Explore the intricacies of representation theory and combinatorics in this 56-minute lecture from the 2021 Women and Mathematics - Terng Course. Delve into the symmetry group and related structures as presented by Monica Vazirani from the University of California, Davis. Gain insights into cycle notation, permutations, restrictions, and linearization. Understand the benefits of linearization and explore the concept of decomposability. Enhance your mathematical knowledge through this comprehensive examination of advanced algebraic concepts and their applications.