The Grundy value for the game of deleting vertices of a graph until it has no edges.

The number of distinct even parts of a partition. See Section 3.3.1 of [1].

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.

The Grundy value of the game of creating an independent set in a graph. Two players alternately add a vertex to an initially empty set, which is not adjacent to any of the vertices it already contains. Alternatively, the game can be described as starting with a graph, the players remove vertices together with their neighbors, until the graph is empty.

The BG-rank of an integer partition. This is the sum of the entries in a checkerboard filling of the Ferrers diagram of the partition, where cells whose sum of coordinates is even have entry $+1$ and the others have entry $-1$.

The number of join prime elements of a lattice. An element $x$ of a lattice $L$ is join-prime (or coprime) if $x \leq a \vee b$ implies $x \leq a$ or $x \leq b$ for every $a, b \in L$.

The radius of a connected graph. This is the minimum eccentricity of any vertex.