Applying the Pólya-Burnside Enumeration Theorem

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The Pólya–Burnside enumeration theorem is an extension of the Pólya–Burnside lemma, Burnside's lemma, the Cauchy–Frobenius lemma, or the orbit‐counting theorem.

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Given a finite group acting on a set of elements, the Pólya–Burnside enumeration theorem counts the number of elements of a given type as a function of their order.

In this Demonstration, a set of binary strings of a given length is acted upon by the group . The first component acts by word-reversing, while the second acts by bit‐wise negation. Rewriting rules and corresponding orbits are explicitly worked out for these reflections.

The number of orbits is for even and for odd .

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Contributed by: Hector Zenil and Oleksandr Pavlyk (March 2011)
Open content licensed under CC BY-NC-SA


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