{
  "abstract": "For a constraint satisfaction problem defined by a relation $R$, its non-redundancy $\\text{NRD}(R,n)$ is the size of largest instance (as a function of the number $n$ of variables) for which no constraint is implied by the rest. Its chain length $\\text{CL}(R,n)$ is the largest such instance where the constraints can be ordered so that no constraint is implied by the preceding ones. Clearly $\\text{CL}(R,n) \\ge \\text{NRD}(R,n)$ but so far no asymptotic separation was known between these quantities. We exhibit an explicit arity $4$ relation for which $\\text{CL}(R,n) \\ge ω(\\text{NRD}(R,n))$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.17914",
  "author_total": 3,
  "authors": [
    {
      "name": "Joshua Brakensiek"
    },
    {
      "name": "Venkatesan Guruswami"
    },
    {
      "name": "Aaron Putterman"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0mx8x0m4dy8c6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.17914",
  "fulltext_url": null,
  "id": "0mx8x0m4dy8c6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.17914",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.CC"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "1705|Constraint Satisfaction and Optimization"
    ]
  ],
  "openalex": "W7213514496",
  "pdf_url": "https://arxiv.org/pdf/2609.17914",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0mx8x0m4dy8c6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.17914",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.17914"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Separating Non-redundancy and Chain Length",
  "title_text": "Separating Non-redundancy and Chain Length",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/0mx8x0m4dy8c6",
  "venue": "arXiv",
  "versions": []
}