Gaussian binomial coefficient
FAMILY OF POLYNOMIALS
Q-binomial coefficient; Q-binomial; Gaussian coefficient; Gaussian binomial; Q-binomial theorem; Gaussian polynomial; Gaussian polynomials; Gaussian binomial coefficients; Q-binomial coefficients
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 \binom nk_q or \begin{bmatrix}n\\ k\end{bmatrix}_q, 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.