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PreprintCC BY 4.0arXiv

Cyclic Latin Eulerian Numbers

  • Madjid Mirzavaziri
  • Daniel Yaqubi
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Abstract

We introduce the directed cyclic difference inventory Dn(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(Lπ) = n asc(π) + π(1) − π(n), yielding a closed-form expression for the cyclic Latin-Eulerian polynomial.

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Cite

BibTeXRIS
BibTeX
@misc{mirzavaziri2026cyclic,
  title = {{Cyclic Latin Eulerian Numbers}},
  author = {Madjid Mirzavaziri and Daniel Yaqubi},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.28808},
  eprint = {2609.28808},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.28808},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Cyclic Latin Eulerian Numbers
AU  - Madjid Mirzavaziri
AU  - Daniel Yaqubi
PY  - 2026
DA  - 2026/09/23
PB  - arXiv
DO  - 10.48550/arxiv.2609.28808
UR  - https://arxiv.org/abs/2609.28808
AB  - We introduce the directed cyclic difference inventory D_n(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 asc(π) + π(1) − π(n), yielding a closed-form expression for the cyclic Latin-Eulerian polynomial.
ER  -