A note on counting labeled and unlabeled trees

Details A note on counting labeled and unlabeled trees A note on counting labeled and unlabeled trees

2010-12-21

arxiv.org/abs/1012.4654v2

Mathematics

Combinatorics

This paper has been withdrawn by the author due to a crucial error in counting unlabeled trees

Scientific paper

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 $n$ vertices is connected to finding the number of partitions of $n-2$

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