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arXiv · 1901.06591

Unsensed enumeration of cubic unicellular maps on orientable and non-orientable surfaces

Alexander Omelchenko·Igor Labutin
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Abstract

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.

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Alexander Omelchenko, Igor Labutin. 2019-01-19. Unsensed enumeration of cubic unicellular maps on orientable and non-orientable surfaces. https://doi.org/10.1016/j.disc.2026.115332

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