3 problems

Let $n \geq 4$. A path tree is the path-tree object used in the paper, and a parse word is a word that parses a binary tree. Double-zero parse-word conjecture. Every pair of $n$-le…

Let $n \geq 4$, and let $T_1$ and $T_2$ be $n$-leaf path trees such that leaf $1$ is on level $1$ in $T_1$ and leaf $n$ is on level $1$ in $T_2$. A pair is mutually crooked if it c…

Let $T_1'$ and $T_2'$ be $(n-1)$-leaf binary trees. Let $1 \leq i \leq n-1$, and let $T_1$ and $T_2$ be the $n$-leaf trees obtained from $T_1'$ and $T_2'$ by duplicating leaf $i$.…