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16.67 (2006)

Solved

Conjecture: Given any integer $k$, there exists an integer $n_0 = n_0(k)$ such that if $n \geqslant n_0$ then the symmetric group of degree $n$ has at least $k$ different ordinary irreducible characters of equal degrees.

Contributor: A. Moretó

Progress

This is proved (D. Craven, Proc. London Math. Soc., 96 (2008), 26–50).

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