{
  "annotation_id": "93851410-c0e3-41ae-90cc-943104be0de8",
  "date_created": "2026-02-17T05:53:07.509000Z",
  "date_modified": "2026-02-17T05:53:07.509000Z",
  "file_hash": "412e8abab660dfc11a8baab3eb2aa1994aca4048ad8aa81dbdb30de0ae0879be",
  "private": false,
  "record": {
    "abstract": "We present an explicit family $\\mathcal{B}$ of $920$ subsets of size $6$ of $[60]=\\{1,\\dots,60\\}$ with the property that every $6$-subset $S\\subset[60]$ intersects at least one block $B\\in\\mathcal{B}$ in at least three elements, i.e.\\ $|S\\cap B|\\ge 3$. The construction is purely combinatorial, based on a partition of the ground set into pairs and a pigeonhole argument. We also record a simple counting lower bound and discuss how different partitions of the ten base blocks affect the emergence of triple intersections.",
    "arxiv_id": "2601.06179",
    "authors": [
      "Paulo Henrique Cunha Gomes"
    ],
    "categories": [
      "math.CO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "A 920-block explicit construction guaranteeing a triple intersection with every 6-subset of [60]",
    "url": "https://arxiv.org/abs/2601.06179",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "b0fd68ab-7894-4a83-a4ea-c3443e258fa0",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}