# Perron transforms and Hironaka's game

## TL;DR

This paper introduces a unified matrix-based framework that generalizes Hironaka's game and Perron transforms, providing insights into their roles in local uniformization proofs.

## Contribution

It presents a new matricial result that simultaneously generalizes Hironaka's game and Perron transforms, linking them in a common theoretical framework.

## Key findings

- Unified matricial framework for Perron transforms and Hironaka's game
- Derivation of Perron algorithm forms in local uniformization proofs
- Enhanced understanding of the relationship between these mathematical concepts

## Abstract

In this paper we present a matricial result that generalizes Hironaka's game and Perron transforms simultaneously. We also show how one can deduce the various forms in which the algorithm of Perron appears in proofs of local uniformization from our main result.