An algorithmic enumeration method for weighted bi-colored plane trees is developed and applied to compute strong Hurwitz numbers for three-point branch data and the number of connected components in the moduli space of HCMU spheres with one conical singularity.
Graphs on Surfaces an d Their Applications
2 Pith papers cite this work. Polarity classification is still indexing.
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Partial duals of orientable hypermaps are Eulerian iff they correspond to crossing-total directions on the medial map with E' = D(Ω) ∪ T' (T' ⊆ T(Ω)), and bipartite iff they correspond to all-crossing directions with E' = C(Φ), plus the obstruction that all original hyperedges must have even length
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Counting Weighted Bi-Colored Plane Trees and Their Geometric Applications
An algorithmic enumeration method for weighted bi-colored plane trees is developed and applied to compute strong Hurwitz numbers for three-point branch data and the number of connected components in the moduli space of HCMU spheres with one conical singularity.