The determinant of the Cartan matrix. This is also the order of the center of the corresponding simply connected group.

The largest coefficient in the highest root in the root system of a Cartan type.

The number of types of reflection subgroups of the associated Weyl group. Let $\mathcal{R} \subseteq W$ be the set of reflections in the Weyl group $W$. A (possibly empty) subset $X \subseteq \mathcal{R}$ generates a subgroup of $W$ that is again a reflection group of some (not necessarily reduced) finite type. This is the number of all pairwise different types of subgroups of $W$ obtained this way (including type $A_0$).

The number of minuscule dominant weights in the weight lattice of a finite Cartan type. In short, this is the number of simple roots that appear with multiplicity one in the hightest root of the root system. By definition, a weight $\lambda \neq 0$ in the weight lattice is '''dominant''' if $\langle \lambda, \alpha\rangle \geq 0$ for all simple roots $\alpha$ and a dominant weight is '''minuscule''' if $\langle \lambda, \beta\rangle \in \{0,\pm 1\}$ for all roots $\beta$. Since $\langle \lambda, \alpha\rangle \in \{0,1\}$ for simple roots $\alpha$, we have that $\lambda$ is minuscule if and only if it is fundamental and $\langle \lambda, \rho\rangle = 1$ for the unique highest root $\rho$. The number of minuscule dominant weights is one less than the determinant of the Cartan matrix [[St000821]]. They index the nontrivial minuscule representations, see [1].

The permanent of the Cartan matrix of a finite Cartan type.

The cardinality of a maximal independent set of vertices of a graph. An independent set of a graph is a set of pairwise non-adjacent vertices. A maximum independent set is an independent set of maximum cardinality. This statistic is also called the independence number or stability number $\alpha(G)$ of $G$.

The number of 2-rim hooks removed from an integer partition to obtain its associated 2-core. For any positive integer $k$, one associates a $k$-core to a partition by repeatedly removing all rim hooks of size $k$. This statistic counts the $2$-rim hooks that are removed in this process to obtain a $2$-core.

The maximal number of occurrences of a colour in a proper colouring of a graph. To any proper colouring with the minimal number of colours possible we associate the integer partition recording how often each colour is used. This statistic records the largest part occurring in any of these partitions. For example, the graph on six vertices consisting of a square together with two attached triangles - ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6) in the list of values - is three-colourable and admits two colouring schemes, $[2,2,2]$ and $[3,2,1]$. Therefore, the statistic on this graph is $3$.

The annihilation number of a graph. For a graph on $m$ edges with degree sequence $d_1\leq\dots\leq d_n$, this is the largest number $k\leq n$ such that $\sum_{i=1}^k d_i \leq m$.

The dissociation number of a graph.