The lattice automorphisms of the dominance ordering

In this paper it is shown that the lattice L_n of partitions of n under the dominance ordering is totally asymmetric, except for the cases n = 6 and 7 where the automorphism group is $\text{Z}$₂ × $\text{Z}$₂. As a consequence, partition conjugation is the only antiautomorphism of L_n if n ≠ 6, 7.