The number of standard Young tableaux whose descent set is the binary word. A descent in a standard Young tableau is an entry $i$ such that $i+1$ appears in a lower row in English notation. For example, the tableaux $[[1,2,4],[3]]$ and $[[1,2],[3,4]]$ are those with descent set $\{2\}$, corresponding to the binary word $010$.

The global dimension of the incidence algebra of the lattice over the rational numbers.

The rank-width of a graph.

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

The 3-weak dynamic number of a graph. A $k$-weak-dynamic coloring of a graph $G$ is a (non-proper) coloring of $G$ in such a way that each vertex $v$ sees at least $\min\{d(v), k\}$ colors in its neighborhood. The $k$-weak-dynamic number of a graph is the smallest number of colors needed to find an $k$-dynamic coloring. This statistic records the $3$-weak-dynamic number of a graph.

The induced matching number of a graph. An induced matching of a graph is a set of independent edges which is an induced subgraph. This statistic records the maximal number of edges in an induced matching.

The number of maximal dissociation sets in a graph.

The 1-improper chromatic number of a graph. This is the least number of colours in a vertex-colouring, such that each vertex has at most one neighbour with the same colour.

The degree of the minimal polynomial of the smallest eigenvalue of a graph.