{"paper":{"title":"The Riemann-Roch theorem for graphs and the rank in complete graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Robert Cori, Yvan Le Borgne","submitted_at":"2013-08-24T13:38:08Z","abstract_excerpt":"The paper by M. Baker and S. Norine in 2007 introduced a new parameter on configurations of graphs and gave a new result in the theory of graphs which has an algebraic geometry flavour. This result was called Riemann-Roch formula for graphs since it defines a combinatorial version of divisors and their ranks in terms of configuration on graphs. The so called chip firing game on graphs and the sandpile model in physics play a central role in this theory.\n  In this paper we give a presentation of the theorem of Baker and Norine in purely combinatorial terms, which is more accessible and shorter "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.5325","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}