{
  "id": "2408.05015",
  "version": "v1",
  "published": "2024-08-09T11:59:20.000Z",
  "updated": "2024-08-09T11:59:20.000Z",
  "title": "An algebraic approach to Erdős-Ko-Rado sets of flags in spherical buildings II",
  "authors": [
    "Jan De Beule",
    "Sam Mattheus",
    "Klaus Metsch"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We continue our investigation of Erd\\H{o}s-Ko-Rado (EKR) sets of flags in spherical buildings. In previous work, we used the theory of buildings and Iwahori-Hecke algebras to obtain upper bounds on their size. As the next step towards the classification of the maximal EKR-sets, we describe the eigenspaces for the smallest eigenvalue of the opposition graphs. We determine their multiplicity and provide a combinatorial description of spanning sets of these subspaces, from which a complete description of the maximal Erd\\H{o}s-Ko-Rado sets of flags may potentially be found. This was recently shown to be possible for type $A_n$, $n$ odd, by Heering, Lansdown, and the last author by making use of the current work.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-09T11:59:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E18",
      "05C50",
      "05E30"
    ],
    "keywords": [
      "spherical buildings",
      "erdős-ko-rado sets",
      "algebraic approach",
      "complete description",
      "combinatorial description"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}