5 problems

Let $m$ be the arity of the search tree, let $4\sigma4$ denote the exponent appearing in the asymptotic analysis, and let $\lambda_4$ be the fourth relevant characteristic root. Nu…

Let an STT be a search tree on a tree, and consider the strategy obtained by adapting Splay trees to the STT setting. Splay-tree competitiveness conjecture. The adapted Splay trees…

Protected-node normality conjecture. For $m\leq26$, every additional eigenvalue of $A$ has real part less than $\frac{1}{2}$. Consequently, the number of protected vertices is asym…

Protected-node non-normality conjecture. For every $m\geq27$, the number of protected nodes is not an exceptional asymptotically normal linear combination and has the same non-norm…

Variance and moment convergence conjecture. The variances, and more generally the higher moments, should also converge in the two limit theorems for $Z_n$ and $Y_n$.