Unsensed enumeration of cubic unicellular maps on orientable and non-orientable surfaces: explicit formulas via orbifolds
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.
Fields of Study & Subjects
Geometric and Algebraic Topology
Mathematical Dynamics and Fractals
Stochastic processes and statistical mechanics
Publication details
- Journal / source
- Discrete Mathematics
- Volume
- 349
- Issue
- 12
- Pages
- 115332–115332
- Publication date
- 20 July 2026
- Language
- EN