# Mathematics Colloquia and Seminars

In this talk we will begin by surveying some of these connections. We will then detail several recent results that characterize various combinatorial properties of Patience Sorting in terms of permutation pattern avoidance. In particular, we will show that Patience Sorting provides an algorithmic description for permutations avoiding the barred (generalized) permutation pattern $3-\bar{1}-42$. We will also characterize those permutations for which Patience Sorting is an invertible algorithm as the set of permutations simultaneously avoiding the barred patterns $3-\bar{1}-42$ and $3-\bar{1}-24$. This is joint work with Alex Burstein (Iowa State University).