Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tutte polynomial, subgraphs, orientations and sandpile model: new
  connections via embeddings   For any graph G with n edges, the spanning subgraphs and the orientations of
G are both counted by the evaluation T_G(2,2)=2^n of its Tutte polynomial. We
define a bijection $\Phi$ between spanning subgraphs and orientations and
explore its enumerative consequences regarding the Tutte polynomial. The
bijection $\Phi$ is closely related to a recent characterization of the Tutte
polynomial relying on a combinatorial embedding of the graph G, that is, on a
choice of cyclic order of the edges around each vertex. Among other results, we
obtain a combinatorial interpretation for each of the evaluations T_G(i,j),
0\leq i,j \leq 2 of the Tutte polynomial in terms of orientations. The strength
of our approach is to derive all these interpretations by specializing the
bijection $\Phi$ in various ways. For instance, we obtain a bijection between
the connected subgraphs of G (counted by T_G(1,2)) and the root-connected
orientations. We also obtain a bijection between the forests (counted by
T_G(2,1)) and outdegree sequences which specializes into a bijection between
spanning trees (counted by T_G(1,1)) and root-connected outdegree sequences. We
also define a bijection between spanning trees and recurrent configurations of
the sandpile model. Combining our results we obtain a bijection between
recurrent configurations and root-connected outdegree sequences which leaves
the configurations at level 0 unchanged.

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The categories of this paper are: quant-ph
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The categories of this paper are: physics
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The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: econ
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: supr-con
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The categories of this paper are: comp-gas
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The categories of this paper are: cmp-lg
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The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: cs
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The categories of this paper are: acc-phys