Lexicographic shellability is a powerful and popular technique used to study the topology of the order complex of a poset. The most useful flavor of lexicographic shellability is CL-shellability, which was introduced by Björner and Wachs in the early 1980s and which was then reformulated by them using the notion of recursive atom orderings. In this talk, I will start by providing a survey of some of the key ideas behind lexicographic shellability, particularly CL-shellability, recursive atom orderings, and CC-shellability, the more general version of lexicographic shellability introduced by Kozlov. Then, inspired by Bjorner and Wachs’ formulation of recursive atom orderings, I will introduce a recursive formulation of CC-shellability called generalized recursive atom orderings. I will then discuss some of the new and surprising results provided by this new formulation of CC-shellability.

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