Pólya theory of hypercubes (revision of preprint 925)

Abstract

The cycle index polynomial is described for the action of the full isometry group of the n-dimensional hypercube on its q-dimensional cells. This group action is interpreted as C n 2 Sn acting on the set of unit basis vectors in R n and their opposites. A kind of generating function that yields all these polynomials at once is obtained by M? obius inversion. The same technique is applied to the simpler case of the n-dimensional simplex.