Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some examples of forms of high rank   We describe some forms with greater Waring rank than previous examples. In
$3$ variables we give forms of odd degree with strictly greater rank than the
ranks of monomials, the previously highest known rank. This narrows the
possible range of values of the maximum Waring rank of forms in $3$ variables.
In $4$ variables we give forms of odd degree with strictly greater than generic
rank. In degrees greater than or equal to $5$ these are the first examples
showing that there exist forms with Waring rank strictly greater than the
generic value.

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The categories of this paper are: stat
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The categories of this paper are: econ
37
The categories of this paper are: supr-con
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The categories of this paper are: cs
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The categories of this paper are: acc-phys
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The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: q-alg
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The categories of this paper are: hep-lat
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The categories of this paper are: comp-gas
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The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: ao-sci