Gaussian binomial coefficient

In mathematics, the Gaussian binomial coefficients (also called Gaussian coefficients, Gaussian numbers, Gaussian polynomials, or q-binomial coefficients) are q-analogs of the binomial coefficients. The Gaussian binomial coefficient, written as [ n k ] q {\displaystyle {\begin{bmatrix}n\\k\end{bmatrix}}_{q}} or ( n k ) q {\displaystyle {\binom {n}{k}}_{\! 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 F q {\displaystyle \mathbb {F} _{q}} , a finite field with q elements; i.e.

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