Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Four generated, squarefree, monomial ideals   Let $I\supsetneq J$ be two squarefree monomial ideals of a polynomial algebra
over a field generated in degree $\geq d$, resp. $\geq d+1$ . Suppose that $I$
is either generated by three monomials of degrees $d$ and a set of monomials of
degrees $\geq d+1$, or by four special monomials of degrees $d$. If the Stanley
depth of $I/J$ is $\leq d+1$ then the usual depth of $I/J$ is $\leq d+1$ too.

3
The categories of this paper are: physics
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The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
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The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: quant-ph