TL;DR
This paper presents a concise proof of the Harer-Zagier formula, which counts the ways to construct genus g Riemann surfaces from polygons, using semi-infinite wedge formalism operators.
Contribution
It introduces a novel, simplified proof of the Harer-Zagier formula leveraging semi-infinite wedge formalism, streamlining previous complex derivations.
Findings
Provides a short, elegant proof of the Harer-Zagier formula
Connects combinatorial enumeration with semi-infinite wedge formalism
Enhances understanding of Riemann surface enumeration methods
Abstract
The goal of this note is to provide a very short proof of Harer-Zagier formula for the number of ways of obtaining a genus g Riemann surface by identifying in pairs the sides of a (2d)-gon, using semi-infinite wedge formalism operators.
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