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Pólya Enumeration Theorem
Graduate+
Definition
Theorem counting indistinguishable structures considering symmetry
Formulas
|X/G| = (1/|G|) Σ |X^g|
Cycle index: Z(G)
Colorings: PG(c₁,c₂,...,cₖ)
Examples
Example 1
Necklace coloring
Example 2
Polyhedra coloring
Example 3
Graph isomorphism
Applications
Chemistry
Graph theory
Molecular structures
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