This article is cited in 5 papers

Generating functions for modular graphs and Burgers's equation

I. V. Artamkin

Moscow State Institute of Radio-Engineering, Electronics and Automation (Technical University)

Abstract: 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.

UDC: 512.772

MSC: Primary 14N10; Secondary 05Cxx, 35Q53

Received: 31.03.2005

DOI: 10.4213/sm1441

 English version: Sbornik: Mathematics, 2005, 196:12, 1715–1743

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