{
  "id": "2404.02669",
  "version": "v1",
  "published": "2024-04-03T12:06:05.000Z",
  "updated": "2024-04-03T12:06:05.000Z",
  "title": "Rays of the deformation cones of graphical zonotopes",
  "authors": [
    "Germain Poullot"
  ],
  "comment": "19 pages, 7 figures, 1 table",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper, we compute a triangulation of certain faces of the submodular cone. More precisely, graphical zonotopes are generalized permutahedra, and hence are associated to faces of the submodular cone. We give a triangulation of these faces for graphs without induced complete sub-graph on 4 vertices. This grants us access to the rays of these faces: Minkowski indecomposable deformations of these graphical zonotopes are segments and triangles. Besides, computer experiments lead to examples of graphs without induced complete sub-graph on 5 vertices, whose graphical zonotopes have high dimensional Minkowski indecomposable deformations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-04-03T12:06:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52B05",
      "52B11",
      "52B12",
      "05C20"
    ],
    "keywords": [
      "graphical zonotopes",
      "deformation cones",
      "induced complete sub-graph",
      "submodular cone",
      "high dimensional minkowski indecomposable deformations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}