{
  "abstract": "Given a positive, non-increasing sequence $a$ with sum $1$, we consider the family $\\mathcal{C}_a$ of closed subsets of $[0,1]$ whose complementary open intervals have lengths given by the terms of $a$. We study which functions $θ\\mapsto\\overline{\\dim}_{\\,θ}E$ arise as the upper intermediate dimensions of sets $E\\in\\mathcal{C}_a$. Under a natural condition on the decay of $a$, we show that these are exactly the functions in the class introduced by Banaji and Rutar that take the value $\\overline{\\dim}_{\\rm B}C_a$ at $θ=1$ and are bounded above by the upper intermediate dimensions of the decreasing Cantor set $C_a$. We also show that the lower bound given by the countable set $D_a$ is rigid: if it is attained at one value of $θ$, then it is attained at all larger values.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35834",
  "author_total": 1,
  "authors": [
    {
      "name": "Nicolas Angelini"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8hh0wcajfkf2q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35834",
  "fulltext_url": null,
  "id": "8hh0wcajfkf2q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35834",
  "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.CA"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7223915497",
  "pdf_url": "https://arxiv.org/pdf/2610.35834",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8hh0wcajfkf2q.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:43Z",
      "native_id": "2610.35834",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35834"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Attainable forms of intermediate dimensions of complementary sets",
  "title_text": "Attainable forms of intermediate dimensions of complementary sets",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:43Z",
  "url": "https://research.draconitic.com/paper/8hh0wcajfkf2q",
  "venue": "arXiv",
  "versions": []
}