Labeled trees, maps, and an algebraic identity
Combinatorics
2016-01-20 v2
Abstract
We give a short and direct proof of a remarkable identity that arises in the enumeration of labeled trees with respect to their indegree sequence, where all edges are oriented from the vertex with lower label towards the vertex with higher label. This solves a problem posed by Shin and Zeng in a recent article. We also provide a generalization of this identity that translates to a formula for the number of rooted spanning forests with given indegree sequence.
Keywords
Cite
@article{arxiv.1106.3221,
title = {Labeled trees, maps, and an algebraic identity},
author = {Stephan Wagner},
journal= {arXiv preprint arXiv:1106.3221},
year = {2016}
}