Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Classes of Lattices Induced by Chip Firing (and Sandpile) Dynamics   In this paper we study three classes of models widely used in physics,
computer science and social science: the Chip Firing Game, the Abelian Sandpile
Model and the Chip Firing Game on a mutating graph. We study the set of
configurations reachable from a given initial configuration, called the
configuration space of a model, and try to determine the main properties of
such sets. We study the order induced over the configurations by the evolution
rule. This makes it possible to compare the power of expression of these
models. It is known that the configuration spaces we obtain are lattices, a
special kind of partially ordered set. Although the Chip Firing Game on a
mutating graph is a generalization of the usual Chip Firing Game, we prove that
these models generate exactly the same configuration spaces. We also prove that
the class of lattices induced by the Abelian Sandpile Model is strictly
included in the class of lattices induced by the Chip Firing Game, but contains
the class of distributive lattices, a very well known class.

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The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: stat
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The categories of this paper are: supr-con
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The categories of this paper are: acc-phys
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The categories of this paper are: funct-an
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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: hep-ph
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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
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The categories of this paper are: q-fin
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The categories of this paper are: nlin
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The categories of this paper are: eess
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The categories of this paper are: nucl-th