A bijective proof of the enumeration of maps in higher genus

11/15/2017

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by   Mathias Lepoutre, et al.

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Bender and Canfield proved in 1991 that the generating series of maps in higher genus is a rational function of the generating series of planar maps. In this paper, we give the first bijective proof of this result. Our approach starts with the introduction of a canonical orientation that enables us to construct a bijection between 4-valent bicolorable maps and a family of unicellular blossoming maps.