{
  "id": "2405.04361",
  "version": "v1",
  "published": "2024-05-07T14:40:42.000Z",
  "updated": "2024-05-07T14:40:42.000Z",
  "title": "On the Iwasawa theory of Cayley graphs",
  "authors": [
    "Sohan Ghosh",
    "Anwesh Ray"
  ],
  "comment": "Version 1: 20 pages",
  "categories": [
    "math.NT",
    "math.CO",
    "math.GR"
  ],
  "abstract": "This paper explores Iwasawa theory from a graph theoretic perspective, focusing on the algebraic and combinatorial properties of Cayley graphs. Using representation theory, we analyze Iwasawa-theoretic invariants within $\\mathbb{Z}_\\ell$-towers of Cayley graphs, revealing connections between graph theory, number theory, and group theory. Key results include the factorization of associated Iwasawa polynomials and the decomposition of $\\mu$- and $\\lambda$-invariants. Additionally, we apply these insights to complete graphs, establishing conditions under which these invariants vanish.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-07T14:40:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R23",
      "05C25",
      "05C31",
      "05C50"
    ],
    "keywords": [
      "cayley graphs",
      "iwasawa theory",
      "analyze iwasawa-theoretic invariants",
      "graph theory",
      "representation theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}