Geodesic
Relating ordinary and fully simple maps via monotone Hurwitz numbers
Gaëtan Borot1 ; Séverin Charbonnier1 ; Norman Do2 ; Elba Garcia-Failde3
1Max Planck Institut für Mathematik
2Monash University
3Institut de Physique Théorique-CEA Saclay
The electronic journal of combinatorics, Tome 26 (2019) no. 3
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A direct relation between the enumeration of ordinary maps and that of fully simple maps first appeared in the work of the first and last authors. The relation is via monotone Hurwitz numbers and was originally proved using Weingarten calculus for matrix integrals. The goal of this paper is to present two independent proofs that are purely combinatorial and generalise in various directions, such as to the setting of stuffed maps and hypermaps. The main motivation to understand the relation between ordinary and fully simple maps is the fact that it could shed light on fundamental, yet still not well-understood, problems in free probability and topological recursion.
DOI : 10.37236/8634
Classification : 05A15, 05A19, 20C30
Mots-clés : maps, fully simple maps, stuffed maps, hypermaps, monotone Hurwitz numbers, dessin d'enfants

Gaëtan Borot  1   ; Séverin Charbonnier  1   ; Norman Do  2   ; Elba Garcia-Failde  3

1 Max Planck Institut für Mathematik
2 Monash University
3 Institut de Physique Théorique-CEA Saclay 
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     author = {Ga\"etan Borot and S\'everin Charbonnier and Norman Do and Elba Garcia-Failde},
     title = {Relating ordinary and fully simple maps via monotone {Hurwitz} numbers},
     journal = {The electronic journal of combinatorics},
     year = {2019},
     volume = {26},
     number = {3},
     doi = {10.37236/8634},
     zbl = {1430.05004},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/8634/}
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Gaëtan Borot; Séverin Charbonnier; Norman Do; Elba Garcia-Failde. Relating ordinary and fully simple maps via monotone Hurwitz numbers. The electronic journal of combinatorics, Tome 26 (2019) no. 3. doi: 10.37236/8634

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