2019/01/19 by Alexander Omelchenko, Omelchenko, Alexander, Igor Labutin +1
Mathematics · #math.CO #msc:05C30
paper · pdf · doi:10.48550/arxiv.1901.06591
published as Discrete Math. 349 (2026), no. 12, Paper No. 115332 · arXiv admin note: substantial text overlap with arXiv:1712.10139
arxiv created 2026/01/24 · arxiv updated 2026/07/30
We enumerate cubic (3-regular) unicellular maps on closed surfaces up to all homeomorphisms. Using the orbifold approach, we reduce the unsensed enumeration to explicit counts of quotient maps and rooted cubic/precubic maps on simpler surfaces. For orientable hosts this yields a compact identity expressed through known sensed and rooted numbers; for non orientable hosts we obtain a fully explicit finite sum expression via precubic counts. Numerical tables are provided, together with a brief asymptotic discussion.