2 problems

Monotonicity conjecture. The sequence $\{K_i\}_{i=1}^{\infty}$ is monotonically increasing and positive, and satisfies

Let $\bar z_i$ be the secondary intermediate nodes and let the first-order partial moments be defined by $\alpha_0=0$ and $\alpha_i=\alpha_{i-1}-2x_iw_i$. Partial-moment conjecture…