4 problems

Universal height lower-bound conjecture. For any permuton $cmu$ and $cvarepsilon>0$,

Let ${\mathcal{A}}$ be an online binary search tree algorithm. Starting with any initial tree $T$ with $n$ elements, let $X$ be the preorder sequence of a binary search tree $T'$ t…

Let ${\mathcal{A}}$ be an online binary search tree algorithm. Starting with any initial tree $T$ with $n$ elements, consider any sequence of $n$ splits. A split at an element $x$…

Let ${\mathcal{A}}$ be an online binary search tree algorithm. Starting with any initial tree $T$ with $n$ elements, consider inserting or deleting the current minimum or maximum e…