Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stanley depth and size of a monomial ideal   Lyubeznik introduced the concept of size of a monomial ideal and showed that
the size of a monomial ideal increased by $1$ is a lower bound for its depth.
We show that the size is also a lower bound for its Stanley depth. Applying
Alexander duality we obtain upper bounds for the regularity and Stanley
regularity of squarefree monomial ideals.

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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-ex
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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: eess
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The categories of this paper are: patt-sol
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The categories of this paper are: chem-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
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The categories of this paper are: quant-ph
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The categories of this paper are: q-bio
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex
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The categories of this paper are: comp-gas