N. Biggs, Algebraic Potential Theory on Graphs, Bulletin of the London Mathematical Society, vol.29, issue.6, pp.641-682, 1997.
DOI : 10.1112/S0024609397003305

M. Baker and S. Norine, Riemann???Roch and Abel???Jacobi theory on a finite graph, Advances in Mathematics, vol.215, issue.2, pp.766-788, 2007.
DOI : 10.1016/j.aim.2007.04.012

F. [. Baker and . Shokrieh, Chip-firing games, potential theory on graphs, and spanning trees, Journal of Combinatorial Theory, Series A, vol.120, issue.1, pp.164-182, 2013.
DOI : 10.1016/j.jcta.2012.07.011

S. [. Conca, R. R. Hos¸tenhos¸ten, and . Thomas, Nice initial complexes of some classical ideals, Algebraic and geometric combinatorics, pp.11-42, 2006.
DOI : 10.1090/conm/423/08073

R. Cori, D. Rossin, and B. Salvy, Polynomial ideals for sandpiles and their Gr??bner bases, Theoretical Computer Science, vol.276, issue.1-2, pp.1-15, 2002.
DOI : 10.1016/S0304-3975(00)00397-2

D. Dhar, Self-organized critical state of sandpile automaton models, Physical Review Letters, vol.64, issue.14, pp.1613-1616, 1990.
DOI : 10.1103/PhysRevLett.64.1613

R. [. Dochtermann and . Sanyal, Laplacian ideals, arrangements, and resolutions, Journal of Algebraic Combinatorics, vol.356, issue.3, 2012.
DOI : 10.1007/s10801-014-0508-7

]. D. Eis95 and . Eisenbud, Commutative algebra, with a view toward algebraic geometry, volume 150 of Graduate Texts in Mathematics, 1995.

A. Gabrielov, Abelian avalanches and Tutte polynomials, Physica A: Statistical Mechanics and its Applications, vol.195, issue.1-2, pp.253-274, 1993.
DOI : 10.1016/0378-4371(93)90267-8

A. Gathmann and M. Kerber, A Riemann???Roch theorem in tropical geometry, Mathematische Zeitschrift, vol.112, issue.1, pp.217-230, 2008.
DOI : 10.1007/s00209-007-0222-4

G. [. Greuel and . Pfister, A Singular introduction to commutative algebra, 2008.
DOI : 10.1007/978-3-662-04963-1

D. Lorenzini, Arithmetical graphs, Mathematische Annalen, vol.96, issue.3, pp.481-501, 1989.
DOI : 10.1007/BF01455069

H. Mania, Wilmes' conjecture and boundary divisors, 2012.

E. Miller and B. Sturmfels, Combinatorial commutative algebra, Graduate Texts in Mathematics, vol.227, 2005.

F. Mohammadi and F. Shokrieh, Divisors on Graphs, Connected Flags, and Syzygies, International Mathematics Research Notices, 2012.
DOI : 10.1093/imrn/rnt186
URL : https://hal.archives-ouvertes.fr/hal-01229678

F. Mohammadi and F. Shokrieh, Divisors on graphs and cellular resolutions, preparation, 2013.
DOI : 10.1007/s00209-015-1589-2
URL : http://arxiv.org/abs/1306.5351

M. Manjunath, F. Schreyer, and J. Wilmes, Minimal free resolutions of the $G$-parking function ideal and the toppling ideal, Transactions of the American Mathematical Society, vol.367, issue.4, 2012.
DOI : 10.1090/S0002-9947-2014-06248-X

G. Mikhalkin and I. Zharkov, Tropical curves, their Jacobians and theta functions, Curves and abelian varieties, pp.203-230, 2008.
DOI : 10.1090/conm/465/09104

J. [. Perkinson, J. Perlman, and . Wilmes, Primer for the algebraic geometry of sandpiles, 2011.
DOI : 10.1090/conm/605/12117

B. [. Postnikov and . Shapiro, Trees, parking functions, syzygies, and deformations of monomial ideals, Transactions of the American Mathematical Society, vol.356, issue.08, pp.3109-3142, 2004.
DOI : 10.1090/S0002-9947-04-03547-0

M. Raynaud, Sp??cialisation du foncteur de Picard, Publications math??matiques de l'IH??S, vol.264, issue.1, pp.27-76, 1970.
DOI : 10.1007/BF02684651
URL : http://archive.numdam.org/article/PMIHES_1970__38__27_0.pdf

F. Schreyer, Die Berechnung von Syzygien mit dem verallgemeinerten Weierstrass'schen Divisionssatz, 1980.