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Enumeration of orientable coverings of a non-orientable manifold

Abstract : In this paper we solve the known V.A. Liskovets problem (1996) on the enumeration of orientable coverings over a non-orientable manifold with an arbitrary finitely generated fundamental group. As an application we obtain general formulas for the number of chiral and reflexible coverings over the manifold. As a further application, we count the chiral and reflexible maps and hypermaps on a closed orientable surface by the number of edges. Also, by this method the number of self-dual and Petri-dual maps can be determined. This will be done in forthcoming papers by authors.
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Jin Ho Kwak, Alexander Mednykh, Roman Nedela. Enumeration of orientable coverings of a non-orientable manifold. 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008), 2008, Viña del Mar, Chile. pp.215-226, ⟨10.46298/dmtcs.3647⟩. ⟨hal-01185183⟩



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