In the area of combinatorics known as ‘permutation patterns’, seemingly innocuous questions can conceal a surprising degree of difficulty, giving rise to combinatorial problems that range from trivial to unsolved (despite decades of work). In this talk, we will explore several ways in which permutation pattern questions interface with probability — sometimes giving rise to probabilistic processes, sometimes illuminated by probabilistic reasoning. Some of these will be generalizations of known processes, others new, and still others conjectural.



Based on forthcoming joint work with Slim Kammoun and Einar Steingrimsson.