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We introduce the notion of fully simple maps, which are maps with non self-intersecting disjoint boundaries.
A census of Hamiltonian polygons
W.T. Tutte · 1962
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W.T. Tutte · 1963
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W.G. Brown · 1966
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Counting rooted maps by genus. I
R.S. Walsh and A.B. Lehman · 1972
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Symmetric polynomials and the center of the symmetric group ring
A.A. Jucys · 1974
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A planar diagram theory for strong interactions
G. t’Hooft · 1974
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Counting rooted maps by genus III: Nonseparable maps
R.S. Walsh and A.B. Lehman · 1975
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Planar diagrams
É. Brézin, C. Itzykson, G. Parisi, and J.-B. Zuber · 1978
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The planar approximation II
C. Itzykson and J.-B. Zuber · 1980
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A new construction of Young’s seminormal representation of the symmetric groups
G.E. Murphy · 1981
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The Euler characteristics of the moduli space of curves
J. Harer and D. Zagier · 1986
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Ising model on a dynamical planar random lattice: Exact solution
V.A. Kazakov · 1986
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Addition of certain non-commuting random variables
D.-V. Voiculescu · 1986
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O ( n ) O(n) on a fluctuating lattice. Some exact results
M. Gaudin and I.K. Kostov · 1989
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Properties of hermitian matrix models in an external field
Yu. Makeenko and G.W. Semenoff · 1991
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Limit laws for random matrices and free products
D.-V. Voiculescu · 1991
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Two dimensional gravity and intersection theory on moduli space
E. Witten · 1991
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Higher genus correlators from the hermitian 1 1 -matrix model
J. Ambjørn, L.O. Chekhov, and Yu. Makeenko · 1992
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Intersection theory on the moduli space of curves and the matrix Airy function
M. Kontsevich · 1992
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2 d 2d gravity and random matrices
P. di Francesco, P. Ginsparg, and J. Zinn-Justin · 1994
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Multiplicative functions on the lattice of noncrossing partitions and free convolution
R. Speicher · 1994
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Exact solution of the O ( n ) O(n) model on a random lattice
B. Eynard and C. Kristjansen · 1995
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Symmetric functions and Hall polynomials
I.G. Macdonald · 1995
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A bijective census of nonseparable planar maps
B. Jacquard and G. Schaeffer · 1998
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Character expansions, Itzykson-Zuber integrals, and the QCD partition function
A.B. Balentekin · 2000
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Toda equations for Hurwitz numbers
A. Okounkov · 2000
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Hypergeometric solutions of soliton equations
A.Yu. Orlov and D.M. Shcherbin · 2001
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Enumeration of nonseparable planar maps
J. Cai and Y. Liu · 2002
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Moments and cumulants of polynomial random variables on unitary groups, the Itzykson-Zuber integral and free probability
B. Collins · 2003
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Topological expansion for the 1 1 -hermitian matrix model correlation functions
B. Eynard · 2004
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Jucys-Murphy elements and the unitary Weingarten function
J. Novak · 2010
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Enumeration of maps with self avoiding loops and the O ( n ) O(n) model on random lattices of all topologies
G. Borot and B. Eynard · 2011
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A matrix model for simple Hurwitz numbers, and topological recursion
G. Borot, B. Eynard, M. Mulase, and B. Safnuk · 2011
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A new combinatorial identity for unicellular maps, via a direct bijective approach
G. Chapuy · 2011
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Formal matrix integrals and combinatorics of maps
B. Eynard · 2011
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The Laplace transform of the cut-and-join equation and the Bouchard-Mariño conjecture on Hurwitz numbers
B. Eynard, M. Mulase, and B. Safnuk · 2011
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Representation theory
W. Fulton and J. Harris · 2004
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Graphs on surfaces and their applications
S.K. Lando and A.K. Zvonkin · 2004
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Applications of the representation theory of finite groups
D. Zagier · 2004
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A direct bijection for the Harer-Zagier formula
I.P. Goulden and A. Nica · 2005
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Hermitean matrix model free energy: Feynman graph technique for all genera
L.O. Chekhov · 2006
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Second order freeness and fluctuations of random matrices: I. Gaussian and Wishart matrices and cyclic Fock spaces
J. Mingo and R. Speicher · 2006
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Loop models on random maps via nested loops: case of domain symmetry breaking and application to the Potts model
G. Borot, J. Bouttier, and E. Guitter · 2012
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More on the O ( n ) O(n) model on random maps via nested loops: loops with bending energy
G. Borot, J. Bouttier, and E. Guitter · 2012
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About the x x - y y symmetry of the F g F_{g} algebraic invariants
B. Eynard and N. Orantin · 2013
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Formal multidimensional integrals, stuffed maps, and topological recursion
G. Borot · 2014
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Monotone Hurwitz numbers and the HCIZ integral
I.P. Goulden, M. Guay-Paquet, and J. Novak · 2014
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Topological recursion for Gaussian means and cohomological field theories
J.E. Andersen, L.O. Chekhov, P. Norbury, and R.C. Penner · 2015
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Abstract loop equations, topological recursion, and applications
G. Borot, B. Eynard, and N. Orantin · 2015
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Diagonal solutions to the 2 2 -Toda hierarchy
S.R. Carrell · 2015
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2 d 2d Toda tau-functions as combinatorial generating functions
M. Guay-Paquet and J. Harnad · 2015
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Ramifications of Hurwitz theory, KP integrability and quantum curves
A. Alexandrov, D. Lewański, and S. Shadrin · 2016
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Hodge-GUE correspondence and the discrete KdV equation
B. Dubrovin, S.-Q. Liu, D. Yang, and Y. Zhang · 2016
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Counting surfaces
B. Eynard · 2016
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Fermionic approach to weighted Hurwitz numbers and topological recursion
A. Alexandrov, G. Chapuy, B. Eynard, and J. Harnad · 2017
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Blobbed topological recursion : properties and applications
G. Borot and S. Shadrin · 2017
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Combinatorics of loop equations for branched covers
P. Dunin-Barkowski, N. Orantin, A. Popolitov, and S. Shadrin · 2017
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Representation theory of symmetric groups
P.-L. Méliot · 2017
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Bijections for planar maps with boundaries
O. Bernardi and É. Fusy · 2018
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