2010/12/21 by Victor Ermolaev, Victor N. Ermolaev, Ermolaev, Victor N. +2
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Bayesian Methods and Mixture Models #Data Management and Algorithms #math.CO
paper · pdf · doi:10.48550/arxiv.1012.4654
This paper has been withdrawn by the author due to a crucial error in counting unlabeled trees
arxiv created 2011/01/31 · arxiv updated 2011/02/01
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