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Weights of partitions and character zeros. (English) Zbl 1068.20011
Summary: We classify partitions which are of maximal \(p\)-weight for all odd primes \(p\). As a consequence, we show that any non-linear irreducible character of the symmetric and alternating groups vanishes on some element of prime order.

20C30 Representations of finite symmetric groups
05A17 Combinatorial aspects of partitions of integers
05E10 Combinatorial aspects of representation theory
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