# A colourful path to matrix-tree theorems

## TL;DR

This paper revisits Zeilberger's proof of the matrix-tree theorem and provides a concise, unified proof for various known and new variants of the theorem, enhancing understanding and simplifying the proof process.

## Contribution

It offers a simplified, unified proof framework for multiple variants of the matrix-tree theorem, including some previously unknown versions.

## Key findings

- Unified proof for classical and variant matrix-tree theorems
- Introduction of new variants of the matrix-tree theorem
- Simplification of proof techniques for these theorems

## Abstract

In this short note, we revisit Zeilberger's proof of the classical matrix-tree theorem and give a unified concise proof of variants of this theorem, some known and some new.