Theorem of Burnside

Burnside's Theorem is a fundamental result in group theory, a branch of mathematics studying symmetrical structures. It states that for certain symmetry groups acting on objects, the number of distinct patterns or configurations (called orbits) can be found by averaging the number of fixed points over all group elements. In simple terms, it provides a method to count unique arrangements after accounting for symmetries, such as rotations or reflections, by examining how each symmetry operation leaves some configurations unchanged. This helps in understanding how objects can be distinguished or classified under symmetry transformations.