A Generating Function for Fatgraphs
P. Di Francesco, C. Itzykson

TL;DR
This paper develops a generating function for fatgraphs with specified properties, providing a compact expression and a matrix integral representation that enables semi-classical computations and explicit formulas for genus zero trees.
Contribution
It introduces a new generating function for fatgraphs with specified valences, offering a compact expression and a matrix integral approach for advanced computations.
Findings
Derived a compact expression for the generating function of fatgraphs.
Established a matrix integral representation enabling semi-classical analysis.
Obtained a closed formula for genus zero, connected trees.
Abstract
We study a generating function for the sum over fatgraphs with specified valences of vertices and faces, inversely weighted by the order of their symmetry group. A compact expression is found for general (i.e. non necessarily connected) fatgraphs. This expression admits a matrix integral representation which enables to perform semi--classical computations, leading in particular to a closed formula corresponding to (genus zero, connected) trees.
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Taxonomy
TopicsProcess Optimization and Integration
