Positivity in classical enumerative geometry: a case study in synchronized AI-assisted mathematics

ArXi:2605.25271v1 Announce Type: cross We study the symmetric polynomial $\prod_{\alpha\in A_{n,d}}\bigl(1+\alpha_1 x_1+\cdots+\alpha_n x_n\bigr)$ where $A_{n,dalpha\in\mathbb{Z}_{\ge 0}^n:|\alpha|=d\}$, which is the total Chern class of $\mathrm{Sym}^d(\mathbb{C}^n)$, viewed as a torus representation whose Chern roots are the weights $\alpha_1 x_1+\cdots+\alpha_n x_n$ for $\alpha\in A_{n,d}$. Its homogeneous degree-$k$ part $c_k(n,d)$ is the $k$-th Chern class of $\mathrm{Sym}^d(\mathbb{C}^n.