{
  "abstract": "In this paper, we study the ${\\rm v}$-number of the symbolic-ordinary discrepancy modules $M_t(I) = I^{(t)} / I^t$ over standard graded Noetherian rings. We show that this coincides with the ${\\rm v}$-number of $I^t$ at embedded primes. Moreover, under mild assumptions on $I$, we show that the ${\\rm v}$-number of $N_t(I) = I^{(t)} / I^{(t+1)}$ is the same as the ${\\rm v}$-number of $I^{(t+1)}$. Furthermore, we provide combinatorial formulas for these ${\\rm v}$-numbers when $t = 2, 3$ and $I$ is the edge ideal of a graph. Consequently, we classify all graphs for which ${\\rm v}(I^2) = {\\rm v}(I^{(2)})$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.22872",
  "author_total": 3,
  "authors": [
    {
      "name": "Manohar Kumar"
    },
    {
      "name": "Nguyen Cong Minh"
    },
    {
      "name": "Thanh Vu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4r62xbjfyav8s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.22872",
  "fulltext_url": null,
  "id": "4r62xbjfyav8s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.22872",
  "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.AC"
    ],
    [
      "openalex",
      "2602|Commutative Algebra and Its Applications"
    ]
  ],
  "openalex": "W7214034237",
  "pdf_url": "https://arxiv.org/pdf/2609.22872",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4r62xbjfyav8s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2609.22872",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.22872"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "v-numbers of symbolic-ordinary discrepancy modules",
  "title_text": "v-numbers of symbolic-ordinary discrepancy modules",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/4r62xbjfyav8s",
  "venue": "arXiv",
  "versions": []
}