2 problems

Let $(\mathbf{f}^{n})_{n \geq 1}$ be a sequence of face degree sequences, and let $(g_n)$ be a sequence such that $v(\mathbf{f}^{n},g_n)\geq 2$ for all $n\geq 1$. Assume that…

Let $n\geq 1$, and let $\tau$, $\mu$, and $\nu$ be partitions of $n$. For the coefficients $h_{\mu,\nu}^{\tau}(\beta)$ defined by the Jack-polynomial generating series, let the sum…