{
  "id": "2311.07133",
  "version": "v1",
  "published": "2023-11-13T08:00:53.000Z",
  "updated": "2023-11-13T08:00:53.000Z",
  "title": "Plane partitions and rowmotion on rectangular and trapezoidal posets",
  "authors": [
    "Joseph Johnson",
    "Ricky Ini Liu"
  ],
  "comment": "40 pages, 17 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "We define a birational map between labelings of a rectangular poset and its associated trapezoidal poset. This map tropicalizes to a bijection between the plane partitions of these posets of fixed height, giving a new bijective proof of a result by Proctor. We also show that this map is equivariant with respect to birational rowmotion, resolving a conjecture of Williams and implying that birational rowmotion on trapezoidal posets has finite order.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-13T08:00:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "plane partitions",
      "birational rowmotion",
      "rectangular poset",
      "birational map",
      "finite order"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}