Authors: Nathan Williams ¹

• 1 Laboratoire de combinatoire et d'informatique mathématique [Montréal]

In this abstract, I will survey the story of two enumerative miracles that relate certain Coxeter-theoretic objects and other poset-theoretic objects. The first miracle relates reduced words and linear extensions, while the second may be thought of as relating group elements and order ideals. The purpose of this abstract is to use a conjecture from my thesis to present both miracles in the same light.