3 problems

Let $\mathcal T_{\boldsymbol{n}_\kappa}$ be a random tree with prescribed degree-count vector $\boldsymbol{n}_\kappa$, and let $N_{m_\kappa}(\mathcal T_{\boldsymbol{n}_\kappa})$ de…

Let $\boldsymbol{p}$ be the limit distribution satisfying Condition1, let $\boldsymbol{n}_\kappa$ be the prescribed degree-count vector, and let $T_\kappa$ be a tree with…

Let $T_n$ be a recursive tree with $n$ vertices, and let $f(T_n)$ denote the set of non-isomorphic fringe subtrees of $T_n$. The expected number of such subtrees is bounded above b…