The Pólya Enumeration Theorem is a powerful combinatorial tool used to count the distinct arrangements of objects under symmetrical transformations. It connects the concept of labelled and unlabelled structures by allowing the enumeration of configurations that are indistinguishable due to symmetries, such as rotations and reflections. This theorem provides a systematic way to count structures while considering these symmetries, making it essential for understanding complex counting problems in combinatorics.
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