Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The cleanness of (symbolic) powers of Stanley-Reisner ideals   Let $\Delta$ be a pure simplicial complex and $I_\Delta$ its Stanley-Reisner
ideal in a polynomial ring $S$. We show that $\Delta$ is a matroid (complete
intersection) if and only if $S/I_\Delta^{(m)}$ ($S/I_\Delta^m$) is clean for
all $m\in\mathbb{N}$. If $\dim(\Delta)=1$, we also prove that
$S/I_\Delta^{(2)}$ ($S/I_\Delta^2$) is clean if and only if $S/I_\Delta^{(2)}$
($S/I_\Delta^2$) is Cohen-Macaulay.

29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio