{
  "id": "2201.08632",
  "version": "v1",
  "published": "2022-01-21T10:41:28.000Z",
  "updated": "2022-01-21T10:41:28.000Z",
  "title": "Cross $t$-intersecting families for symplectic polar spaces",
  "authors": [
    "Tian Yao",
    "Kaishun Wang"
  ],
  "comment": "arXiv admin note: substantial text overlap with arXiv:2201.08084",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $\\mathscr{P}$ be a symplectic polar space over a finite field $\\mathbb{F}_q$, and $\\mathscr{P}_m$ denote the collection of all $k$-dimensional totally isotropic subspace in $\\mathscr{P}$. Let $\\mathscr{F}_1\\subset\\mathscr{P}_{m_1}$ and $\\mathscr{F}_2\\subset\\mathscr{P}_{m_2}$ satisfy $\\dim(F_1\\cap F_2)\\ge t$ for any $F_1\\in\\mathscr{F}_1$ and $F_2\\in\\mathscr{F}_2$. We say they are cross $t$-intersecting families. Moreover, we say they are trivial if each member of them contains a fixed $t$-dimensional totally isotropic subspace. In this paper, we show that cross $t$-intersecting families with maximum product of sizes are trivial. We also describe the structure of non-trivial $t$-intersecting families with maximum product of sizes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-01-21T10:41:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05D05",
      "05A30",
      "51A50"
    ],
    "keywords": [
      "symplectic polar space",
      "intersecting families",
      "dimensional totally isotropic subspace",
      "maximum product",
      "finite field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}