Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on counting labeled and unlabeled trees   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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The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
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The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: funct-an
16
The categories of this paper are: stat
14
The categories of this paper are: math-ph
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The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg