{
  "abstract": "For $n\\geq1$, choose one residue class $r_k\\pmod{k}$ for every $2\\leq k\\leq n$, and retain those $m\\in\\{2,\\ldots,n+1\\}$ for which $m\\not\\equiv r_k\\pmod{k}$ whenever $k<m$. Let $N(n)$ be the number of distinct survivor sets obtained in this way. We prove \\[ \\log 2\\leq \\liminf_{n\\to\\infty}\\frac{\\log N(n)}{n/\\log n} \\leq \\limsup_{n\\to\\infty}\\frac{\\log N(n)}{n/\\log n} \\leq2\\log 2. \\] If $A_{\\rm adm}(n)$ denotes the number of subsets of $\\{2,\\ldots,n+1\\}$ that omit at least one residue class modulo every prime, then our main comparison is \\[ \\log N(n)=\\log A_{\\rm adm}(n)+o\\!\\left(\\frac{n}{\\log n}\\right). \\] We also obtain an asymptotic formula for the number of distinct intersections of survivor sets with the primes, and an exact recurrence $N(n+1)=N(n)+E(n)$, where $E(n)$ counts the survivor sets that can be extended by the new point $n+2$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08528",
  "author_total": 2,
  "authors": [
    {
      "name": "Mario Raso"
    },
    {
      "name": "Daniele Venturi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b0jt8fjdsyt1v.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08528",
  "fulltext_url": null,
  "id": "b0jt8fjdsyt1v",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08528",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7212053768",
  "pdf_url": "https://arxiv.org/pdf/2609.08528",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b0jt8fjdsyt1v.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.08528",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08528"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Counting Residue-Class Survivor Sets: An Asymptotic Comparison with Prime-Admissible Sets",
  "title_text": "Counting Residue-Class Survivor Sets: An Asymptotic Comparison with Prime-Admissible Sets",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/b0jt8fjdsyt1v",
  "venue": "arXiv",
  "versions": []
}