# Morse sequences

arXiv: https://arxiv.org/abs/2402.07526 · HTML: https://mlsanity.com/paper/2402.07526/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 52 references that are in the map.
- First posted on arXiv 12 Feb 2024.

## Builds on (most cited first, 3 of 3)

- [Random Discrete Morse Theory and a New Library of Triangulations](https://mlsanity.com/paper/1303.6422/) (2013)
- [Extremal examples of collapsible complexes and random discrete Morse theory](https://mlsanity.com/paper/1404.4239/) (2014)
- [Computing discrete Morse complexes from simplicial complexes](https://mlsanity.com/paper/1811.04485/) (2018)

## Abstract (arXiv)

We introduce the notion of a Morse sequence, which provides a simple and effective approach to discrete Morse theory. A Morse sequence is a sequence composed solely of two elementary operations, that is, expansions (the inverse of a collapse), and fillings (the inverse of a perforation). We show that a Morse sequence may be seen as an alternative way to represent the gradient vector field of an arbitrary discrete Morse function. We also show that it is possible, in a straightforward manner, to make a link between Morse sequences and different kinds of Morse functions. At last, we introduce maximal Morse sequences, which formalize two basic schemes for building a Morse sequence from an arbitrary simplicial complex.