The Mullineux involution is an important map that appears in the study of representations of the symmetric group and the alternating group in characteristic p. The fixed points of this map are certain partitions of particular interest. It is known that the cardinality of the set of these self-Mullineux partitions is equal to the cardinality of a
distinguished subset of self-conjugate partitions. In this talk, I will show an explicit bijection between the two families of partitions in terms of the Mullineux symbol. I will also explain why it is interesting to have such a correspondence, this has to do with decomposition matrices of the symmetric group and labelling of its simple modules in the modular case.