Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Counting Free Abelian Actions   We consider the problem of counting commuting r-tuples of elements of the
symmetric group S_n, i.e. computing |Hom(Z^r,S_n)|. The cases r=1,2 are
well-known; a product formula for the case r=3 was conjectured by Adams-Watters
and later proved by Britnell. In this note we solve the problem for arbitrary
r.

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The categories of this paper are: math-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: cond-mat
3
The categories of this paper are: physics
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The categories of this paper are: nucl-th
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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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The categories of this paper are: quant-ph
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The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-th
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The categories of this paper are: nlin
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The categories of this paper are: q-alg