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We introduce the set of (non-spanning) tree-decorated planar maps, and show that they are in bijection with the Cartesian product between the set of trees and the set of maps with a simple boundary.
A combinatorial representation of polyhedral surfaces
Jack Edmonds · 1960
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A new branch of enumerative graph theory
William Tutte · 1962
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On the enumeration of tree-rooted maps
Ronald Mullin · 1967
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Enumeration of almost cubic maps
Arak Mathai and Pushpa Rathie · 1972
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Counting rooted maps by genus ii
Timothy Walsh and Alfred Lehman · 1972
Earlier work this paper cites.
Shuffle of parenthesis systems and baxter permutations
Robert Cori, Serge Dulucq, and Gérard Viennot · 1986
Earlier work this paper cites.
Conformal spectra of polymers on a random surface
Bertrand Duplantier and Ivan Kostov · 1988
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Conjugaison d’arbres et cartes combinatoires aléatoires
Gilles Schaeffer · 1998
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Enumerative combinatorics. Vol. 2
Richard P. Stanley · 1999
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Planar maps as labeled mobiles
Jérémie Bouttier, Philippe Di Francesco, and Emmanuel Guitter · 2004
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Combinatorial enumeration
Ian Goulden and David Jackson · 2004
Earlier work this paper cites.
Geometrical vs. fortuin–kasteleyn clusters in the two-dimensional q-state potts model
Wolfhard Janke and Adriaan Schakel · 2004
Cited alongside, same era.
Random trees and applications
Jean-François Le Gall · 2005
Cited alongside, same era.
Limit of normalized quadrangulations: the brownian map
Jean-François Marckert and Abdelkader Mokkadem · 2006
Cited alongside, same era.
Bijective counting of tree-rooted maps and shuffles of parenthesis systems
Olivier Bernardi · 2007
Cited alongside, same era.
Explicit enumeration of triangulations with multiple boundaries
Maxim Krikun · 2007
Cited alongside, same era.
Distance statistics in quadrangulations with a boundary, or with a self-avoiding loop
Jérémie Bouttier and Emmanuel Guitter · 2009
Cited alongside, same era.
Boundary behaviour of conformal maps
Christian Pommerenke · 2013
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Scaling limit of random planar quadrangulations with a boundary
Jérémie Bettinelli · 2015
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Comparing two statistical ensembles of quadrangulations: a continued fraction approach
Éric Fusy and Emmanuel Guitter · 2015
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Self-avoiding walks on the uipq
Alessandra Caraceni and Nicolas Curien · 2016
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Quantum gravity and inventory accumulation
Scott Sheffield · 2016
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Compact brownian surfaces I: Brownian disks
Jérémie Bettinelli and Grégory Miermont · 2017
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Analytic combinatorics
Philippe Flajolet and Robert Sedgewick · 2009
Cited alongside, same era.
A recursive approach to the O (n) model on random maps via nested loops
Gaetan Borot, Jérémie Bouttier, and Emmanuel Guitter · 2011
Cited alongside, same era.
Counting planar maps, coloured or uncoloured
Mireille Bousquet-Mélou · 2011
Cited alongside, same era.
Uniqueness and universality of the brownian map
Jean-François Le Gall · 2013
Cited alongside, same era.
The brownian map is the scaling limit of uniform random plane quadrangulations
Grégory Miermont · 2013
Cited alongside, same era.
Convergence of the self-avoiding walk on random quadrangulations to SLE
Ewain Gwynne and Jason Miller
Cited in the paper.
Later among the works it cites.
A mating-of-trees approach to graph distances in random planar maps
Ewain Gwynne, Nina Holden, and Xin Sun · 2017
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Bijections for planar maps with boundaries
Olivier Bernardi and Éric Fusy · 2018
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The fractal dimension of Liouville quantum gravity: universality, monotonicity, and bounds
Jian Ding and Ewain Gwynne · 2018
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Limits of tree-decorated maps
Luis Fredes and Avelio Sepúlveda · 2019
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Convergence of the free Boltzmann quadrangulation with simple boundary to the brownian disk
Ewain Gwynne and Jason Miller · 2019
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