The cardinality of a minimal edge-isolating set of a graph. Let $\mathcal F$ be a set of graphs. A set of vertices $S$ is $\mathcal F$-isolating, if the subgraph induced by the vertices in the complement of the closed neighbourhood of $S$ does not contain any graph in $\mathcal F$. This statistic returns the cardinality of the smallest isolating set when $\mathcal F$ contains only the graph with one edge.

The number of descents of type 2 in a permutation. A position $i\in[1,n-1]$ is a descent of type 2 of a permutation $\pi$ of $n$ letters, if it is a descent and if $\pi(j) < \pi(i)$ for all $j < i$.

The minimum jump of a permutation. This is $\min_i |\pi_{i+1}-\pi_i|$, see [1].

The dominant dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$.

The number of monotone factorisations of genus zero of a permutation of given cycle type. A monotone factorisation of genus zero of a permutation $\pi\in\mathfrak S_n$ with $\ell$ cycles, including fixed points, is a tuple of $r = n - \ell$ transpositions $$ (a_1, b_1),\dots,(a_r, b_r) $$ with $b_1 \leq \dots \leq b_r$ and $a_i < b_i$ for all $i$, whose product, in this order, is $\pi$. For example, the cycle $(2,3,1)$ has the two factorizations $(2,3)(1,3)$ and $(1,2)(2,3)$.

The order dimension of the partition. Given a partition $\lambda$, let $I(\lambda)$ be the principal order ideal in the Young lattice generated by $\lambda$. The order dimension of a partition is defined as the order dimension of the poset $I(\lambda)$.

The total number of irreducible representations contained in the higher Lie character for an integer partition.