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单词 orbit-counting formula
释义

orbit-counting formula

Also known as the Cauchy-Frobenius lemma and, incorrectly, as Burnside's lemma. For a group action of a finite group G on a finite set S, the number of orbits equals

where fix(g) is the number of elements s ∈ S fixed by g, that is g.s = s. The formula is useful in combinatorics.

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更新时间:2025/4/29 20:50:21