Identitied Satisfied by Iterated Polynomials, and (Q,x)-Binomial Coefficients
We show that a theorem of Lagarias and Reeds can be interpreted as providing a generalization of the result "the (p = 1)-st difference of a polynomial of degree p is identically zero", in which powers of an independent variable are replaced by iterates of a polynomial transformation. When this transformation is linear, the result involves q generalized binomial coefficients. We show by example that other q formulae can be generalized in a similar way.