The problem of finding appropriate bases for the free module of polynomials in countably many indeterminates with coefficients in a given commutative ring R (even when restricted to the special case of R being the ring of integers) is interesting both to mathematicians and to computer scientists, since it has important and direct applications in areas ranging from the construction of symbolic algebra programs to modeling certain problems in chemistry and physics. The key word here is “appropriate,” since different problems can best be tackled by considering bases of different sorts. The approach here is based on a highly sophisticated use of Young tableaux, a combinatorial tool that has already found extensive use in group representation theory and ring theory. Clausen briefly discusses the use of this construction in group representation theory.