There is a natural action of the permutation group \mathcal{S}_3 on a Ferrers diagram of a plane partition—this corresponds to simultaneously permuting the three coordinates of all nodes. This generalizes the conjugation operation for integer partitions. The action of \mathcal{S}_3 can generate new plane partitions starting from a given plane partition. Below there are shown six plane partitions of 4 that are generated by the \mathcal{S}_3 action. Only the exchange of the first two coordinates is manifest in the representation given below.
