{
  "abstract": "We introduce \\emph{Latin Eulerian numbers} $\\LE{n\\atop k_1,\\dots,k_n}$, a multivariate refinement of classical Eulerian numbers counting order-$n$ Latin squares by column ascents. We establish their fundamental symmetries, univariate marginals, and an exact multiplicity divisibility property. For the total ascent statistic $Σ(L)=\\sum_i k_i(L)$, we prove the sharp, isolated bounds $n-1 \\le Σ(L) \\le (n-1)^2$, demonstrating that the adjacent values $n$ and $(n-1)^2-1$ are strictly unattainable. To analyze intermediate values, we show that symbol permutations typically ignored in classical enumeration directly govern $Σ$ via an exact formula. This insight yields explicit constructions for the interior range, motivates a unimodality conjecture for the total ascent distribution.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.25100",
  "author_total": 2,
  "authors": [
    {
      "name": "Madjid Mirzavaziri"
    },
    {
      "name": "Daniel Yaqubi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eqvb0j9d18y86.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.25100",
  "fulltext_url": null,
  "id": "eqvb0j9d18y86",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.25100",
  "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": "W7214111181",
  "pdf_url": "https://arxiv.org/pdf/2609.25100",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/eqvb0j9d18y86.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2609.25100",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.25100"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Latin Eulerian Numbers",
  "title_text": "Latin Eulerian Numbers",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/eqvb0j9d18y86",
  "venue": "arXiv",
  "versions": []
}