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 and generalize these techniques so as to give an alternative and purely combinatorial solution to the problem of counting arbitrary planar maps with prescribed vertex degrees.
Publié le : 2002-12-02
Classification:
[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO],
[PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech],
[PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th]
@article{hal-00586664,
author = {Bouttier, J\'er\'emie and Di Francesco, Philippe and Guitter, Emmanuel},
title = {Census of planar maps: from the one-matrix model solution to a combinatorial proof},
journal = {HAL},
volume = {2002},
number = {0},
year = {2002},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00586664}
}
Bouttier, Jérémie; Di Francesco, Philippe; Guitter, Emmanuel. Census of planar maps: from the one-matrix model solution to a combinatorial proof. HAL, Tome 2002 (2002) no. 0, . http://gdmltest.u-ga.fr/item/hal-00586664/