{
  "abstract": "Let $f_α(x)=(x^q-(1-α))^d-α^d x^z$, where $0<α<1$, $q\\ge 2$, $d\\ge 2$, $1\\le z\\le q-1$, and $\\gcd(q,z)=1$. These are the non-degenerate full-degree Type II reduced Ito polynomials of order $n=qd$. We give a complete parametrisation, up to permutation similarity, of the stochastic matrices whose characteristic polynomial is $f_α$. The support data are a composition $a_0+\\cdots+a_{d-1}=z$ and a cyclic origin $ρ\\in\\mathbb{Z}_q$. The transfer support in block 0 is an arbitrary nonempty subset of $[ρ,ρ+a_0]_q$, while the support in block $t\\ge 1$ is an arbitrary nonempty subset of $[ρ-\\sum_{j=1}^t(a_j+1),ρ-\\sum_{j=1}^t(a_j+1)+a_t]_q$. The horizontal weights at the selected positions are arbitrary elements of $(0,1)$ whose product in every block is $1-α$. The proof first shows that the order-$n$ Type II arc lies strictly outside $Θ_{n-1}$, which permits the Dmitriev--Dynkin/Kirkland--Smigoc two-shift reduction. A circular separation theorem then classifies the possible supports, and Coates' formula supplies the characteristic polynomial. This resolves the non-sparse full-degree Type II characteristic-polynomial realiser problem.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.26055",
  "author_total": 2,
  "authors": [
    {
      "name": "Brecht F. Verbeken"
    },
    {
      "name": "Vincent Ginis"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9ffs7t7wxq513.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.26055",
  "fulltext_url": null,
  "id": "9ffs7t7wxq513",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.26055",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "arxiv",
      "math.RA"
    ],
    [
      "arxiv",
      "math.SP"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7214099081",
  "pdf_url": "https://arxiv.org/pdf/2609.26055",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9ffs7t7wxq513.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2609.26055",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.26055"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.SP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Stochastic realisers of non-degenerate full-degree Type II reduced Ito polynomials",
  "title_text": "Stochastic realisers of non-degenerate full-degree Type II reduced Ito polynomials",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/9ffs7t7wxq513",
  "venue": "arXiv",
  "versions": []
}