Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Results and questions on matchings in groups and vector subspaces of
  fields   A matching from a finite subset $A$ of an abelian group to another subset $B$
is a bijection $f:A\rightarrow B$ with the property that $a+f(a)$ never lies in
$A$. A matching is called acyclic if it is uniquely determined by its
multiplicity function. Motivated by a question of E. K. Wakeford on canonical
forms for symmetric tensors, the study of matchings and acyclic matchings in
abelian groups was initiated by C. K. Fan and J. Losonczy in [16, 26], and was
later generalized to the context of vector subspaces in a field extension [13,
1]. We discuss the acyclic matching and weak acyclic matching properties and we
provide results on the existence of acyclic matchings in finite cyclic groups.
As for field extensions, we completely classify field extensions with the
linear acyclic matching property. The analogy between matchings in abelian
groups and in field extensions is highlighted throughout the paper and numerous
open questions are presented for further inquiry.

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The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
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The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
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The categories of this paper are: physics
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-th
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph