Abstract
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. Dans ce résumé, j’étudie l’histoire de deux miracles énumératifs qui relient certains objets de la théorie de Coxeter et d’autres objets de la théorie des posets. Le premier miracle relie des mots réduits et des extensions linéaires, tandis que le second relie des éléments du groupe et des idéaux d’ordre. Le but de ce résumé est d’utiliser une conjecture de ma thèse afin de présenter les deux miracles sous la même lumière.
Highlights
I will survey the story of two enumerative miracles that relate certain Coxeter-theoretic objects and other poset-theoretic objects
We quickly review the geometric representation of finite Coxeter systems
Order ideals of the root poset may be used to label the regions of Shi(W ) in the following way (i)
Summary
I will survey the story of two enumerative miracles that relate certain Coxeter-theoretic objects and other poset-theoretic objects. Let w = s1 · · · sk be a reduced S-word for a fully commutative element w. Note that when w is fully commutative, inver1 sion sets for elements in Weak(W, w) are order ideals in Φ+ (W, w).
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
