Gaussian binomial coefficient

Summary

The Gaussian binomial coefficient $\binom{n}{k}_q$ is the q-analog of the binomial coefficient $\binom{n}{k}$, see the definition. It is a polynomial in $q$ with nonnegative integer coefficients, and it equals $\binom{n}{k}$ at $q = 1$. When $q$ is a prime power, it counts the $k$-dimensional subspaces of the vector space $\F_q^n$. Its coefficients count the integer partitions whose Young diagram fits in a $k \times (n - k)$ box.