{
  "id": "1809.07728",
  "version": "v1",
  "published": "2018-09-20T16:34:06.000Z",
  "updated": "2018-09-20T16:34:06.000Z",
  "title": "The Abelian sandpile model on Ferrers graphs - A classification of recurrent configurations",
  "authors": [
    "Mark Dukes",
    "Thomas Selig",
    "Jason P. Smith",
    "Einar Steingrimsson"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We classify all recurrent configurations of the Abelian sandpile model (ASM) on Ferrers graphs. The classification is in terms of decorations of EW-tableaux, which undecorated are in bijection with the minimal recurrent configurations. We introduce decorated permutations, extending to decorated EW-tableaux a bijection between such tableaux and permutations, giving a direct bijection between the decorated permutations and all recurrent configurations of the ASM. We also describe a bijection between the decorated permutations and the intransitive trees of Postnikov, the breadth-first search of which corresponds to a canonical toppling of the corresponding configurations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-20T16:34:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "abelian sandpile model",
      "ferrers graphs",
      "classification",
      "decorated permutations",
      "minimal recurrent configurations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}