{
  "id": "2212.13592",
  "version": "v1",
  "published": "2022-12-27T19:51:22.000Z",
  "updated": "2022-12-27T19:51:22.000Z",
  "title": "A linear programming approach to Fuglede's conjecture in $\\mathbb{Z}_p^3$",
  "authors": [
    "Romanos Diogenes Malikiosis"
  ],
  "comment": "13 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "We present an approach to Fuglede's conjecture in $\\mathbb{Z}_p^3$ using linear programming bounds, obtaining the following partial result: if $A\\subseteq\\mathbb{Z}_p^3$ with $p^2-p\\sqrt{p}+\\sqrt{p}<|A|<p^2$, then $A$ is not spectral.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-27T19:51:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "43A46",
      "90C05",
      "52C22",
      "11L03",
      "20K01",
      "05B45"
    ],
    "keywords": [
      "linear programming approach",
      "fugledes conjecture",
      "linear programming bounds",
      "partial result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}