{
  "id": "2110.07257",
  "version": "v3",
  "published": "2021-10-14T11:08:23.000Z",
  "updated": "2023-11-07T19:09:31.000Z",
  "title": "$P$-associahedra",
  "authors": [
    "Pavel Galashin"
  ],
  "comment": "30 pages, 10 figures; v2: minor bibliography updates; v3: updated title and terminology. Final version to appear in Selecta Mathematica",
  "categories": [
    "math.CO",
    "math.GT"
  ],
  "abstract": "For each poset $P$, we construct a polytope $A(P)$ called the $P$-associahedron. Similarly to the case of graph associahedra, the faces of $A(P)$ correspond to certain nested collections of subsets of $P$. The Stasheff associahedron is a compactification of the configuration space of $n$ points on a line, and we recover $A(P)$ as an analogous compactification of the space of order-preserving maps $P\\to\\mathbb{R}$. Motivated by the study of totally nonnegative critical varieties in the Grassmannian, we introduce affine poset cyclohedra and realize these polytopes as compactifications of configuration spaces of $n$ points on a circle. For particular choices of (affine) posets, we obtain associahedra, cyclohedra, permutohedra, and type B permutohedra as special cases.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2023-11-07T19:09:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52B11",
      "05E99",
      "06A07",
      "54D35"
    ],
    "keywords": [
      "configuration space",
      "affine poset cyclohedra",
      "compactification",
      "graph associahedra",
      "stasheff associahedron"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}