Young's lattice and dihedral symmetries
The set of all partitions \(\lambda=(\lambda_1,\dots,\lambda_k)\) has a natural graph structure (the Hasse graph) where the partitions are the vertices of the graph and two partitions are connected with an edge if the diagram of one of them can be obtained from the other diagram by adding a box. The author considers the automorphisms of a subgraph \(Y_n\) of the Hasse graph defined by the property that the diagram of \(\lambda\in Y_n\) is contained in a rectangular diagram which is a subset of the diagram of \((n-1,n-2,\dots,2,1)\). The main result is that for \(n\geq 3\) the dihedral group \(D_n\) acts naturally on the graph \(Y_n\) and is isomorphic to its automorphism group.
scientific article; zbMATH DE number 1740612