In this talk, we will discuss an interesting connection between certain permutations of the symmetric group, pattern avoidance, and Catalan numbers. Along the way, we will explore visual representations of permutations in terms string diagrams and heaps, as well as touch on an open problem involving Coxeter groups.
This talk was given by my undergraduate research student Molly Green (Northern Arizona University) on March 1, 2014 at the Southwestern Undergraduate Mathematics Research Conference (SUnMaRC) at Mesa Community College, Mesa, AZ.