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math.CO2026
Affine weighted Motzkin paths and the differential kernel method
Alexander Omelchenko
We study Motzkin paths whose up-, level-, and down-step weights are affine functions of the height: alpha_k = A k + alpha_0, gamma_k = B k + gamma_0, beta_k = C k + beta_0. Let w_{…
math.CO2026
Unsensed enumeration of cubic unicellular maps on orientable and non-orientable surfaces
Alexander Omelchenko, Igor Labutin
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 q…