{
  "id": "2502.05930",
  "version": "v1",
  "published": "2025-02-09T15:13:52.000Z",
  "updated": "2025-02-09T15:13:52.000Z",
  "title": "A short proof of generalized Conway--Gordon--Sachs theorem",
  "authors": [
    "Ryo Nikkuni"
  ],
  "comment": "8 pages, 2 figures",
  "categories": [
    "math.GT",
    "math.CO"
  ],
  "abstract": "The famous Conway--Gordon--Sachs theorem for the complete graph on six vertices was extended to the general complete graph on $n$ vertices by Kazakov--Korablev as a congruence modulo $2$, and its integral lift was given by Morishita--Nikkuni. However, the proof is complicated and long. In this paper, we provide a shorter proof of the generalized Conway--Gordon--Sachs theorem over integers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-02-09T15:13:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M15",
      "57K10"
    ],
    "keywords": [
      "generalized conway-gordon-sachs theorem",
      "short proof",
      "general complete graph",
      "integral lift",
      "shorter proof"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}