Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Chorded complexes and a necessary condition for a monomial ideal to have
  a linear resolution   In this paper we extend one direction of Fr\"oberg's theorem on a
combinatorial classification of quadratic monomial ideals with linear
resolutions. We do this by generalizing the notion of a chordal graph to higher
dimensions with the introduction of d-chorded and orientably-d-cycle-complete
simplicial complexes. We show that a certain class of simplicial complexes, the
d-dimensional trees, correspond to ideals having linear resolutions over fields
of characteristic 2 and also give a necessary combinatorial condition for a
monomial ideal to be componentwise linear over all fields.

6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
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The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
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The categories of this paper are: alg-geom