Identifier
Values
['A',1] => ([],1) => [2] => 2
['A',2] => ([(0,2),(1,2)],3) => [3,2] => 1
['B',2] => ([(0,3),(1,3),(3,2)],4) => [4,2] => 2
['G',2] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => [6,2] => 2
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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.
Map
to root poset
Description
The root poset of a finite Cartan type.
This is the poset on the set of positive roots of its root system where $\alpha \prec \beta$ if $\beta - \alpha$ is a simple root.
Map
rowmotion cycle type
Description
The cycle type of rowmotion on the order ideals of a poset.