The Dynkin index of the Lie algebra of given type. This is the greatest common divisor of the Dynkin indices of the representations of the Lie algebra. It is computed in [2, prop.2.6].

The sum of the coefficients of the character polynomial of an integer partition. The definition of the character polynomial can be found in [1].

The number of even parts of a partition.

The number of invariant subsets of size 2 when acting with a permutation of given cycle type.

The number of distinct even parts of a partition. See Section 3.3.1 of [1].

The multiplicity of the sign representation in the Kronecker square corresponding to a partition. The Kronecker coefficient is the multiplicity $g_{\mu,\nu}^\lambda$ of the Specht module $S^\lambda$ in $S^\mu\otimes S^\nu$: $$ S^\mu\otimes S^\nu = \bigoplus_\lambda g_{\mu,\nu}^\lambda S^\lambda $$ This statistic records the Kronecker coefficient $g_{\lambda,\lambda}^{1^n}$, for $\lambda\vdash n$. It equals $1$ if and only if $\lambda$ is self-conjugate.

Half the sum of the even parts of a partition.

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

Half of the largest even part of an integer partition. The largest even part is recorded by [[St000995]].

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