Combinatorics, transvectants and superalgebras. An elementary constructive approach to Hilbert's finiteness theorem

We describe a constructive method to produce a minimal set of generators for the algebra of SL(n)-invariants of an n-ary form. The main feature of this approach is that it provides a “running bound” for the degrees of the generating invariants. The techniques are based on a superalgebraic description of transvectants and a systematic use of the symbolic method.