{
  "abstract": "For each nonempty finite simple graph, we study five full multivariate partial-twuality polynomials defined using matrix ranks and coranks over $\\mathbb{F}_2$. Over an arbitrary coefficient field $K$, we give a necessary and sufficient criterion for nontrivial factorization in the Laurent polynomial ring by additive separation of the exponent function across a nontrivial vertex partition. For $\\bullet\\in\\{τ,δτ,τδ,δτδ\\}$, the full multivariate partial-$\\langle\\bullet\\rangle$ polynomial is irreducible in $K[z^{\\pm1},\\mathbf{u},\\mathbf{v}]$ if and only if the graph is connected. For $δ$, we characterize the connected graphs whose polynomials are reducible by a condition on the parities of vertex degrees and of the numbers of common neighbors, and determine their irreducible factors. For each operation, the corresponding polynomial is irreducible in $K[z,\\mathbf{u},\\mathbf{v}]$ if and only if the graph is connected and at least one state has zero $z$-exponent. In particular, the full multivariate partial-$\\langleδ\\rangle$ polynomial is irreducible in $K[z,\\mathbf{u},\\mathbf{v}]$ if and only if the graph is connected and bipartite.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01445",
  "author_total": 2,
  "authors": [
    {
      "name": "Qingying Deng"
    },
    {
      "name": "Chaoyang Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0x6pwhe0ectwx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01445",
  "fulltext_url": null,
  "id": "0x6pwhe0ectwx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01445",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01445",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0x6pwhe0ectwx.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01445",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01445"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Irreducibility of Full Multivariate Partial-Twuality Polynomials",
  "title_text": "Irreducibility of Full Multivariate Partial-Twuality Polynomials",
  "type": "preprint",
  "updated_at": "2026-11-04T15:21:05Z",
  "url": "https://research.draconitic.com/paper/0x6pwhe0ectwx",
  "venue": "arXiv",
  "versions": []
}