Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Abelian networks III. The critical group   The critical group of an abelian network is a finite abelian group that
governs the behavior of the network on large inputs. It generalizes the
sandpile group of a graph. We show that the critical group of an irreducible
abelian network acts freely and transitively on recurrent states of the
network. We exhibit the critical group as a quotient of a free abelian group by
a subgroup containing the image of the Laplacian, with equality in the case
that the network is rectangular. We generalize Dhar's burning algorithm to
abelian networks, and estimate the running time of an abelian network on an
arbitrary input up to a constant additive error.

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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
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The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
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The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph