{
  "id": "2308.07409",
  "version": "v1",
  "published": "2023-08-14T18:56:43.000Z",
  "updated": "2023-08-14T18:56:43.000Z",
  "title": "Painted Tropical Complexes",
  "authors": [
    "Gabriel Kerr",
    "Sophia Palcic"
  ],
  "comment": "18 pages, 8 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "We define the notion of a painted tropical $A$-complex and describe a poset structure on the set of all such complexes. This poset is equivalent to the face lattice of a secondary polytope $\\Sigma (\\bar{A}_\\alpha )$ where $\\bar{A}_\\alpha$ is built from $A$ and an additional point $\\alpha$. As a central application, we show that multiplihedra are also secondary polytopes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-14T18:56:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52B12",
      "51M20"
    ],
    "keywords": [
      "painted tropical complexes",
      "secondary polytope",
      "face lattice",
      "poset structure",
      "central application"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}