The conjugacy character ofS n tends to be regular
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Consider the regular and the conjugacy characters ofS n as vectors in Euclidean space, with the standard inner product. Asn grows, the angle between them tends to zero and the ratio of their lengths tends to one. The two characters have therefore asymptotically similar decompositions into irreducible components.
KeywordsAsymptotic Expansion Finite Group Conjugacy Class Class Function Irreducible Component
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