Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rotor-routing and spanning trees on planar graphs   The sandpile group Pic^0(G) of a finite graph G is a discrete analogue of the
Jacobian of a Riemann surface which was rediscovered several times in the
contexts of arithmetic geometry, self-organized criticality, random walks, and
algorithms. Given a ribbon graph G, Holroyd et al. used the "rotor-routing"
model to define a free and transitive action of Pic^0(G) on the set of spanning
trees of G. However, their construction depends a priori on a choice of
basepoint vertex. Ellenberg asked whether this action does in fact depend on
the choice of basepoint. We answer this question by proving that the action of
Pic^0(G) is independent of the basepoint if and only if G is a planar ribbon
graph.

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The categories of this paper are: acc-phys
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The categories of this paper are: chem-ph
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The categories of this paper are: math-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: alg-geom
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The categories of this paper are: cs
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th
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The categories of this paper are: nlin
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The categories of this paper are: bayes-an