Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pivotal decomposition schemes inducing clones of operations   We study pivotal decomposition schemes and investigate classes of pivotally
decomposable operations. We provide sufficient conditions on pivotal operations
that guarantee that the corresponding classes of pivotally decomposable
operations are clones, and show that under certain assumptions these conditions
are also necessary. In the latter case, the pivotal operation together with the
constant operations generate the corresponding clone.

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The categories of this paper are: nlin
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The categories of this paper are: physics
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: cs
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The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: mtrl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: q-bio
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The categories of this paper are: hep-th
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The categories of this paper are: adap-org
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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph
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The categories of this paper are: q-alg