{
  "abstract": "Agreement expansion asks whether local assignments to faces of a poset that usually agree on a sampled common face must agree with a single global function on most faces. Agreement expansion is exact (approximate) if local assignments need to exactly (approximately) agree with the global function. We suggest a new proof technique for agreement expansion that enables agreement expansion in settings which were previously beyond reach, such as: exact agreement expansion for Grassmannian posets (before only simplicial complexes support exact agreement expansion); agreement expansion based on assignments to top faces of the a complex (before agreement expansion is generally proven only for assignments to low dimensional faces); agreement expansion from one-sided spectral expansion (before, two sided spectral assumption was needed in general settings). Specifically, for down-closed simplicial and Grassmannian complexes, we prove an exact agreement theorem between any two layers assuming one-sided spectral expansion in links of singletons. As an application, we show that full bases of every rank-$k$ matroid admit exact agreement with soundness $O(k^2/[h(k-h)])$ when tested through $h$-element independent sets. We also obtain exact agreement on Grassmannian posets under one-sided spectral expansion, with stronger soundness under a local distance guarantee. Our key proof ideas center around non-polarity of the distributions of local assignments, probed via a random exposure of elements.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.03261",
  "author_total": 2,
  "authors": [
    {
      "name": "Tali Kaufman"
    },
    {
      "name": "Huy Tuan Pham"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9g38ck8njfa64.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.03261",
  "fulltext_url": null,
  "id": "9g38ck8njfa64",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.03261",
  "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",
      "cs.DM"
    ],
    [
      "arxiv",
      "math.CO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.03261",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9g38ck8njfa64.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:14Z",
      "native_id": "2611.03261",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.03261"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Exact Agreement Expansion up to the Top via Non-polarity",
  "title_text": "Exact Agreement Expansion up to the Top via Non-polarity",
  "type": "preprint",
  "updated_at": "2026-11-08T21:20:42Z",
  "url": "https://research.draconitic.com/paper/9g38ck8njfa64",
  "venue": "arXiv",
  "versions": []
}