{
  "id": "2212.12473",
  "version": "v1",
  "published": "2022-12-23T17:02:30.000Z",
  "updated": "2022-12-23T17:02:30.000Z",
  "title": "Counterexample to a Conjecture of Dombi in Additive Number Theory",
  "authors": [
    "Jeffrey Shallit"
  ],
  "categories": [
    "math.NT",
    "cs.DM",
    "cs.FL",
    "math.CO"
  ],
  "abstract": "We disprove a 2002 conjecture of Dombi from additive number theory. More precisely, we find a set $A \\subset N$ with the property that $N \\setminus A$ is infinite, but the sequence $n \\rightarrow |\\{ (a,b,c) : n=a+b+c$ and $a,b,c \\in A \\}|$ counting the number of $3$-compositions is strictly increasing.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-23T17:02:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "additive number theory",
      "conjecture",
      "counterexample"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}