{
  "abstract": "Let $d\\geq 3$ and consider the generic family of monic normalized polynomials $f_{\\mathbf{t}}(z)=z^d+t_1z^{d-2}+t_2z^{d-3}+\\cdots+t_{d-2}z+t_{d-1}$, where $\\mathbf{t}=(t_1,\\ldots,t_{d-1})$. Given pairwise distinct starting points $α_1,\\ldots,α_d\\in\\bar{\\mathbb{Q}}$ and a target point $β\\in\\bar{\\mathbb{Q}}$, we show that the set of parameters $\\boldsymbolλ\\in\\mathbb{A}^{d-1}(\\bar{\\mathbb{Q}})$ for which $β$ belongs to the forward orbit of every $α_i$ under $f_{\\boldsymbolλ}$ is not Zariski dense in $\\mathbb{A}^{d-1}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.05785",
  "author_total": 2,
  "authors": [
    {
      "name": "Dragos Ghioca"
    },
    {
      "name": "Negin Shadgar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dnajdg9dqm0rq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.05785",
  "fulltext_url": null,
  "id": "dnajdg9dqm0rq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.05785",
  "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.NT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.05785",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dnajdg9dqm0rq.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.05785",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.05785"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Collision Parameters in Higher-Dimensional Families of Polynomials",
  "title_text": "Collision Parameters in Higher-Dimensional Families of Polynomials",
  "type": "preprint",
  "updated_at": "2026-11-07T18:20:08Z",
  "url": "https://research.draconitic.com/paper/dnajdg9dqm0rq",
  "venue": "arXiv",
  "versions": []
}