{
  "abstract": "We show that if $X$ and $Y$ are self-similar sets in $\\mathbb{R}$ with multiplicatively independent contraction ratios, then the Assouad dimension of $X+Y$ is one. As an application, we show that for a large class of self-affine carpets, the Assouad dimension of any non-principal orthogonal projection is one. The latter result is new even for the simplest case of Bedford-McMullen carpets.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.26119",
  "author_total": 2,
  "authors": [
    {
      "name": "Roope Anttila"
    },
    {
      "name": "Jonathan M. Fraser"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bpr3waf5tg4sr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.26119",
  "fulltext_url": null,
  "id": "bpr3waf5tg4sr",
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  "landing_url": "https://arxiv.org/abs/2610.26119",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DS"
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      "arxiv",
      "math.MG"
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      "2610|Mathematical Dynamics and Fractals"
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  "openalex": "W7223070369",
  "pdf_url": "https://arxiv.org/pdf/2610.26119",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bpr3waf5tg4sr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.26119",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.26119"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Local structure of sumsets and projections of self-affine carpets",
  "title_text": "Local structure of sumsets and projections of self-affine carpets",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/bpr3waf5tg4sr",
  "venue": "arXiv",
  "versions": []
}