Root-interlacing conjecture for eigenpolynomials of exactly solvable operators
Let d(z)\mathfrak d(z)d(z) be an exactly solvable operator, and let {Sn(z)}n∈N, n≥n0\{S_n(z)\}_{n\in\mathbb N,\,n\geq n_0}{Sn(z)}n∈N,n≥n0 be its eigenpolynomials with degSn(z)=n\deg S_n(z)=ndegSn(z)=n. Let Sμ\mathfrak S_\muSμ denote th…