Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lengths of paths in rooted trees   We provide formulas for generating functions of many types of paths in
various rooted tree structures. We compute the $k$th moment of the generating
functions for various types of vertical paths. In two specific familes of trees
we find exact closed formulas for expectations and their asymptotic values.
Some of these closed formulas are surprisingly simple.

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The categories of this paper are: solv-int
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
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The categories of this paper are: chem-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: eess
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The categories of this paper are: cond-mat
1
The categories of this paper are: cs
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The categories of this paper are: nucl-th