3 problems

Consider the generating series … Set … where $\mathsf{S}^\bullet$ denotes the plethystic exponential, and let $[H(q,t)]^{i,j}$ denote the coefficient of $q^it^j$ in the expansion a…

For the local $\mathbb{P}^2$, let $\widetilde{n}_d^{i,j}$ denote the combinatorial refined BPS invariants obtained from the Nekrasov partition function, and let $n_d^{i,j}$ denote…

Let $t_{\mathrm{con}}$ be the flat coordinate near the conifold point, and let $F_{g,\mathrm{con}}^{\mathbb{P}^2\!/\!E}$ denote the genus-$g$ free energy expressed as a function of…