Permutation pattern avoidance, alternating sign matrices, and asymptotics (Justin Troyka, Cal State LA)

A big area in combinatorics over the last several decades has been the study of pattern-avoiding permutations, whose enumeration is exciting and mysterious. Alternating sign matrices (ASMs) are a generalization of permutations whose study in combinatorics has also been exciting and mysterious. In this talk, I will explain some new asymptotic results involving the number of ASMs that avoid a given permutation pattern, from my joint work with Mathilde Bouvel, Eric Egge, Rebecca Smith, and Jessica Striker. I will also show some of the highlights in the histories of both pattern-avoiding permutations and ASMs.