What is the asymptotic variance of the height of rooted plane trees (ie rooted, unlabelled, ordered trees with unbounded node degree) and of ordered binary trees (ie rooted, unlabelled, plane trees, ...
I've been working on a combinatorics assignment, and while the last few questions had clever solutions which didn't involve functional equations and the use LIFT, I fear I'm at my end. Given a ...
Let $T_v(z)$ be the (exponential) generating function for vertex-rooted (non-plane) trees. Im trying to construct the generating function $T_e(z)$ for edge-rooted trees from this. I know the ...
It is known that the Catalan numbers count the number of binary trees with $k$-internal nodes. I was thinking of how to count ternary trees or in general $n$-ary trees with $k$ internal nodes and got ...
Let be B(z) the exponential generating function for the number $b_n$ of different rooted unordered binary trees with exactly n leaves labeled only at their leaves (so the internal nodes are ...