Polya Enumeration Theorem

The Polya Enumeration Theorem is a mathematical tool used to count how many unique arrangements or patterns can be created when objects are assigned to positions, considering symmetrical transformations like rotations or reflections. It helps to avoid overcounting arrangements that are essentially the same due to symmetry. For example, it can determine how many different color patterns exist on a Rubik’s Cube's face, taking into account rotations that make some patterns indistinguishable. In essence, it simplifies complex counting problems involving symmetry by systematically accounting for equivalent arrangements.