Erdős Problem #1161

The problem

Let $f_k(n)$ count the number of elements of $S_n$ of order $k$. For which values of $k$ will $f_k(n)$ be maximal?

Statement quoted from erdosproblems.com/1161, maintained by Thomas Bloom. Original source: [Va99,5.72]. Current status there: solved.

AI contributions

As recorded in Terence Tao's wiki AI contributions to Erdős problems (data as of 30 Jun 2026). 🟢 full, 🟡 partial, ⚪ unverified, 🔴 incorrect.

Caveats

The wiki's classifications are provisional and are not a benchmark. Many Erdős problems have never had a thorough literature review, so a result that looks new may later turn out to be known; some problems were also stated ambiguously or incorrectly. See the problem page for the full discussion.

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