4 problems

Let $d\geq 2$ and $k\geq 1$ be fixed positive integers. Let $E_n^d$ denote the even $d$-ary tree with $n$ leaves, let $c(E_k^d,T)$ denote the number of copies of $E_k^d$ in a $d$-a…

Let $d$ and $k$ be positive integers, and let $E_k^d$ be an even $d$-ary tree. For strictly $d$-ary trees $T$ with $(d-1)n+1$ leaves, write $\gamma(E_k^d,T)$ for the normalized num…

Arity-dependence conjecture. Among all $d$-ary trees $D$, only binary trees satisfy

Czabarka–et al. conjecture. For every binary tree $B$, the asymptotic formula