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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.

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