Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Stanley Depth in the Upper Half of the Koszul Complex   Let $R = K[X_1, ..., X_n]$ be a polynomial ring over some field $K$. In this
paper, we prove that the $k$-th syzygy module of the residue class field $K$ of
$R$ has Stanley depth $n-1$ for $\lfloor n/2 \rfloor \leq k < n$, as it had
been conjectured by Bruns et. al. in 2010. In particular, this gives the
Stanley depth for a whole family of modules whose graded components have
dimension greater than $1$. So far, the Stanley depth is known only for a few
examples of this type. Our proof consists in a close analysis of a matching in
the Boolean algebra.

11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
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The categories of this paper are: stat