{
  "abstract": "We classify the maximum scattered $\\mathbb{F}_q$-linear sets of $\\mathrm{PG}(1,q^5)$, proving that every such set is of pseudoregulus type or of Lunardon-Polverino type. Building on the reduction obtained by Lia, Longobardi and Zanella in [S. Lia, G. Longobardi and C. Zanella, Towards the classification of maximum scattered linear sets of $\\mathrm{PG}(1,q^5)$, Algebraic Combinatorics 9 (2026), 327-355], we show that the two remaining candidate families contain no scattered linear sets. Our approach reduces these candidates to two normal forms and establishes their non-scatteredness through the existence of rational points on associated algebraic varieties.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.35617",
  "author_total": 2,
  "authors": [
    {
      "name": "Giovanni Longobardi"
    },
    {
      "name": "Valentina Pepe"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/96er92xy41nt9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.35617",
  "fulltext_url": null,
  "id": "96er92xy41nt9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.35617",
  "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.CO"
    ],
    [
      "openalex",
      "1702|Coding theory and cryptography"
    ]
  ],
  "openalex": "W7214749819",
  "pdf_url": "https://arxiv.org/pdf/2609.35617",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/96er92xy41nt9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2609.35617",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.35617"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "The classification of maximum scattered linear sets of $\\mathrm{PG}(1,q^5)$",
  "title_text": "The classification of maximum scattered linear sets of PG(1,q^5)",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/96er92xy41nt9",
  "venue": "arXiv",
  "versions": []
}