Welcome to the website for Implementing Fully Commutative Elements in SageMath, an Experimental Mathematics Lab project at the University of Colorado Boulder. Our team includes mentors Sarah Salmon, Tianyuan Xu and undergraduate students Natalie Schoenhals, Saurabh Totey and Wei Qu. The goal of our project is to implement fully commutative (FC) elements of Coxeter groups and the heaps of FC elements in the software SageMath, with a view towards applications to combinatorial representation theory. SageMath, or Sage, is a computer algebra system based on Python, and a main component of the project is writing Sage code to create, identify, and count FC elements for any given Coxeter group. A more detailed overview of the project is available here.
The main references for the project are: