{
  "annotation_id": "a4ddd7d2-7e4b-4e19-957a-329e54366a0b",
  "date_created": "2026-02-17T05:53:07.826000Z",
  "date_modified": "2026-02-17T05:53:07.826000Z",
  "file_hash": "eb375be57b9aeab171dd95c7ce4a9473c12f3b46e32942cad1c097d01c8864f3",
  "private": false,
  "record": {
    "abstract": "Inspired by the Erd\\H{o}s R\\\u0027enyi model, we propose a new model for freesquare random monomial ideals generated by edges and covers of a graph. This permit us to investigate the conditions of normality for which we obtain asymptotic results. We also elaborate on asymptotic results for other invariants such as the Krull dimension (for which we obtain threshold function), the regularity and the $v$-number.",
    "arxiv_id": "2601.06739",
    "authors": [
      "Daniel Munoz George",
      "Humberto Mu\u00f1oz-George",
      "Kevin Mu\u00f1oz George"
    ],
    "categories": [
      "math.AC",
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Probabilities of random monomial ideals associated to large graphs",
    "url": "https://arxiv.org/abs/2601.06739",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "84fb90d2-6e52-4e28-b1e3-549de9d9c0b9",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}