in mathematics, the gaussian binomial coefficients (also called gaussian coefficients, gaussian polynomials, or "q"-binomial coefficients) are "q"-analogs of the binomial coefficients. the gaussian binomial coefficient, written as formula_1 or formula_2, is a polynomial in "q" with integer coefficients, whose value when "q" is set to a prime power counts the number of subspaces of dimension "k" in a vector space of dimension "n" over a finite field with "q" elements.