=>0 [3,3,1]=>0 [3,4]=>0 [4,1,1,1]=>0 [4,1,2]=>1 [4,2,1]=>0 [4,3]=>0 [5,1,1]=>0 [5,2]=>0 [6,1]=>0 [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]=>0 [1,1,1,1,1,3]=>0 [1,1,1,1,2,1,1]=>0 [1,1,1,1,2,2]=>0 [1,1,1,1,3,1]=>0 [1,1,1,1,4]=>0 [1,1,1,2,1,1,1]=>0 [1,1,1,2,1,2]=>1 [1,1,1,2,2,1]=>0 [1,1,1,2,3]=>0 [1,1,1,3,1,1]=>0 [1,1,1,3,2]=>0 [1,1,1,4,1]=>0 [1,1,1,5]=>0 [1,1,2,1,1,1,1]=>0 [1,1,2,1,1,2]=>1 [1,1,2,1,2,1]=>1 [1,1,2,1,3]=>1 [1,1,2,2,1,1]=>0 [1,1,2,2,2]=>0 [1,1,2,3,1]=>0 [1,1,2,4]=>0 [1,1,3,1,1,1]=>0 [1,1,3,1,2]=>1 [1,1,3,2,1]=>0 [1,1,3,3]=>0 [1,1,4,1,1]=>0 [1,1,4,2]=>0 [1,1,5,1]=>0 [1,1,6]=>0 [1,2,1,1,1,1,1]=>0 [1,2,1,1,1,2]=>1 [1,2,1,1,2,1]=>1 [1,2,1,1,3]=>1 [1,2,1,2,1,1]=>1 [1,2,1,2,2]=>1 [1,2,1,3,1]=>1 [1,2,1,4]=>1 [1,2,2,1,1,1]=>0 [1,2,2,1,2]=>1 [1,2,2,2,1]=>0 [1,2,2,3]=>0 [1,2,3,1,1]=>0 [1,2,3,2]=>0 [1,2,4,1]=>0 [1,2,5]=>0 [1,3,1,1,1,1]=>0 [1,3,1,1,2]=>1 [1,3,1,2,1]=>1 [1,3,1,3]=>1 [1,3,2,1,1]=>0 [1,3,2,2]=>0 [1,3,3,1]=>0 [1,3,4]=>0 [1,4,1,1,1]=>0 [1,4,1,2]=>1 [1,4,2,1]=>0 [1,4,3]=>0 [1,5,1,1]=>0 [1,5,2]=>0 [1,6,1]=>0 [1,7]=>0 [2,1,1,1,1,1,1]=>0 [2,1,1,1,1,2]=>1 [2,1,1,1,2,1]=>1 [2,1,1,1,3]=>1 [2,1,1,2,1,1]=>1 [2,1,1,2,2]=>1 [2,1,1,3,1]=>1 [2,1,1,4]=>1 [2,1,2,1,1,1]=>1 [2,1,2,1,2]=>2 [2,1,2,2,1]=>1 [2,1,2,3]=>1 [2,1,3,1,1]=>1 [2,1,3,2]=>1 [2,1,4,1]=>1 [2,1,5]=>1 [2,2,1,1,1,1]=>0 [2,2,1,1,2]=>1 [2,2,1,2,1]=>1 [2,2,1,3]=>1 [2,2,2,1,1]=>0 [2,2,2,2]=>0 [2,2,3,1]=>0 [2,2,4]=>0 [2,3,1,1,1]=>0 [2,3,1,2]=>1 [2,3,2,1]=>0 [2,3,3]=>0 [2,4,1,1]=>0 [2,4,2]=>0 [2,5,1]=>0 [2,6]=>0 [3,1,1,1,1,1]=>0 [3,1,1,1,2]=>1 [3,1,1,2,1]=>1 [3,1,1,3]=>1 [3,1,2,1,1]=>1 [3,1,2,2]=>1 [3,1,3,1]=>1 [3,1,4]=>1 [3,2,1,1,1]=>0 [3,2,1,2]=>1 [3,2,2,1]=>0 [3,2,3]=>2 [3,3,1,1]=>0 [3,3,2]=>0 [3,4,1]=>0 [3,5]=>0 [4,1,1,1,1]=>0 [4,1,1,2]=>1 [4,1,2,1]=>1 [4,1,3]=>1 [4,2,1,1]=>0 [4,2,2]=>0 [4,3,1]=>0 [4,4]=>0 [5,1,1,1]=>0 [5,1,2]=>1 [5,2,1]=>0 [5,3]=>0 [6,1,1]=>0 [6,2]=>0 [7,1]=>0 [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]=>0 [1,1,1,1,1,1,3]=>0 [1,1,1,1,1,2,1,1]=>0 [1,1,1,1,1,2,2]=>0 [1,1,1,1,1,3,1]=>0 [1,1,1,1,1,4]=>0 [1,1,1,1,2,1,1,1]=>0 [1,1,1,1,2,1,2]=>1 [1,1,1,1,2,2,1]=>0 [1,1,1,1,2,3]=>0 [1,1,1,1,3,1,1]=>0 [1,1,1,1,3,2]=>0 [1,1,1,1,4,1]=>0 [1,1,1,1,5]=>0 [1,1,1,2,1,1,1,1]=>0 [1,1,1,2,1,1,2]=>1 [1,1,1,2,1,2,1]=>1 [1,1,1,2,1,3]=>1 [1,1,1,2,2,1,1]=>0 [1,1,1,2,2,2]=>0 [1,1,1,2,3,1]=>0 [1,1,1,2,4]=>0 [1,1,1,3,1,1,1]=>0 [1,1,1,3,1,2]=>1 [1,1,1,3,2,1]=>0 [1,1,1,3,3]=>0 [1,1,1,4,1,1]=>0 [1,1,1,4,2]=>0 [1,1,1,5,1]=>0 [1,1,1,6]=>0 [1,1,2,1,1,1,1,1]=>0 [1,1,2,1,1,1,2]=>1 [1,1,2,1,1,2,1]=>1 [1,1,2,1,1,3]=>1 [1,1,2,1,2,1,1]=>1 [1,1,2,1,2,2]=>1 [1,1,2,1,3,1]=>1 [1,1,2,1,4]=>1 [1,1,2,2,1,1,1]=>0 [1,1,2,2,1,2]=>1 [1,1,2,2,2,1]=>0 [1,1,2,2,3]=>0 [1,1,2,3,1,1]=>0 [1,1,2,3,2]=>0 [1,1,2,4,1]=>0 [1,1,2,5]=>0 [1,1,3,1,1,1,1]=>0 [1,1,3,1,1,2]=>1 [1,1,3,1,2,1]=>1 [1,1,3,1,3]=>1 [1,1,3,2,1,1]=>0 [1,1,3,2,2]=>0 [1,1,3,3,1]=>0 [1,1,3,4]=>0 [1,1,4,1,1,1]=>0 [1,1,4,1,2]=>1 [1,1,4,2,1]=>0 [1,1,4,3]=>0 [1,1,5,1,1]=>0 [1,1,5,2]=>0 [1,1,6,1]=>0 [1,1,7]=>0 [1,2,1,1,1,1,1,1]=>0 [1,2,1,1,1,1,2]=>1 [1,2,1,1,1,2,1]=>1 [1,2,1,1,1,3]=>1 [1,2,1,1,2,1,1]=>1 [1,2,1,1,2,2]=>1 [1,2,1,1,3,1]=>1 [1,2,1,1,4]=>1 [1,2,1,2,1,1,1]=>1 [1,2,1,2,1,2]=>2 [1,2,1,2,2,1]=>1 [1,2,1,2,3]=>1 [1,2,1,3,1,1]=>1 [1,2,1,3,2]=>1 [1,2,1,4,1]=>1 [1,2,1,5]=>1 [1,2,2,1,1,1,1]=>0 [1,2,2,1,1,2]=>1 [1,2,2,1,2,1]=>1 [1,2,2,1,3]=>1 [1,2,2,2,1,1]=>0 [1,2,2,2,2]=>0 [1,2,2,3,1]=>0 [1,2,2,4]=>0 [1,2,3,1,1,1]=>0 [1,2,3,1,2]=>1 [1,2,3,2,1]=>0 [1,2,3,3]=>0 [1,2,4,1,1]=>0 [1,2,4,2]=>0 [1,2,5,1]=>0 [1,2,6]=>0 [1,3,1,1,1,1,1]=>0 [1,3,1,1,1,2]=>1 [1,3,1,1,2,1]=>1 [1,3,1,1,3]=>1 [1,3,1,2,1,1]=>1 [1,3,1,2,2]=>1 [1,3,1,3,1]=>1 [1,3,1,4]=>1 [1,3,2,1,1,1]=>0 [1,3,2,1,2]=>1 [1,3,2,2,1]=>0 [1,3,2,3]=>2 [1,3,3,1,1]=>0 [1,3,3,2]=>0 [1,3,4,1]=>0 [1,3,5]=>0 [1,4,1,1,1,1]=>0 [1,4,1,1,2]=>1 [1,4,1,2,1]=>1 [1,4,1,3]=>1 [1,4,2,1,1]=>0 [1,4,2,2]=>0 [1,4,3,1]=>0 [1,4,4]=>0 [1,5,1,1,1]=>0 [1,5,1,2]=>1 [1,5,2,1]=>0 [1,5,3]=>0 [1,6,1,1]=>0 [1,6,2]=>0 [1,7,1]=>0 [1,8]=>0 [2,1,1,1,1,1,1,1]=>0 [2,1,1,1,1,1,2]=>1 [2,1,1,1,1,2,1]=>1 [2,1,1,1,1,3]=>1 [2,1,1,1,2,1,1]=>1 [2,1,1,1,2,2]=>1 [2,1,1,1,3,1]=>1 [2,1,1,1,4]=>1 [2,1,1,2,1,1,1]=>1 [2,1,1,2,1,2]=>2 [2,1,1,2,2,1]=>1 [2,1,1,2,3]=>1 [2,1,1,3,1,1]=>1 [2,1,1,3,2]=>1 [2,1,1,4,1]=>1 [2,1,1,5]=>1 [2,1,2,1,1,1,1]=>1 [2,1,2,1,1,2]=>2 [2,1,2,1,2,1]=>2 [2,1,2,1,3]=>2 [2,1,2,2,1,1]=>1 [2,1,2,2,2]=>1 [2,1,2,3,1]=>1 [2,1,2,4]=>1 [2,1,3,1,1,1]=>1 [2,1,3,1,2]=>2 [2,1,3,2,1]=>1 [2,1,3,3]=>1 [2,1,4,1,1]=>1 [2,1,4,2]=>1 [2,1,5,1]=>1 [2,1,6]=>1 [2,2,1,1,1,1,1]=>0 [2,2,1,1,1,2]=>1 [2,2,1,1,2,1]=>1 [2,2,1,1,3]=>1 [2,2,1,2,1,1]=>1 [2,2,1,2,2]=>1 [2,2,1,3,1]=>1 [2,2,1,4]=>1 [2,2,2,1,1,1]=>0 [2,2,2,1,2]=>1 [2,2,2,2,1]=>0 [2,2,2,3]=>0 [2,2,3,1,1]=>0 [2,2,3,2]=>0 [2,2,4,1]=>0 [2,2,5]=>0 [2,3,1,1,1,1]=>0 [2,3,1,1,2]=>1 [2,3,1,2,1]=>1 [2,3,1,3]=>1 [2,3,2,1,1]=>0 [2,3,2,2]=>0 [2,3,3,1]=>0 [2,3,4]=>0 [2,4,1,1,1]=>0 [2,4,1,2]=>1 [2,4,2,1]=>0 [2,4,3]=>0 [2,5,1,1]=>0 [2,5,2]=>0 [2,6,1]=>0 [2,7]=>0 [3,1,1,1,1,1,1]=>0 [3,1,1,1,1,2]=>1 [3,1,1,1,2,1]=>1 [3,1,1,1,3]=>1 [3,1,1,2,1,1]=>1 [3,1,1,2,2]=>1 [3,1,1,3,1]=>1 [3,1,1,4]=>1 [3,1,2,1,1,1]=>1 [3,1,2,1,2]=>2 [3,1,2,2,1]=>1 [3,1,2,3]=>1 [3,1,3,1,1]=>1 [3,1,3,2]=>1 [3,1,4,1]=>1 [3,1,5]=>1 [3,2,1,1,1,1]=>0 [3,2,1,1,2]=>1 [3,2,1,2,1]=>1 [3,2,1,3]=>1 [3,2,2,1,1]=>0 [3,2,2,2]=>0 [3,2,3,1]=>2 [3,2,4]=>2 [3,3,1,1,1]=>0 [3,3,1,2]=>1 [3,3,2,1]=>0 [3,3,3]=>0 [3,4,1,1]=>0 [3,4,2]=>0 [3,5,1]=>0 [3,6]=>0 [4,1,1,1,1,1]=>0 [4,1,1,1,2]=>1 [4,1,1,2,1]=>1 [4,1,1,3]=>1 [4,1,2,1,1]=>1 [4,1,2,2]=>1 [4,1,3,1]=>1 [4,1,4]=>1 [4,2,1,1,1]=>0 [4,2,1,2]=>1 [4,2,2,1]=>0 [4,2,3]=>2 [4,3,1,1]=>0 [4,3,2]=>0 [4,4,1]=>0 [4,5]=>0 [5,1,1,1,1]=>0 [5,1,1,2]=>1 [5,1,2,1]=>1 [5,1,3]=>1 [5,2,1,1]=>0 [5,2,2]=>0 [5,3,1]=>0 [5,4]=>0 [6,1,1,1]=>0 [6,1,2]=>1 [6,2,1]=>0 [6,3]=>0 [7,1,1]=>0 [7,2]=>0 [8,1]=>0 [9]=>0 [1,1,1,1,1,1,1,1,1,1]=>0 [1,1,1,1,1,1,2,2]=>0 [1,1,1,1,2,1,1,2]=>1 [1,1,1,1,2,2,1,1]=>0 [1,1,1,1,3,3]=>0 [1,1,1,1,5,1]=>0 [1,1,2,1,1,1,1,2]=>1 [1,1,2,1,1,2,1,1]=>1 [1,1,2,1,2,3]=>1 [1,1,2,2,1,1,1,1]=>0 [1,1,2,2,2,2]=>0 [1,1,3,1,1,3]=>1 [1,1,3,2,1,2]=>1 [1,1,3,3,1,1]=>0 [1,1,4,4]=>0 [1,1,7,1]=>0 [1,2,1,1,4,1]=>1 [1,2,6,1]=>0 [1,3,1,1,3,1]=>1 [1,3,5,1]=>0 [1,4,1,1,2,1]=>1 [1,4,4,1]=>0 [1,5,1,1,1,1]=>0 [1,5,3,1]=>0 [1,6,1,2]=>1 [1,6,2,1]=>0 [1,7,1,1]=>0 [1,8,1]=>0 [1,9]=>0 [2,1,1,1,1,1,1,2]=>1 [2,1,1,1,1,2,1,1]=>1 [2,1,1,1,2,3]=>1 [2,1,1,2,1,1,1,1]=>1 [2,1,1,2,2,2]=>1 [2,1,2,1,1,3]=>2 [2,1,2,2,1,2]=>2 [2,1,2,3,1,1]=>1 [2,1,3,4]=>1 [2,1,6,1]=>1 [2,2,1,1,1,1,1,1]=>0 [2,2,1,1,2,2]=>1 [2,2,2,1,1,2]=>1 [2,2,2,2,1,1]=>0 [2,2,3,3]=>0 [3,1,1,1,1,3]=>1 [3,1,1,2,1,2]=>2 [3,1,1,3,1,1]=>1 [3,1,2,4]=>1 [3,2,1,1,1,2]=>1 [3,2,1,2,1,1]=>1 [3,2,2,3]=>2 [3,3,1,1,1,1]=>0 [3,3,2,2]=>0 [4,1,1,4]=>1 [4,2,1,3]=>1 [4,3,1,2]=>1 [4,4,1,1]=>0 [5,5]=>0 [8,1,1]=>0 [9,1]=>0 [1,10]=>0 [1,8,1,1]=>0 [1,7,2,1]=>0 [1,6,3,1]=>0 [1,5,4,1]=>0 [1,4,5,1]=>0 [1,3,6,1]=>0 [1,2,7,1]=>0 [1,1,8,1]=>0 [10,1]=>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]=>0 [1,1,1,1,1,1,2,1,1,2]=>1 [1,1,1,1,1,1,3,3]=>0 [1,1,1,1,2,2,1,1,1,1]=>0 [1,1,1,1,2,2,2,2]=>0 [1,1,1,1,2,1,1,2,1,1]=>1 [1,1,1,1,2,1,1,1,1,2]=>1 [1,1,1,1,2,1,2,3]=>1 [1,1,1,1,3,3,1,1]=>0 [1,1,1,1,3,2,1,2]=>1 [1,1,1,1,3,1,1,3]=>1 [1,1,1,1,4,4]=>0 [1,1,2,2,1,1,1,1,1,1]=>0 [1,1,2,2,1,1,2,2]=>1 [1,1,2,2,2,2,1,1]=>0 [1,1,2,2,2,1,1,2]=>1 [1,1,2,2,3,3]=>0 [1,1,2,1,1,2,1,1,1,1]=>1 [1,1,2,1,1,2,2,2]=>1 [1,1,2,1,1,1,1,2,1,1]=>1 [1,1,2,1,1,1,1,1,1,2]=>1 [1,1,2,1,1,1,2,3]=>1 [1,1,2,1,2,3,1,1]=>1 [1,1,2,1,2,2,1,2]=>2 [1,1,2,1,2,1,1,3]=>2 [1,1,2,1,3,4]=>1 [1,1,3,3,1,1,1,1]=>0 [1,1,3,3,2,2]=>0 [1,1,3,2,1,2,1,1]=>1 [1,1,3,2,1,1,1,2]=>1 [1,1,3,2,2,3]=>2 [1,1,3,1,1,3,1,1]=>1 [1,1,3,1,1,2,1,2]=>2 [1,1,3,1,1,1,1,3]=>1 [1,1,3,1,2,4]=>1 [1,1,4,4,1,1]=>0 [1,1,4,3,1,2]=>1 [1,1,4,2,1,3]=>1 [1,1,4,1,1,4]=>1 [1,1,5,5]=>0 [2,2,1,1,1,1,1,1,1,1]=>0 [2,2,1,1,1,1,2,2]=>1 [2,2,1,1,2,2,1,1]=>1 [2,2,1,1,2,1,1,2]=>2 [2,2,1,1,3,3]=>1 [2,2,2,2,1,1,1,1]=>0 [2,2,2,2,2,2]=>0 [2,2,2,1,1,2,1,1]=>1 [2,2,2,1,1,1,1,2]=>1 [2,2,2,1,2,3]=>1 [2,2,3,3,1,1]=>0 [2,2,3,2,1,2]=>1 [2,2,3,1,1,3]=>1 [2,2,4,4]=>0 [2,1,1,2,1,1,1,1,1,1]=>1 [2,1,1,2,1,1,2,2]=>2 [2,1,1,2,2,2,1,1]=>1 [2,1,1,2,2,1,1,2]=>2 [2,1,1,2,3,3]=>1 [2,1,1,1,1,2,1,1,1,1]=>1 [2,1,1,1,1,2,2,2]=>1 [2,1,1,1,1,1,1,2,1,1]=>1 [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]=>1 [2,1,1,1,2,2,1,2]=>2 [2,1,1,1,2,1,1,3]=>2 [2,1,1,1,3,4]=>1 [2,1,2,3,1,1,1,1]=>1 [2,1,2,3,2,2]=>1 [2,1,2,2,1,2,1,1]=>2 [2,1,2,2,1,1,1,2]=>2 [2,1,2,2,2,3]=>1 [2,1,2,1,1,3,1,1]=>2 [2,1,2,1,1,2,1,2]=>3 [2,1,2,1,1,1,1,3]=>2 [2,1,2,1,2,4]=>2 [2,1,3,4,1,1]=>1 [2,1,3,3,1,2]=>2 [2,1,3,2,1,3]=>2 [2,1,3,1,1,4]=>2 [2,1,4,5]=>1 [3,3,1,1,1,1,1,1]=>0 [3,3,1,1,2,2]=>1 [3,3,2,2,1,1]=>0 [3,3,2,1,1,2]=>1 [3,3,3,3]=>0 [3,2,1,2,1,1,1,1]=>1 [3,2,1,2,2,2]=>1 [3,2,1,1,1,2,1,1]=>1 [3,2,1,1,1,1,1,2]=>1 [3,2,1,1,2,3]=>1 [3,2,2,3,1,1]=>2 [3,2,2,2,1,2]=>1 [3,2,2,1,1,3]=>1 [3,2,3,4]=>2 [3,1,1,3,1,1,1,1]=>1 [3,1,1,3,2,2]=>1 [3,1,1,2,1,2,1,1]=>2 [3,1,1,2,1,1,1,2]=>2 [3,1,1,2,2,3]=>1 [3,1,1,1,1,3,1,1]=>1 [3,1,1,1,1,2,1,2]=>2 [3,1,1,1,1,1,1,3]=>1 [3,1,1,1,2,4]=>1 [3,1,2,4,1,1]=>1 [3,1,2,3,1,2]=>2 [3,1,2,2,1,3]=>2 [3,1,2,1,1,4]=>2 [3,1,3,5]=>1 [4,4,1,1,1,1]=>0 [4,4,2,2]=>0 [4,3,1,2,1,1]=>1 [4,3,1,1,1,2]=>1 [4,3,2,3]=>2 [4,2,1,3,1,1]=>1 [4,2,1,2,1,2]=>2 [4,2,1,1,1,3]=>1 [4,2,2,4]=>2 [4,1,1,4,1,1]=>1 [4,1,1,3,1,2]=>2 [4,1,1,2,1,3]=>2 [4,1,1,1,1,4]=>1 [4,1,2,5]=>1 [5,5,1,1]=>0 [5,4,1,2]=>1 [5,3,1,3]=>1 [5,2,1,4]=>1 [5,1,1,5]=>1 [6,6]=>0
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 sum of the heights of the valleys of the associated bargraph.
Interpret the composition as the sequence of heights of the bars of a bargraph. A valley is a contiguous subsequence consisting of an up step, a sequence of horizontal steps, and a down step. This statistic is the sum of the heights of the valleys.
References
[1] Deutsch, E., Elizalde, S. A bijection between bargraphs and Dyck paths arXiv:1705.05984
Code
def statistic(c):
    v = 0
    found_DH = False
    for i in range(1,len(c)):
        if found_DH:
            if c[i] > c[i-1]:
                found_DH = False
                v += c[i-1]
        else:
            if c[i] < c[i-1]:
                found_DH = True
    return v
Created
May 18, 2017 at 09:37 by Martin Rubey
Updated
Jan 11, 2018 at 10:01 by Martin Rubey