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 ...