{
  "id": "1907.06019",
  "version": "v1",
  "published": "2019-07-13T06:34:35.000Z",
  "updated": "2019-07-13T06:34:35.000Z",
  "title": "Combinatorics in the exterior algebra and the Bollobás Two Families Theorem",
  "authors": [
    "Alex Scott",
    "Elizabeth Wilmer"
  ],
  "comment": "20 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We investigate the combinatorial structure of subspaces of the exterior algebra of a finite-dimensional real vector space, working in parallel with the extremal combinatorics of hypergraphs. As an application, we prove a new extension of the Two Families Theorem of Bollob\\'{a}s.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-13T06:34:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05D05",
      "15A75",
      "14N20"
    ],
    "keywords": [
      "exterior algebra",
      "families theorem",
      "finite-dimensional real vector space",
      "combinatorial structure",
      "extremal combinatorics"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}