On normalizing discrete Morse functions

TL;DR

This paper introduces a method to normalize combinatorial Morse functions into a unique integer-valued form, facilitating comparison and analysis of discrete Morse functions with the same gradient field.

Contribution

The authors propose a normalization technique that produces a canonical integer-valued representative for discrete Morse functions inducing a specific gradient field.

Findings

Provides a normalization method for discrete Morse functions

Ensures a canonical form for functions with the same gradient field

Simplifies comparison of Morse functions

Abstract

We present a way to normalize a combinatorial Morse function into an integer-valued canonical representative of the set of discrete Morse functions inducing a given gradient field.