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arXiv · 1712.10139

Enumeration of Unsensed Orientable Maps on Surfaces of a Given Genus

Evgeniy Krasko·Alexander Omelchenko
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Abstract

In this work for the first time we enumerate unlabelled maps on orientable genus $g$ surfaces with respect to all homeomorphisms, including both orientation-preserving and orientation-reversing. We show that in the latter case as an intermediate step one has to enumerate rooted maps of a special kind (quotient maps) on orientable and non-orientable surfaces possibly having a boundary and a certain number of branch points. In this work we develop a special technique for enumerating such maps.

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Evgeniy Krasko, Alexander Omelchenko. 2019-01-19. Enumeration of Unsensed Orientable Maps on Surfaces of a Given Genus. https://arxiv.org/abs/1712.10139

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