Strict monotonicity conjecture for the threshold m_0(n)

For $n\in\mathbb N$, let $m_0(n)$ be the least positive integer such that the associated Fock-Bargmann-Hartogs domain $D_{n,m}$ is a Lu Qi-Keng domain. Strict monotonicity conjecture. The sequence

$$\{m_0(n)\}_{n=1}^{\infty}$$

is strictly monotonically increasing. The paper proves only that this sequence is monotonically increasing; strictness is suggested by numerical computation and remains open.