{
  "abstract": "We introduce invariants we call $k$-divisibility and $d$-dominance, which are combinatorial constraints on the minimal generators of monomial ideals. We then prove that $k$ (respectively, $d$) is an upper bound (respectively, lower bound) for the projective dimension of a $k$-divisible (respectively, $d$-dominant) monomial ideal. This leads us to an explicit minimal resolution of $k$-divisible, $d$-dominant ideals when $d=k-1$ via a Lyubeznik resolution. This framework allows us to prove a conjecture made by Alesandroni. Using these invariants, we also provide a characterization of monomial ideals whose minimal free resolution is attainable from the Taylor resolution by performing exactly one consecutive cancellation. We also prove that for all $q,k,d$ in the range $1\\leq d<k \\leq q-1$, there exist monomial ideals that are $k$-divisible and $d$-dominant with $q$ minimal generators.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.20565",
  "author_total": 2,
  "authors": [
    {
      "name": "Patrick Welte"
    },
    {
      "name": "Guillermo Alesandroni"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1h4ptf88kcym3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.20565",
  "fulltext_url": null,
  "id": "1h4ptf88kcym3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.20565",
  "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"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2602|Commutative Algebra and Its Applications"
    ]
  ],
  "openalex": "W7222350273",
  "pdf_url": "https://arxiv.org/pdf/2610.20565",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1h4ptf88kcym3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.20565",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.20565"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Minimal Resolutions of $k$-divisible and $(k-1)$-dominant Ideals",
  "title_text": "Minimal Resolutions of k-divisible and (k−1)-dominant Ideals",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/1h4ptf88kcym3",
  "venue": "arXiv",
  "versions": []
}