{
  "abstract": "We develop a theory of partial matchings between finite-dimensional subspaces $A,B$ in a field extension $K \\subsetneq L$, providing structural, quantitative, and extremal results for their deficiency. Our main results include (1) a characterization of those pairs $(A,B)$ that are partially matchable up to a specified defect, (2) a decomposition theorem for pairs $(A,B)$ having positive deficiency, (3) an existence criterion for pairs having a prescribed dimension and satisfying a deficiency bound, and (4) a formula for the maximum attainable deficiency at each dimension, assuming $1 \\notin B$ and the extension has a proper nontrivial intermediate field of finite $K$-dimension. We use these results to recover and extend various parts of this area of matching theory. Our approach blends algebraic techniques with tools from matroidal transversal theory, and utilizes a linearized version of the $e$-transform from additive number theory.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.12725",
  "author_total": 2,
  "authors": [
    {
      "name": "Mohsen Aliabadi"
    },
    {
      "name": "Jozsef Losonczy"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3mjznkdzqtnw3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.12725",
  "fulltext_url": null,
  "id": "3mjznkdzqtnw3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.12725",
  "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",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7164509441",
  "pdf_url": "https://arxiv.org/pdf/2606.12725",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3mjznkdzqtnw3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:28Z",
      "native_id": "2606.12725",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.12725"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "On partially matchable subspaces in a field extension",
  "title_text": "On partially matchable subspaces in a field extension",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:28Z",
  "url": "https://research.draconitic.com/paper/3mjznkdzqtnw3",
  "venue": "arXiv",
  "versions": []
}