2 problems

Let $g\geq 2$, let $\ell$ be a positive integer, and let $\mu=(m_1,\ldots,m_k)$ be a partition of $\ell(2g-2)$ with $m_i\neq-\ell$ for every $i$. Let $\mathcal{P}^\ell(\mu)$ be the…

Let $g,n\geq 0$ and let $k$ be a positive odd integer. Let $\mu=(m_1,\ldots,m_n)\in\mathbb{Z}^n\setminus k\mathbb{Z}^n_{\geq 0}$ satisfy … with all entries of $\mu$ even. Let…