Nested Witt vectors and their q-deformation

Let N⊆N be a truncation set. We study the ring of N-nested Witt vectors and its q-deformation. Given two arbitrary integers q and r, we provide a necessary and sufficient condition of A so that and should be strictly isomorphic to each other. Also, an isomorphism of functors, , will be established for coprime truncation sets M and N. As a byproduct, we deal with interesting connections between nested Witt-vectors and other areas such as generalized Möbius μ-functions and numerical polynomials, i.e., polynomials which take integral values at integer arguments.