The number of commutative positive roots in the root system of the given finite Cartan type. An upper ideal $I$ in the root poset $\Phi^+$ is called '''abelian''' if $\alpha,\beta \in I$ implies that $\alpha+\beta \notin \Phi^+$. A positive root is called '''commutative''' if the upper ideal it generates is abelian. The numbers are then given in [1, Theorem 4.4].

The maximal number of elements covering an element of a poset.

The number of potential covers of a poset. A potential cover is a pair of uncomparable elements $(x, y)$ which can be added to the poset without adding any other relations. For example, let $P$ be the disjoint union of a single relation $(1, 2)$ with the one element poset $0$. Then the relation $(0, 1)$ cannot be added without adding also $(0, 2)$, however, the relations $(0, 2)$ and $(1, 0)$ are potential covers.

The number of distinct eigenvalues of a graph.

The number of different non-empty partial sums of an integer partition.

The number of different neighbourhoods in a graph.

The sum of the entries in the column specified by the partition of the change of basis matrix from elementary symmetric functions to Schur symmetric functions. For example, $e_{22} = s_{1111} + s_{211} + s_{22}$, so the statistic on the partition $22$ is $3$.

The evaluation of the Tutte polynomial of the graph at x and y equal to 3.

The 2-dynamic chromatic number of a graph. A $k$-dynamic coloring of a graph $G$ is a proper coloring of $G$ in such a way that each vertex $v$ sees at least $\min\{d(v), k\}$ colors in its neighborhood. The $k$-dynamic chromatic number of a graph is the smallest number of colors needed to find an $k$-dynamic coloring. This statistic records the $2$-dynamic chromatic number of a graph.

The number of dominating sets of vertices of a graph. This is, the number of subsets of vertices such that every vertex is either in this subset or adjacent to an element therein [1].