Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Maximum, Typical and Generic Ranks   We show that for several notions of rank including tensor rank, Waring rank,
and generalized rank with respect to a projective variety, the maximum value of
rank is at most twice the generic rank. We show that over the real numbers, the
maximum value of the real rank is at most twice the smallest typical rank,
which is equal to the (complex) generic rank.

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The categories of this paper are: patt-sol
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The categories of this paper are: econ
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The categories of this paper are: hep-th
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The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ex
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The categories of this paper are: stat
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The categories of this paper are: nucl-ex