Superpatterns Containing Special Subsets of Permutations

Pattern containment is a concept for how a permutation can be contained in a larger permutation, and arises naturally in many contexts. Let Sk be the set of permutations of length k. We say that a permutation p is a k-superpattern if it contains every element of Sk as a pattern. Then, a natural question to ask is, ”What is the shortest length that a k-superpattern can be?” In this talk, we will discuss the general superpattern problem and some of its variations.