All Questions

Is there an algorithmic way to map the natural numbers to unique k-ary trees? I am familiar with the work of Tychonievich who created a mapping from integers to binary trees. https://www.cs.virginia....

I wonder what is known on the following: 1) What is the number $T_k(n)$ of $k$-tuples of (pairwise) edge-disjoint trees $(T_1,T_2,\dots, T_k)$ with $n$ labelled vertices? 2) (harder, it seems) What ...

Recall that rooted trees may be generated by starting with a trivial rooted tree (just a vertex), along with the operations of grafting a number of trees (identify their roots) and adding a new vertex ...