The dimension of the subspace of the complex vector space for the associated Grassmannian. Given an affine permutation, this is $$\frac{1}{n} \sum^n_{i=1} (f(i)-i)$$ This value is seen as $k$ in the notation Gr($k,n$), ($k,n$)-bounded affine permutations, ($k,n$)-Grassmann necklaces, and ($k,n$)-Le diagrams.

The number of weak exceedances of a decorated permutation. A '''weak exceedance''' of a decorated permutation $\tau$ is a position $i$ such that $i > \tau(i)$ or $i = \tau(i)$ and $\tau(i)$ has positive decoration.

The acyclic chromatic index of a graph. An acyclic edge coloring of a graph is a proper colouring of the edges of a graph such that the union of the edges colored with any two given colours is a forest. The smallest number of colours such that such a colouring exists is the acyclic chromatic index.

The diameter of a connected graph. This is the greatest distance between any pair of vertices.

The distinguishing index of a graph. This is the smallest number of colours such that there is a colouring of the edges which is not preserved by any automorphism. If the graph has a connected component which is a single edge, or at least two isolated vertices, this statistic is undefined.

The number of simple modules in the algebra $eAe$ with projective dimension at most 1 in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$.

The number of simple modules in $eAe$ with projective dimension at most 2 in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$.

The maximal dimension of an indecomposable projective $eAe$-module (that is the height of the corresponding Dyck path) of the corresponding Nakayama algebra with minimal faithful projective-injective module $eA$.