Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The converse of a theorem by Bayer and Stillman   Bayer-Stillman showed that $reg(I) = reg(gin_\tau(I))$ when $\tau$ is the
graded reverse lexicographic order. We show that the reverse lexicographic
order is the unique monomial order $\tau$ satisfying $reg(I) =
reg(gin_\tau(I))$ for all ideals $I$. We also show that if $gin_{\tau_1}(I) =
gin_{\tau_2}(I)$ for all $I$, then $\tau_1 = \tau_2$.

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The categories of this paper are: gr-qc
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The categories of this paper are: cs
31
The categories of this paper are: ao-sci
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ph
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The categories of this paper are: stat
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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: nucl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
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The categories of this paper are: econ