{
  "annotation_id": "37017bef-fe4c-4f64-a641-0780a65a2499",
  "date_created": "2026-02-17T05:53:12.482000Z",
  "date_modified": "2026-02-17T05:53:12.482000Z",
  "file_hash": "b16b0f1e515a4d20170e788f645d7691e8ca116359a216c09b6423f1259dfdec",
  "private": false,
  "record": {
    "abstract": "We provide precise asymptotics for the number of antichains in the poset $\\{0,1,2\\}^n$, answering a question of Sapozhenko. Finding improved estimates for this number was also a problem suggested by Noel, Scott, and Sudakov, who obtained asymptotics for the logarithm of the number. Key ingredients for the proof include a graph-container lemma to bound the number of expanding sets in a class of irregular graphs, isoperimetric inequalities for generalizations of the Boolean lattice, and methods from statistical physics based on the cluster expansion.",
    "arxiv_id": "2601.07650",
    "authors": [
      "Matthew Jenssen",
      "Jinyoung Park",
      "Michail Sarantis"
    ],
    "categories": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "On the number of antichains in $\\{0,1,2\\}^n$",
    "url": "https://arxiv.org/abs/2601.07650",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "9b7e7695-19f0-4e98-aa6d-6608b1bbce98",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}