{
  "abstract": "We study the cyclic inequality \\[ \\sum_{i=1}^n x_i\\,\\sum_{i=1}^n x_i^a x_{i+1}^b\\;\\le\\;\\Big(\\sum_{i=1}^n x_i^{(1+a+b)/2}\\Big)^2, \\] where $x_1,\\dots,x_n\\ge 0$ and indices are taken modulo $n$. Let $N(a,b)$ be the largest $n$ for which the inequality holds for all nonnegative $x_i$. We show that $N(a,b)$ is bounded above by an explicit quantity $N^*(a,b)$ obtained from the second variation at the constant vector, and we conjecture that $N(a,b)=N^*(a,b)$. For $a=b=1$ we prove that the inequality holds if and only if $n\\le 8$, which settles the case left open in the original version of this paper. For $n=4$ the inequality holds whenever $1,a,b$ are the sides of a triangle, with an explicit remainder term. We show that $N$ is monotone along rays emanating from the line $a+b=1$; this corrects and extends an earlier monotonicity statement. Finally, any $n$ nonnegative numbers can be arranged so that the inequality holds; for $n\\neq 6$ this is achieved by one of $n-1$ prescribed arrangements, which yields a volume bound for every such $n$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: M. Javaheri, A new arrangement inequality, J. Inequal. Pure Appl. Math. 7 (2006), no. 5, Article 162",
  "arxiv": "2610.33653",
  "author_total": 1,
  "authors": [
    {
      "name": "Mohammad Javaheri"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bzt3krstc114z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.33653",
  "fulltext_url": null,
  "id": "bzt3krstc114z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.33653",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GM"
    ],
    [
      "openalex",
      "2604|Mathematical Inequalities and Applications"
    ]
  ],
  "openalex": "W7223914144",
  "pdf_url": "https://arxiv.org/pdf/2610.33653",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bzt3krstc114z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.33653",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.33653"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GM",
      "subfield": "general"
    }
  ],
  "title": "A new arrangement inequality (revised and extended version)",
  "title_text": "A new arrangement inequality (revised and extended version)",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/bzt3krstc114z",
  "venue": "arXiv",
  "versions": []
}