{
  "abstract": "Let $q=p^k$, and let $A_1,\\ldots,A_{r-1}$ be invertible $n\\times n$ matrices over ${\\mathbb F}_q$. We prove that, if $k\\ge r$, there is a vector $x$ for which \\[ x,A_1x,\\ldots,A_{r-1}x \\] are all nowhere zero. For $r=2$ this recovers the theorem of Alon and Tarsi over nonprime finite fields. The proof tracks one monomial in the product of the coordinate forms. Frobenius powers keep every exponent below $p^r$, and finite-field polynomial nonvanishing supplies the required vector. The same method treats rectangular matrices with independent rows and prescribed forbidden values. The method also gives an extension-degree criterion for representable matroids and clarifies an unpublished prime-field conjecture of M. J. Moghaddamzadeh. Projective-geometric examples explain why the analogous field-size statement fails over proper extensions and, translated back to matrices, give lower bounds for the large-field problem.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.23647",
  "author_total": 1,
  "authors": [
    {
      "name": "Amir Jafari"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fvw38vhtfxzaw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.23647",
  "fulltext_url": null,
  "id": "fvw38vhtfxzaw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.23647",
  "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": "W7204241278",
  "pdf_url": "https://arxiv.org/pdf/2608.23647",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fvw38vhtfxzaw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2608.23647",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.23647"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A nowhere-zero point for several linear mappings simultaneously",
  "title_text": "A nowhere-zero point for several linear mappings simultaneously",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/fvw38vhtfxzaw",
  "venue": "arXiv",
  "versions": []
}