Multilinear enumerative techniques
Dennis E. White · Linear and Multilinear Algebra · 1975
When S is a finite set and G a finite group acting on S, we consider the problem of rejecting isomorphs in a G-stable subset of S. In previous work we developed a linear algebraic context for this problem by constructing the finite dimensional vector spaceF s whereF is a field of characteristic zero. When S is a finite function space, or a finite direct product of finite function spacesF s acquires a multilinear structure By various specializations ofG and S and by applications of results which have appeared elsewhere, identities of Sheehan, deBruijn and P61ya are obtained. Furthermore, these same techniques are applied to examples which do not have a clear resolution using the more common formulas