{
  "abstract": "We introduce the directed cyclic difference inventory $D_n(\\mathbf{m})$ to study Latin Eulerian numbers restricted to row-reorderings of the cyclic Latin square, offering an orientation-sensitive refinement of the prescribed-edge-length Hamiltonian path problem. We establish exact enumeration formulas, symmetries, and realizability obstructions for this inventory. Furthermore, we reduce the cyclic total-ascent statistic directly to endpoint-refined Eulerian statistics via the identity $Σ(L_π) = n \\operatorname{asc}(π) + π(1) - π(n)$, yielding a closed-form expression for the cyclic Latin-Eulerian polynomial.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.28808",
  "author_total": 2,
  "authors": [
    {
      "name": "Madjid Mirzavaziri"
    },
    {
      "name": "Daniel Yaqubi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7x8dh4zsp09ka.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28808",
  "fulltext_url": null,
  "id": "7x8dh4zsp09ka",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.28808",
  "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": "W7214390211",
  "pdf_url": "https://arxiv.org/pdf/2609.28808",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7x8dh4zsp09ka.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.28808",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28808"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Cyclic Latin Eulerian Numbers",
  "title_text": "Cyclic Latin Eulerian Numbers",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/7x8dh4zsp09ka",
  "venue": "arXiv",
  "versions": []
}