Some New Methods and Results in Tree Enumeration

A wide variety of new results in combinatorial enumeration have been obtained recently. Many of these results were prompted by new problems in computer science, while others answered old questions in combinatorics and other fields. The purpose of this note is to survey a subset of these new results, namely those dealing with tree enumeration. A selection of tree enumeration results is presented, together with a discussion of the methods that led to their derivation. No complete proofs are given; instead, the concentration is on heuristics and on the extent to which these methods can be generalized. The selection of techniques and results is made from those the author has worked on, and several other survey papers on related results could also be written without exhausting the subject.