A new proof of Cayley's formula for counting labeled trees
The author gives another proof of Cayley's formula \(n^{n- 2}\) for the number of rooted trees with \(n\) labelled nodes. The argument is by induction and involves classifying the trees according to the number of edges \(uv\) contained such that if \(u\) is the node closer to the root then the label of \(u\) exceeds the label of some node in the subtree rooted at \(v\).
scientific article; zbMATH DE number 774651