{
  "abstract": "We prove a generalized circular rearrangement inequality: among all circular arrangements of a finite collection of positive numbers, the greedy arrangement simultaneously maximizes the sums of products of $k$ consecutive entries for every $k$. This resolves a 2023 conjecture of Holmes-Holroyd-Ramírez and extends the classical circular rearrangement inequality for products of adjacent entries. As an application, we show that the greedy ordering minimizes the speed of a cyclic birth-and-death chain, resolving another conjecture of the same authors.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11774",
  "author_total": 1,
  "authors": [
    {
      "name": "Gabriel Raposo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5j1gjgyk2gv1p.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11774",
  "fulltext_url": null,
  "id": "5j1gjgyk2gv1p",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11774",
  "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.CO"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2604|Mathematical Inequalities and Applications"
    ]
  ],
  "openalex": "W7212224344",
  "pdf_url": "https://arxiv.org/pdf/2609.11774",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5j1gjgyk2gv1p.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.11774",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11774"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Circular Rearrangement Inequality and Optimal Cyclic Birth and Death Chains",
  "title_text": "Circular Rearrangement Inequality and Optimal Cyclic Birth and Death Chains",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/5j1gjgyk2gv1p",
  "venue": "arXiv",
  "versions": []
}