A note on counting labeled and unlabeled trees
Combinatorics
2011-02-01 v2
Abstract
We provide a short combinatorial proof of Cayley's formula by means of a bijective map to an outcome space of an urn-drawing problem. Furthermore we introduce an algebraic structure on the set of labeled trees, which provides a more standard approach to Cayley's formula. Moreover, this algebraic structure sheds light on the problem of counting the unlabeled trees. In particular, it indicates how counting the number of unlabeled trees on vertices is connected to finding the number of partitions of
Cite
@article{arxiv.1012.4654,
title = {A note on counting labeled and unlabeled trees},
author = {Victor N. Ermolaev and Giulio Iacobelli},
journal= {arXiv preprint arXiv:1012.4654},
year = {2011}
}
Comments
This paper has been withdrawn by the author due to a crucial error in counting unlabeled trees