# CL-Shellable Posets with No EL-Shellings

## TL;DR

This paper constructs specific examples of CL-shellable posets that are not EL-shellable, demonstrating differences between these shellability concepts.

## Contribution

It introduces the first known ungraded and graded CL-shellable posets that lack EL-shellability, highlighting distinctions in poset shellability.

## Key findings

- Constructed ungraded CL-shellable poset without EL-shellability
- Constructed graded CL-shellable poset without EL-shellability
- Shows that CL-shellability does not imply EL-shellability

## Abstract

We construct an ungraded CL-shellable poset and a graded CL-shellable poset and show that neither is EL-shellable.