{
  "abstract": "For positive integers $n\\ge r$, let $λ(r,n)$ denote the \\emph{maximal relative projection constant} of $r$-dimensional subspaces of $\\ell_\\infty^n$ and $λ(r)$ denote the \\emph{maximal absolute projection constant}, respectively. It is known that for any fixed $r$, $λ(r,n)$ is a non-decreasing sequence with limit $λ(r)$ as $n\\to \\infty$. A natural question is whether $λ(r,n)$ stabilizes at $λ(r)$ for some $n>r$. We prove that for any fixed $r$, \\[λ(r,n)=λ(r) \\qquad \\text{for every}\\qquad n\\ge 2^{r}\\binom{r+1}{2}.\\] This answers a question of Basso. The technique used is of independent interest.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.03200",
  "author_total": 4,
  "authors": [
    {
      "name": "Hitesh Kumar"
    },
    {
      "name": "Bojan Mohar"
    },
    {
      "name": "Seyed Ahmad Mojallal"
    },
    {
      "name": "Shivaramakrishna Pragada"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/brcmkqqkbp1zq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.03200",
  "fulltext_url": null,
  "id": "brcmkqqkbp1zq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.03200",
  "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.CO"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2610|Advanced Banach Space Theory"
    ]
  ],
  "openalex": "W7208790276",
  "pdf_url": "https://arxiv.org/pdf/2609.03200",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/brcmkqqkbp1zq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:36Z",
      "native_id": "2609.03200",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.03200"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Stability of maximal relative projection constants",
  "title_text": "Stability of maximal relative projection constants",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:36Z",
  "url": "https://research.draconitic.com/paper/brcmkqqkbp1zq",
  "venue": "arXiv",
  "versions": []
}