Séminaire Lotharingien de Combinatoire, 80B.67 (2018), 12 pp.
Mathias Lepoutre
Bijective Proof of the Rationality of the Generating Series of Higher-Genus Maps
Abstract.
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.
Received: November 14, 2017.
Accepted: February 17, 2018.
Final version: April 1, 2018.
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