{
  "annotation_id": "6ff7b2da-58b9-4808-b58a-f17ab2cfd13c",
  "date_created": "2026-02-17T05:53:20.519000Z",
  "date_modified": "2026-02-17T05:53:20.519000Z",
  "file_hash": "6f21069b5e0c6c081d0fd6443f5bcf899ce3b117df7eafe11d109480b2b5703d",
  "private": false,
  "record": {
    "abstract": "In this note, we characterize affine Coxeter systems among all Coxeter systems in terms of the structure of their reflection orders. For an infinite irreducible system $(W,S)$, we show that affineness is equivalently characterized by the scatteredness of all reflection orders, by the existence of a reflection order of type $\\omega+\\omega^*$, and by a finiteness property of intervals determined by dihedral reflection subgroups. Our proof exploits the geometry of projective roots, the isotropic cone and the universal reflection subgroups in an infinite non-affine Coxeter group.",
    "arxiv_id": "2601.09275",
    "authors": [
      "Weijia Wang",
      "Rui Wang"
    ],
    "categories": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "A note on the scatteredness of reflection orders",
    "url": "https://arxiv.org/abs/2601.09275",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "d947961b-0a48-49ef-bf53-5b473b6c1283",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}