{
  "id": "1511.03568",
  "version": "v1",
  "published": "2015-11-11T16:48:03.000Z",
  "updated": "2015-11-11T16:48:03.000Z",
  "title": "Riemann--Roch theorem on directed graphs",
  "authors": [
    "Bálint Hujter",
    "Lilla Tóthmérész"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Baker and Norine proved a Riemann--Roch theorem for divisors on undirected graphs. The notions of graph divisor theory are in duality with the notions of the chip-firing game. Based on this connection, we give a new proof for the Riemann--Roch theorem on graphs which can be generalized to Eulerian directed graphs, improving a result of Amini and Manjunath. We also give a graph-theoretic version of the abstract Riemann--Roch criterion of Baker and Norine, and explore the natural Riemann--Roch property introduced by Asadi and Backman.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-11-11T16:48:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "riemann-roch theorem",
      "graph divisor theory",
      "abstract riemann-roch criterion",
      "natural riemann-roch property",
      "eulerian directed graphs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}