{
  "abstract": "An ideal $I$ of a polynomial ring $R=k[x_1,\\dots,x_n]$ is called weakly Newton-nondegenerate, or weakly NND, if its integral closure $\\overline{I}$ is a monomial ideal. We study weak Newton nondegeneracy for the family of quadratic binomial ideals \\[ I=(x_1^2+ε_1x_{a_1}x_{b_1},\\ \\dots,\\ x_n^2+ε_nx_{a_n}x_{b_n}),\\qquad ε_i\\in\\{\\pm1\\},\\ a_i\\neq b_i, \\] over an algebraically closed field. We prove that $I$ is weakly NND if and only if $\\overline I=\\mathfrak{m}^2$, if and only if the given generators form a regular sequence, and if and only if an explicit combinatorial condition on the pair (support pattern, sign pattern) holds: no nonempty subset $S\\subseteq\\{1,\\dots,n\\}$ is simultaneously closed for the support data and sign-trivial for the associated lattice of relations. The last equivalence rests on a solvability criterion for systems of monomial equations over a divisible abelian group, in the spirit of Eisenbud and Sturmfels. As an application, we classify all such ideals for $n=3$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.29039",
  "author_total": 2,
  "authors": [
    {
      "name": "Takayuki Hibi"
    },
    {
      "name": "Vinh Anh Pham"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6mfvfbh1eya99.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.29039",
  "fulltext_url": null,
  "id": "6mfvfbh1eya99",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.29039",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AC"
    ],
    [
      "openalex",
      "2602|Commutative Algebra and Its Applications"
    ]
  ],
  "openalex": "W7204928717",
  "pdf_url": "https://arxiv.org/pdf/2608.29039",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6mfvfbh1eya99.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.29039",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.29039"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Weakly Newton-nondegenerate binomial ideals",
  "title_text": "Weakly Newton-nondegenerate binomial ideals",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/6mfvfbh1eya99",
  "venue": "arXiv",
  "versions": []
}