{
  "id": "2204.04255",
  "version": "v1",
  "published": "2022-04-08T19:11:29.000Z",
  "updated": "2022-04-08T19:11:29.000Z",
  "title": "Birational Rowmotion and the Octahedron Recurrence",
  "authors": [
    "Joseph Johnson",
    "Ricky Ini Liu"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We use the octahedron recurrence to give a simplified statement and proof of a formula for iterated birational rowmotion on a product of two chains, first described by Musiker and Roby. Using this, we show that weights of certain chains in rectangles shift in a predictable way under the action of rowmotion. We then define generalized Stanley-Thomas words whose cyclic rotation uniquely determines birational rowmotion on the product of two chains. We also discuss the relationship between rowmotion and birational RSK and give a birational analogue of Greene's theorem in this setting.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-08T19:11:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "octahedron recurrence",
      "cyclic rotation uniquely determines birational",
      "rotation uniquely determines birational rowmotion",
      "define generalized stanley-thomas words",
      "rectangles shift"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}