The Robinson-Schensted correspondence is one between the set of permutations and pairs of same-shape standard Young tableaux. I'll recall a few of the combinatorial aspects of this. The Steinberg scheme (for $GL_n$) is a set of triples, one nilpotent matrix and two flags invariant under the nilpotent, whose components correspond to permutations. I'll recall why this is (for those who haven't been coming to the seminar), and show that they also correspond to pairs of standard Young tableaux. The basic linkage between the linear algebra and the combinatorics is that Jordan canonical forms of nilpotent matrices correspond to partitions. This talk will only require linear algebra, and a willingness to talk about the ``components'' of an algebraic set.