Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Conjugation of injections by permutations   Let X be a countably infinite set, and let f, g, and h be any three injective
self-maps of X, each having at least one infinite cycle. (For instance, this
holds if f, g, and h are not bijections.) We show that there are permutations a
and b of X such that h=afa^{-1}bgb^{-1} if and only if |X\Xf|+|X\Xg|=|X\Xh|. We
also prove a version of this statement that holds for infinite sets X that are
not necessarily countable. This generalizes results of Droste and Ore about
permutations.

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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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The categories of this paper are: econ
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The categories of this paper are: quant-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-th
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The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
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The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg
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The categories of this paper are: physics
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The categories of this paper are: eess
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The categories of this paper are: chao-dyn
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The categories of this paper are: math-ph