{
  "abstract": "A family of permutations in $S_n$ is called even-intersecting if every two distinct members agree in an even number of positions. Let $M(n)$ denote the maximum size of such a family. For even $n$, we prove that $$n!!\\leq M(n)\\leq e^{\\frac{n}{2}+o(n)}n!!,$$ improving the bound obtained from a theorem of Cameron, Deza and Frankl (1987) by an exponential factor. This problem may be viewed as a permutation analogue of the classical Eventown problem for set systems. For odd $n$, we give a construction yielding $M(n)\\geq n^2/4$. We further extend this construction to obtain $$ M(n)\\geq\\bigl(n-\\sqrt{n-1}\\bigr)^2 ,$$ whenever $n=(q+1)^2+1$ and $q$ is an odd prime power. The latter bound asymptotically matches the upper bound $M(n)\\leq(n-1)^2+1$ obtained by Cameron, Deza and Frankl.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.21645",
  "author_total": 3,
  "authors": [
    {
      "name": "Anirban Banerjee"
    },
    {
      "name": "Abisek Dewan"
    },
    {
      "name": "Rajiv Mishra"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/53sas4f9q4j8c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.21645",
  "fulltext_url": null,
  "id": "53sas4f9q4j8c",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.21645",
  "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"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7213944532",
  "pdf_url": "https://arxiv.org/pdf/2609.21645",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/53sas4f9q4j8c.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:07Z",
      "native_id": "2609.21645",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.21645"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Even-Intersecting Families of Permutations",
  "title_text": "Even-Intersecting Families of Permutations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:07Z",
  "url": "https://research.draconitic.com/paper/53sas4f9q4j8c",
  "venue": "arXiv",
  "versions": []
}