Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000755
Mapping
St000755: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1]
 => 1
[2]
 => 2
[1,1]
 => 1
[3]
 => 1
[2,1]
 => 2
[1,1,1]
 => 1
[4]
 => 2
[3,1]
 => 1
[2,2]
 => 2
[2,1,1]
 => 2
[1,1,1,1]
 => 1
[5]
 => 1
[4,1]
 => 2
[3,2]
 => 1
[3,1,1]
 => 1
[2,2,1]
 => 2
[2,1,1,1]
 => 2
[1,1,1,1,1]
 => 1
[6]
 => 2
[5,1]
 => 1
[4,2]
 => 2
[4,1,1]
 => 2
[3,3]
 => 1
[3,2,1]
 => 1
[3,1,1,1]
 => 1
[2,2,2]
 => 2
[2,2,1,1]
 => 2
[2,1,1,1,1]
 => 2
[1,1,1,1,1,1]
 => 1
[7]
 => 1
[6,1]
 => 2
[5,2]
 => 1
[5,1,1]
 => 1
[4,3]
 => 2
[4,2,1]
 => 2
[4,1,1,1]
 => 2
[3,3,1]
 => 1
[3,2,2]
 => 3
[3,2,1,1]
 => 1
[3,1,1,1,1]
 => 1
[2,2,2,1]
 => 2
[2,2,1,1,1]
 => 2
[2,1,1,1,1,1]
 => 2
[1,1,1,1,1,1,1]
 => 1
[8]
 => 2
[7,1]
 => 1
[6,2]
 => 2
[6,1,1]
 => 2
[5,3]
 => 1
[5,2,1]
 => 1
Description
The number of real roots of the characteristic polynomial of a linear recurrence associated with an integer partition. Consider the recurrence $$f(n)=\sum_{p\in\lambda} f(n-p).$$ This statistic returns the number of distinct real roots of the associated characteristic polynomial. For example, the partition $(2,1)$ corresponds to the recurrence $f(n)=f(n-1)+f(n-2)$ with associated characteristic polynomial $x^2-x-1$, which has two real roots.