In this talk, we will take you on a journey from some ostensibly inauspicious boxes all the way to a sneak peek at the Macdonald polynomials, which were introduced by Ian G. Macdonald in 1987 and have since been an area of great research interest.
Symmetric functions are functions that remain the same when interchanging variables. They appear in all sorts of areas in mathematics and have many well-known examples, such as the elementary symmetric functions, the Schur functions and the Hall–Littlewood symmetric functions. Wouldn’t it be nice to have a general form that captures them all? Especially when it starts with something as simple as counting boxes?