{
  "abstract": "We construct infinite $B_h$ sets that repeatedly attain the density scale of finite $B_h$ sets. For every integer $h\\geq2$ and every finite $B_h$ set $F$ of positive integers, we obtain an infinite $B_h$ set $A\\supseteq F$ such that $$ \\limsup_{x\\to\\infty}\\frac{A(x)}{x^{1/h}}=\\frac1h, \\qquad \\liminf_{x\\to\\infty}\\frac{A(x)}{x^{1/h}}=0. $$ The key is to preserve density while preventing additive relations between successive blocks. A positional encoding of the finite-field moment curve has $q$ elements in an interval of length $O_h(q^h)$, while, for each $1\\leq r<h$, sums arising from distinct $r$-element multisets are separated by more than $q$. This separation allows whole blocks to be appended to a prescribed finite set without a further dilation. In particular, our result gives a negative answer to a problem posed by Szemerédi \\cite{szemeredi}.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01871",
  "author_total": 2,
  "authors": [
    {
      "name": "Guoqing Wang"
    },
    {
      "name": "Wenkai Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ezvfx29mbjjmk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01871",
  "fulltext_url": null,
  "id": "ezvfx29mbjjmk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01871",
  "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.NT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01871",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ezvfx29mbjjmk.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01871",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01871"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Infinite Generalized Sidon Sets with a Negative Answer to a Problem of Szemerédi",
  "title_text": "Infinite Generalized Sidon Sets with a Negative Answer to a Problem of Szemerédi",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/ezvfx29mbjjmk",
  "venue": "arXiv",
  "versions": []
}