The number of small weak excedances. A small weak excedance is an index $i$ such that $\pi_i \in \{i,i+1\}$. This is the sum of [[St000022]] and [[St000237]].

The radius of a connected graph. This is the minimum eccentricity of any vertex.

The number of positive values of the symmetric group character corresponding to the partition. For example, the character values of the irreducible representation $S^{(2,2)}$ are $2$ on the conjugacy classes $(4)$ and $(2,2)$, $0$ on the conjugacy classes $(3,1)$ and $(1,1,1,1)$, and $-1$ on the conjugacy class $(2,1,1)$. Therefore, the statistic on the partition $(2,2)$ is $2$.

The product of the parts of an integer partition.

The number of characters of the symmetric group whose value on the partition is positive.

The Grundy value of Chomp on Ferrers diagrams. Players take turns and choose a cell of the diagram, cutting off all cells below and to the right of this cell in English notation. The player who is left with the single cell partition looses. The traditional version is played on chocolate bars, see [1]. This statistic is the Grundy value of the partition, that is, the smallest non-negative integer which does not occur as value of a partition obtained by a single move.