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Combinatorics of Hard Particles on Planar Graphs
J. Bouttier, P. Di Francesco, E. Guitter
We revisit the problem of hard particles on planar random tetravalent graphs in view of recent combinatorial techniques relating planar diagrams to decorated trees. We show how to…
Rectangular Matrix Models and Combinatorics of Colored Graphs
P. Di Francesco
We present applications of rectangular matrix models to various combinatorial problems, among which the enumeration of face-bicolored graphs with prescribed vertex degrees, and ver…
Census of Planar Maps: From the One-Matrix Model Solution to a Combinatorial Proof
J. Bouttier, P. Di Francesco, E. Guitter
We consider the problem of enumeration of planar maps and revisit its one-matrix model solution in the light of recent combinatorial techniques involving conjugated trees. We adapt…
Counting Colored Random Triangulations
J. Bouttier, P. Di Francesco, E. Guitter
We revisit the problem of enumeration of vertex-tricolored planar random triangulations solved in [Nucl. Phys. B 516 [FS] (1998) 543-587] in the light of recent combinatorial devel…
Critical and Tricritical Hard Objects on Bicolorable Random Lattices: Exact Solutions
J. Bouttier, P. Di Francesco, E. Guitter
We address the general problem of hard objects on random lattices, and emphasize the crucial role played by the colorability of the lattices to ensure the existence of a crystalliz…