{
  "abstract": "In this paper we study the resultant of systems of homogeneous multivariate polynomials which are equivariant under the action of a direct product of symmetric groups. We first treat, in detail, the case of a product of two symmetric groups, and establish a decomposition formula for the resultant of such systems. We then show that this decomposition, together with the underlying combinatorics, extends to an arbitrary (finite) direct product of $r$ symmetric groups. Thanks to these decomposition formulas, we prove that the discriminant of a multivariate homogeneous polynomial invariant under a direct product of $r$ symmetric groups splits into a product of resultants of smaller size that are easier to compute.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.26127",
  "author_total": 4,
  "authors": [
    {
      "name": "Sonagnon Julien Owolabi"
    },
    {
      "name": "Ollé Grégroire Kam"
    },
    {
      "name": "Ibrahim Nonkane"
    },
    {
      "name": "Joel Tossa"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6kwxmksm1nr8w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.26127",
  "fulltext_url": null,
  "id": "6kwxmksm1nr8w",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.26127",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AC"
    ],
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.GR"
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      "arxiv",
      "math.NT"
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    [
      "openalex",
      "1703|Polynomial and algebraic computation"
    ]
  ],
  "openalex": "W7214083332",
  "pdf_url": "https://arxiv.org/pdf/2609.26127",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6kwxmksm1nr8w.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2609.26127",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.26127"
    }
  ],
  "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 a direct product of $r$ symmetric groups",
  "title_text": "Resultant of an equivariant polynomial system with respect to a direct product of r symmetric groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/6kwxmksm1nr8w",
  "venue": "arXiv",
  "versions": []
}