{
  "id": "2408.13755",
  "version": "v1",
  "published": "2024-08-25T07:44:58.000Z",
  "updated": "2024-08-25T07:44:58.000Z",
  "title": "On the Elementary Proof of the Inverse Erdős-Heilbronn Problem",
  "authors": [
    "Shengning Zhang"
  ],
  "comment": "14 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this article, we studied the inverse Erd\\H{o}s-Heilbronn problem with the restricted sumset from two components $A$ and $B$ that are not necessarily the same. We give a completely elementary proof for the problem in $\\mathbb{Z}$ and some partial results that contributes to the elementary proof of the problem in $\\mathbb{Z}/p\\mathbb{Z}$, avoiding the usage of the powerful polynomial method and the Combinatorial Nullstellensatz.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-25T07:44:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "elementary proof",
      "inverse erdős-heilbronn problem",
      "partial results",
      "powerful polynomial method",
      "combinatorial nullstellensatz"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}