Symmetric functions

Symmetric functions are mathematical expressions involving variables where the function’s value remains unchanged if you swap any of the variables. For example, if you have variables x, y, and z, swapping x and y doesn’t change the value of the function. These functions are fundamental in algebra and combinatorics because they capture properties that don't depend on the order of variables, making them useful for understanding symmetrical patterns and solving equations with multiple variables. They are also central to areas like polynomial theory and representation theory.