Burnside's theorem

Burnside's theorem is a principle in group theory that helps count distinct objects under symmetry transformations. It states that the number of unique arrangements (or orbits) of a set, when you consider symmetrical operations (like rotations or reflections), can be found by averaging the number of arrangements fixed by these operations. Essentially, it provides a method to determine how many different ways a set can be organized while accounting for repeated patterns due to symmetry, making it useful in areas like combinatorics, chemistry, and even art.