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Cyclic Latin Eulerian Numbers — arXiv:2609.28808

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.28808
License (as archived): CC0-1.0
Archived: 2026-10-08T06:36:40.868Z
SHA-256 of the archived text: 1f0e271c01f2070e4c3da81108c4e5d44d51269b464b3fa0a9a61a09e5ad7e2d
Stable URL of this page: https://metraipolis.com/documento/dc_0eaeed05e191

How to cite

Cyclic Latin Eulerian Numbers — arXiv:2609.28808 — arXiv (en), https://arxiv.org/abs/2609.28808 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_0eaeed05e191 (Metraipolis archive dc_0eaeed05e191, sha256 1f0e271c01f2070e4c3da81108c4e5d44d51269b464b3fa0a9a61a09e5ad7e2d)

BibTeX

@misc{dc0eaeed05e191,
  title = {Cyclic Latin Eulerian Numbers — arXiv:2609.28808},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.28808},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_0eaeed05e191; sha256 1f0e271c01f2070e4c3da81108c4e5d44d51269b464b3fa0a9a61a09e5ad7e2d},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.28808. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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 $\Sigma(L_\pi) = n \operatorname{asc}(\pi) + \pi(1) - \pi(n)$, yielding a closed-form expression for the cyclic Latin-Eulerian polynomial.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-25 in math.CO).
Categorie arXiv: Combinatorics (math.CO).
Pagina del lavoro: https://arxiv.org/abs/2609.28808 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-08T06:02:10.009Z dalla pagina https://arxiv.org/catchup/math.CO/2026-09-25?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).