The lattice automorphisms of the dominance ordering (Q791551)

The author proves the following theorem: Let \(L_ n\) denote the lattice of partitions of the integer n under the dominance ordering. (That is, if \(\alpha =(\alpha_ 1\geq \alpha_ 2\geq...\geq 0)\) and \(\beta =(\beta_ 1\geq \beta_ 2\geq...\geq 0)\) are two partitions of n, then \(\alpha\geq \beta\) iff \(\alpha_ 1+\alpha_ 2+...+\alpha_ i\geq \beta_ 1+\beta_ 2+...+\beta_ i\) for \(i=1,2,...,n.)\) If \(n\neq 6,7\) then \(L_ n\) admits only the trivial automorphism. For \(L_ 6\) and \(L_ 7\) the automorphism group is isomorphic to \(Z_ 2\times Z_ 2\).