Suppose $Gr_k(k,n)$ the Grassmannian which classifies all the dimension $k+1$ sub-spaces of a dimension $n+1$ linear space over the field $k$. For the case over a finite field $\mathbb F_{q}$, we can calculate the number of $Gr_{\mathbb F_q}(k,n)(\mathbb F_q)$.
Could someone give me a direct reference of this result? I know it is not very hard to calculate, but for some reasons I don't want to write the calculation in my paper but I need a reference for this. Thank you.
Best Answer
Stanley's Enumerative Combinatorics Volume I (2nd Edition), Proposition 1.7.2. But like Ben I think not including a proof or reference would probably be fine.