This talk introduces the new notion of global pattern avoidance. Unlike classical pattern containment, which looks for signed permutations embedded in signed permutations, global pattern containment identifies unsigned permutations discreetly embedded in size 2n, centro-symmetric writings of signed permutations. In this talk, we explore natural questions of classification and enumeration of the signed permutations that don’t globally contain certain patterns to find pleasant results, interesting bijections, and unexpected set equivalences. The theorems presented can be used to classify a great variety of enumerative and qualitative results. We then explore when global pattern containment is equivalent to classical signed pattern containment and how the notions diverge. Permutations arise naturally and frequently, and the permutations avoiding a particular set of patterns often carry a deep connection to interesting mathematical objects. We conclude with a discussion of how the global and classical pattern notions compare at succinctly classifying mathematical objects, such as type B Boolean and Vexillary permutations.

This talk introduces the notion of global pattern avoidance and focuses on equivalences and containments of permutation sets defined by globally avoiding certain patterns. We focused on bijective and combinatorial arguments and concluded with an in-depth look at our enumerative results and techniques.