Introduction to Superpatterns

In the Combinatorics of permutations, patterns describe how a smaller permutation can be 'contained' in a larger permutation. There has been an explosion of research papers in permutation patterns since it was first defined by Donald Knuth in 1968. Within the realm of permutation patterns is a relatively new topic called the superpattern problem, which asks, "If P is a set of permutations, what is the smallest n such that there exists a permutation of length n which contains every element of P as a pattern?" In this talk, we will detail some known results on the superpattern problem and explore some variations to this question.