{
  "id": "2211.04081",
  "version": "v1",
  "published": "2022-11-08T08:20:58.000Z",
  "updated": "2022-11-08T08:20:58.000Z",
  "title": "A note on distinct differences in $t$-intersecting families",
  "authors": [
    "Jagannath Bhanja",
    "Sayan Goswami"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "For a family $\\mathcal{F}$ of subsets of $\\{1,2,\\ldots,n\\}$, let $\\mathcal{D}(\\mathcal{F}) = \\{F\\setminus G: F, G \\in \\mathcal{F}\\}$ be the collection of all (setwise) differences of $\\mathcal{F}$. The family $\\mathcal{F}$ is called a $t$-intersecting family, if for some positive integer $t$ and any two members $F, G \\in \\mathcal{F}$ we have $|F\\cap G| \\geq t$. The family $\\mathcal{F}$ is simply called intersecting if $t=1$. Recently, Frankl proved an upper bound on the size of $\\mathcal{D}(\\mathcal{F})$ for the intersecting families $\\mathcal{F}$. In this note we extend the result of Frankl to $t$-intersecting families.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-08T08:20:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "intersecting family",
      "distinct differences",
      "upper bound",
      "collection"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}