A group action is a formal way in which a group interacts with a set, allowing each group element to move or rearrange elements of that set. This concept connects group theory to combinatorics by enabling the study of symmetries and orbits within sets, which is crucial for understanding how to count distinct objects when symmetries are present. Group actions provide the foundation for several key results, including methods for calculating the number of distinct arrangements under group symmetry, leading to powerful tools like Burnside's lemma.
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