Asymptotics of trees with a prescribed degree sequence and applications

Nicolas Broutin, Jean-François Marckert

Let $t$ be a rooted tree and $n_i(t)$ the number of nodes in $t$ having $i$ children. The degree sequence $(n_i(t),i\ge 0)$ of $t$ satisfies $\sum_{i\ge 0} n_i(t)=1+\sum_{i\ge 0}…