{
  "abstract": "Let $K=K(n,m,Γ)$ be a Bedford-McMullen carpet with $n>m\\geq2$ and $1<\\#Γ<nm$, and let $μ$ be a self-affine measure on $K$ with strictly positive weights. We prove that every similitude $f(z)=rOz+a$ satisfying $μ(K\\cap f(K))>0$ has a diagonal or anti-diagonal orthogonal part $O$, without any arithmetic restrictions on the defining bases. Under the same intersection hypothesis, we also show that $r\\in n^{\\mathbb{Q}}\\cup m^{\\mathbb{Q}}$ whenever $K$ is not a segment. For isometries satisfying this hypothesis, we further prove that $f(K)$ is simply a translate of $K$, thereby establishing a strengthened form of the 2010 conjecture of Elekes, Keleti and Máthé in this planar self-affine context.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.09277",
  "author_total": 3,
  "authors": [
    {
      "name": "Ding-Kun Hu"
    },
    {
      "name": "Huo-Jun Ruan"
    },
    {
      "name": "Jian-Ci Xiao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4a0hng3hyj9qh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.09277",
  "fulltext_url": null,
  "id": "4a0hng3hyj9qh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.09277",
  "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.CA"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "arxiv",
      "math.MG"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7221062262",
  "pdf_url": "https://arxiv.org/pdf/2610.09277",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4a0hng3hyj9qh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.09277",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.09277"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Positive-measure intersections of Bedford-McMullen carpets under similitudes",
  "title_text": "Positive-measure intersections of Bedford-McMullen carpets under similitudes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/4a0hng3hyj9qh",
  "venue": "arXiv",
  "versions": []
}