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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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