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.

翻译：我们引入了Morse序列的概念，其为离散Morse理论提供了一种简单且有效的方法。Morse序列由仅两种基本操作构成，即扩展（坍缩的逆操作）与填充（穿孔的逆操作）。我们证明了Morse序列可视为表示任意离散Morse函数梯度向量场的替代方式。同时，本文还展示了Morse序列与不同类型Morse函数之间建立联系的直接方法。最后，我们提出了最大Morse序列，该序列形式化了从任意单纯复形构建Morse序列的两种基本方案。