{
  "abstract": "Let $I\\subseteq S$ be a monomial ideal with minimal generator degrees between $e$ and $d$, where $2\\leq e\\leq d$. We prove that if $t_a(S/I)<ea$, then $$ t_{a+b}(S/I)\\leq t_a(S/I)+ \\left\\lceil\\frac{(2d-1)b}{2}\\right\\rceil $$ for $a\\geq2$, $b\\geq0$, and $a+b\\leq\\operatorname{pd}_S(S/I)$. Consequently, $$ t_{a+b}(S/I)\\leq ae+db-1-\\left\\lfloor\\frac b2\\right\\rfloor. $$ In particular, if $t_2(S/I)<2e$, then $$ t_i(S/I)\\leq \\left\\lceil\\frac{(2d-1)i}{2}\\right\\rceil-2(d-e) $$ for $2\\leq i\\leq\\operatorname{pd}_S(S/I)$. We also obtain a regularity bound and give a quadratic family in which our estimate for the last shift is smaller than every bound obtained from ordinary subadditivity. The constant $2d-1$ is sharp for $d=2$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.32135",
  "author_total": 1,
  "authors": [
    {
      "name": "Abed Abedelfatah"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ftns9r084yvy9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.32135",
  "fulltext_url": null,
  "id": "ftns9r084yvy9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.32135",
  "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": "W7214713415",
  "pdf_url": "https://arxiv.org/pdf/2609.32135",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ftns9r084yvy9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.32135",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.32135"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Maximal shifts below the Taylor bound",
  "title_text": "Maximal shifts below the Taylor bound",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/ftns9r084yvy9",
  "venue": "arXiv",
  "versions": []
}