The number of pairwise different full-rank 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. This is the number of all pairwise different full-rank subgroups of $W$ obtained this way. If $\Phi^+$ is an associated set of positive roots, then this also is the number of subsets $Y \subseteq \Phi^+$ such that $Y$ is a simple system of some type and $|Y| = n$, where $n$ is the rank of $W$. For example the group of type $B_2$ has two different subgroups of type $A_1 \times A_1$ and itself as full-rank reflection subgroups.

The number of conjugacy classes in the Weyl group of finite Cartan type whose elements are involutions.

The number of non-empty open intervals in a poset. An open interval $(x, y)$, for $x < y$, is the set of elements $\{z | x < z < y\}$.

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

The number of self-evacuating tableaux of given shape. This is the same as the number of standard domino tableaux of the given shape.

Half the sum of the even parts of a partition.

The largest nonnegative integer which is not a part and is smaller than the largest part of the partition.

The number of graphs with the same edge polytope as the given graph. The symmetric edge polytope of a graph on $n$ vertices is the polytope in $\mathbb R^n$ defined as the convex hull of $e_i + e_j$ for each edge $(i, j)$, where $e_1,\dots, e_n$ denotes the standard basis.

The size of the orbit of an integer partition in Bulgarian solitaire. Bulgarian solitaire is the dynamical system where a move consists of removing the first column of the Ferrers diagram and inserting it as a row. This statistic returns the number of partitions that can be obtained from the given partition.

The largest even part of an integer partition.