{
  "id": "2104.13089",
  "version": "v1",
  "published": "2021-04-27T10:19:58.000Z",
  "updated": "2021-04-27T10:19:58.000Z",
  "title": "Large non-trivial $t$-intersecting families for signed sets",
  "authors": [
    "Tian Yao",
    "Benjian Lv",
    "Kaishun Wang"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "For positive integers $n,r,k$ with $n\\ge r$ and $k\\ge2$, a set $\\{(x_1,y_1),(x_2,y_2),\\dots,(x_r,y_r)\\}$ is called a $k$-signed $r$-set on $[n]$ if $x_1,\\dots,x_r$ are distinct elements of $[n]$ and $y_1\\dots,y_r\\in[k]$. We say a $t$-intersecting family consisting of $k$-signed $r$-sets on $[n]$ is trivial if each member of this family contains a fixed $k$-signed $t$-set. In this paper, we determine the structure of large maximal non-trivial $t$-intersecting families. In particular, we characterize the non-trivial $t$-intersecting families with maximum size for $t\\ge2$, extending a Hilton-Milner-type result for signed sets given by Borg.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-27T10:19:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05D05"
    ],
    "keywords": [
      "intersecting family",
      "signed sets",
      "large non-trivial",
      "large maximal non-trivial",
      "distinct elements"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}