Geodesic
Generating functions for modular graphs and Burgers's equation
Sbornik. Mathematics, Tome 196 (2005) no. 12, pp. 1715-1743

Voir la notice de l'article provenant de la source Math-Net.Ru

It is shown that the generating functions of modular graphs satisfy Burgers's equations, which enable one to obtain in a unified way the generating functions for the virtual Euler characteristic and the Poincaré polynomial of the moduli space of punctured curves $\overline M_{g,n}$ and for the number (with weights $1/|{\operatorname{Aut}G}|$) of modular graphs $G$ of a definite type. 
@article{SM_2005_196_12_a0,
     author = {I. V. Artamkin},
     title = {Generating functions for modular graphs and {Burgers's} equation},
     journal = {Sbornik. Mathematics},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2005_196_12_a0/}
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I. V. Artamkin. Generating functions for modular graphs and Burgers's equation. Sbornik. Mathematics, Tome 196 (2005) no. 12, pp. 1715-1743. http://geodesic.mathdoc.fr/item/SM_2005_196_12_a0/