where the LGLn(λ) are irreducible GLn(C)-modules and the S λ k are irreducible Sk-modules. The decomposition in (0.1) essentially makes the study of the representations of GLn(C) and the study of representations of the symmetric group Sk two sides of the same coin. The group GLn(C) has interesting subgroups, GLn(C) ⊇ On(C) ⊇ Sn ⊇ Sn−1, and corresponding centralizer algebras, CSk ⊆ CBk(n) ⊆ CAk(...

We consider two kinds of partition of a graph, namely orbit partitions and equitable partitions. Although an orbit partition is always an equitable partition, the converse is not true in general. We look at some classes of graphs for which the converse is true.

The Satisfactory Partition problem asks for deciding if a given graph has a partition of its vertex set into two nonempty parts such that each vertex has at least as many neighbors in its part as in the other part. This problem was introduced by Gerber and Kobler [EJOR, 125 (2000), 283–291] and studied further by other authors. In this paper we first review some applications and related problem...