Coefficients of Gaussian Polynomials Modulo N

This paper proves a conjecture of Richard Stanley about reductions modulo N of the coefficients of q-binomial coefficients (hence the change to the less used “Gaussian Polynomials”). It shows that the residue counting function for n choose k is quasipolynomial as a corollary of a more interesting result about the decomposition of the coefficients modulo N into various periodic classes.