[n]_q = 1+q+q²+⋯+q^(n-1) = (qⁿ−1)/(q−1)
[n]_q! = [1]_q·[2]_q·⋯·[n]_q
[n choose k]_q = [n]_q! / ([k]_q! · [n−k]_q!)
[n]_q! = [1]_q·[2]_q·⋯·[n]_q
[n choose k]_q = [n]_q! / ([k]_q! · [n−k]_q!)
At q=1: [n choose k]_q → C(n,k). At q→0: → 0 or 1. At q=prime: counts subspaces of 𝔽_q^n.
[n choose k]_q vs q for fixed n (lines = different k values)
[n choose k]_q as partition generating function: coefficients = Young diagram counts