{
  "id": "0803.4486",
  "version": "v1",
  "published": "2008-03-31T16:00:01.000Z",
  "updated": "2008-03-31T16:00:01.000Z",
  "title": "On the maximum size of a $(k,l)$-sum-free subset of an abelian group",
  "authors": [
    "Bela Bajnok"
  ],
  "comment": "To appear in the International Journal of Number Theory",
  "categories": [
    "math.CO",
    "math.NT"
  ],
  "abstract": "A subset $A$ of a given finite abelian group $G$ is called $(k,l)$-sum-free if the sum of $k$ (not necessarily distinct) elements of $A$ does not equal the sum of $l$ (not necessarily distinct) elements of $A$. We are interested in finding the maximum size $\\lambda_{k,l}(G)$ of a $(k,l)$-sum-free subset in $G$. A $(2,1)$-sum-free set is simply called a sum-free set. The maximum size of a sum-free set in the cyclic group $\\mathbb{Z}_n$ was found almost forty years ago by Diamanda and Yap; the general case for arbitrary finite abelian groups was recently settled by Green and Ruzsa. Here we find the value of $\\lambda_{3,1}(\\mathbb{Z}_n)$. More generally, a recent paper of Hamidoune and Plagne examines $(k,l)$-sum-free sets in $G$ when $k-l$ and the order of $G$ are relatively prime; we extend their results to see what happens without this assumption.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-03-31T16:00:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11P70"
    ],
    "keywords": [
      "sum-free subset",
      "maximum size",
      "sum-free set",
      "arbitrary finite abelian groups",
      "necessarily distinct"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0803.4486B"
    }
  }
}