Bijective proof of the rationality of the generating series of higher-genus maps

zbMath1411.05125MaRDI QIDQ2632710

Mathias Lepoutre

Publication date: 15 May 2019

Published in: Séminaire Lotharingien de Combinatoire (Search for Journal in Brave)

Full work available at URL: http://www.mat.univie.ac.at/~slc/wpapers/FPSAC2018//67-Lepoutre.html

zbMATH Keywords

mapsrational parametrizationhigher genusbijective combinatorics

Mathematics Subject Classification ID

Enumeration in graph theory (05C30)

Cites Work

• Unified bijections for maps with prescribed degrees and girth
• A generic method for bijections between blossoming trees and planar maps
• Encoding toroidal triangulations
• A bijection for covered maps, or a shortcut between Harer-Zagiers and Jacksons formulas
• A bijection for triangulations, quadrangulations, pentagulations, etc.
• Census of planar maps: From the one-matrix model solution to a combinatorial proof
• Optimal coding and sampling of triangulations
• Bijective counting of tree-rooted maps and shuffles of parenthesis systems
• Counting surfaces. CRM Aisenstadt chair lectures
• The asymptotic number of tree-rooted maps on a surface
• The number of rooted maps on an orientable surface
• Bijective census and random generation of Eulerian planar maps with prescribed vertex degrees
• Graphs on surfaces and their applications. Appendix by Don B. Zagier
• Planar maps as labeled mobiles
• Lattice structures from planar graphs
• ULD-Lattices and Δ-Bonds
• Asymptotic Enumeration of Constellations and Related Families of Maps on Orientable Surfaces
• A Bijection for Rooted Maps on Orientable Surfaces
• Tessellations of random maps of arbitrary genus
• A Census of Slicings

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