A curious identity that implies Faber's conjecture

TL;DR

This paper demonstrates that a specific generating series identity implies Faber's intersection number conjecture and provides a new proof by directly establishing this identity.

Contribution

It introduces a novel generating series identity that implies Faber's conjecture and offers a new proof through direct combinatorial verification.

Findings

The generating series identity implies Faber's intersection number conjecture.

A new proof of Faber's conjecture is provided based on this identity.

The approach connects combinatorial identities with geometric conjectures.

Abstract

We prove that a curious generating series identity implies Faber's intersection number conjecture (by showing that it implies a combinatorial identity already given in arXiv:1902.02742) and give a new proof of Faber's conjecture by directly proving this identity.