Your data matches 1 statistic following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000763
Mapping
St000763: Integer compositions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => 1
[1,1] => 1
[2] => 1
[1,1,1] => 1
[1,2] => 3
[2,1] => 1
[3] => 1
[1,1,1,1] => 1
[1,1,2] => 4
[1,2,1] => 3
[1,3] => 3
[2,1,1] => 1
[2,2] => 1
[3,1] => 1
[4] => 1
[1,1,1,1,1] => 1
[1,1,1,2] => 5
[1,1,2,1] => 4
[1,1,3] => 4
[1,2,1,1] => 3
[1,2,2] => 3
[1,3,1] => 3
[1,4] => 3
[2,1,1,1] => 1
[2,1,2] => 1
[2,2,1] => 1
[2,3] => 3
[3,1,1] => 1
[3,2] => 1
[4,1] => 1
[5] => 1
[1,1,1,1,1,1] => 1
[1,1,1,1,2] => 6
[1,1,1,2,1] => 5
[1,1,1,3] => 5
[1,1,2,1,1] => 4
[1,1,2,2] => 4
[1,1,3,1] => 4
[1,1,4] => 4
[1,2,1,1,1] => 3
[1,2,1,2] => 3
[1,2,2,1] => 3
[1,2,3] => 6
[1,3,1,1] => 3
[1,3,2] => 3
[1,4,1] => 3
[1,5] => 3
[2,1,1,1,1] => 1
[2,1,1,2] => 1
[2,1,2,1] => 1
Description
The sum of the positions of the strong records of an integer composition. A strong record is an element $a_i$ such that $a_i > a_j$ for all $j < i$. This statistic is the sum of the positions of the strong records.