{
  "abstract": "We consider systems of homogeneous multivariate polynomials equivariant under the complex reflection group $G(r,n) = (\\mathbb{Z}/r\\mathbb{Z})^n \\rtimes S_n$. Using divided differences indexed by partitions of $n$, we establish a decomposition formula expressing the resultant of such a system as a product of resultants of smaller, partition-indexed subsystems. Combining this with the classical resultant--discriminant relation, we show that the discriminant of a $G(r,n)$-invariant homogeneous polynomial splits explicitly into a product of resultants of smaller subsystems, considerably easier to compute; we illustrate both decompositions with worked examples.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27886",
  "author_total": 3,
  "authors": [
    {
      "name": "Sonagnon Julien Owolabi"
    },
    {
      "name": "Ibrahim Nonkané"
    },
    {
      "name": "Joel Tossa"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1ndt87j4nqhne.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27886",
  "fulltext_url": null,
  "id": "1ndt87j4nqhne",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27886",
  "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.AC"
    ],
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.CO"
    ],
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      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "1703|Polynomial and algebraic computation"
    ]
  ],
  "openalex": "W7214186438",
  "pdf_url": "https://arxiv.org/pdf/2609.27886",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1ndt87j4nqhne.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.27886",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27886"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Resultant of an equivariant polynomial system with respect to the reflection group $G(r,n)$",
  "title_text": "Resultant of an equivariant polynomial system with respect to the reflection group G(r,n)",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/1ndt87j4nqhne",
  "venue": "arXiv",
  "versions": []
}