The largest mu-coefficient of the Kazhdan Lusztig polynomial occurring in the Weyl group of given type. The $\mu$-coefficient of the Kazhdan-Lusztig polynomial $P_{u,w}(q)$ is the coefficient of $q^{\frac{l(w)-l(u)-1}{2}}$ in $P_{u,w}(q)$.

The side length of the Durfee square of an integer partition. Given a partition $\lambda = (\lambda_1,\ldots,\lambda_n)$, the Durfee square is the largest partition $(s^s)$ whose diagram fits inside the diagram of $\lambda$. In symbols, $s = \max\{ i \mid \lambda_i \geq i \}$. This is also known as the Frobenius rank.

The number of singletons of an integer partition. A singleton in an integer partition is a part that appear precisely once.

The floored half-sum of the multiplicities of a partition. This statistic is equidistributed with [[St000143]] and [[St000149]], see [1].

The number of distinct parts of a partition that occur at least twice. See Section 3.3.1 of [2].

The Kreweras number of an integer partition. This is defined for $\lambda \vdash n$ with $k$ parts as $$\frac{1}{n+1}\binom{n+1}{n+1-k,\mu_1(\lambda),\ldots,\mu_n(\lambda)}$$ where $\mu_j(\lambda)$ denotes the number of parts of $\lambda$ equal to $j$, see [1]. This formula indeed counts the number of noncrossing set partitions where the ordered block sizes are the partition $\lambda$. These numbers refine the Narayana numbers $N(n,k) = \frac{1}{k}\binom{n-1}{k-1}\binom{n}{k-1}$ and thus sum up to the Catalan numbers $\frac{1}{n+1}\binom{2n}{n}$.

The number of distinct odd parts smaller than the largest even part in an integer partition.

The number of parts that are equal to their multiplicity in the integer partition.

The number of distinct parts that are equal to their multiplicity in the integer partition.

The number of subpartitions of an integer partition that do not dominate the conjugate subpartition. In particular, partitions with statistic $0$ are wide partitions.