How do excedances structure the symmetric group?

Define an equivalence relation on the symmetric group S_n by declaring two permutations equivalent if their weak excedances occur in the same positions and share the same values, up to reordering. This talk explores the resulting “excedance equivalence classes” of S_n: their number, the size of each class, and additional structure. Connections to the Bruhat order and Catalan numbers will be discussed. This is based on joint works with Nantel Bergeron and Antoine Abram.