An Elementary Proof of the Cayley Formula Using Random Maps
Combinatorics
2014-09-08 v1
Abstract
Cayley's formula states that the number of labelled trees on vertices is , and many of the current proofs involve complex structures or rigorous computation. We present a bijective proof of the formula by providing an elementary calculation of the probability that a cycle occurs in a random map from an -element set to an -element set.
Keywords
Cite
@article{arxiv.1409.1614,
title = {An Elementary Proof of the Cayley Formula Using Random Maps},
author = {Steven Hao and Andrew He and Ray Li and Scott Wu},
journal= {arXiv preprint arXiv:1409.1614},
year = {2014}
}