Combinatorial Morse flows are hard to find

TL;DR

This paper studies the difficulty of randomly finding combinatorial Morse flows on simplicial complexes, demonstrating that the probability of success is very low through rigorous quantification.

Contribution

It provides a theoretical analysis quantifying how unlikely it is to detect combinatorial Morse flows using random search methods.

Findings

Probability of detection is very small.

Quantitative bounds on detection likelihood.

Implications for algorithms searching for Morse flows.

Abstract

We investigate the probability of detecting combinatorial Morse flows on a simplicial complex via a random search. We prove that it is really small, in a quantifiable way.