{
  "id": "2401.04699",
  "version": "v1",
  "published": "2024-01-09T18:02:00.000Z",
  "updated": "2024-01-09T18:02:00.000Z",
  "title": "Extended inverse theorems for $h$-fold sumsets in integers",
  "authors": [
    "Mohan",
    "Ram Krishna Pandey"
  ],
  "comment": "To be appear in contrib. discrete math., 17 pages, correct some typographical errors, Statement and proof of some results changed",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $h \\geq 2$, $k \\geq 5$ be integers and $A$ be a nonempty finite set of $k$ integers. Very recently, Tang and Xing studied extended inverse theorems for $hk-h+1 < \\left|hA\\right| \\leq hk+2h-3$. In this paper, we extend the work of Tang and Xing and study all possible inverse theorems for $hk-h+1<\\left|hA\\right| \\leq hk+3h-4$. Furthermore, we give a range of $|hA|$ for which inverse problems are not possible.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-09T18:02:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B75",
      "11B13"
    ],
    "keywords": [
      "extended inverse theorems",
      "fold sumsets",
      "nonempty finite set",
      "inverse problems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}