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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.

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    $\begingroup$ I would just write the result without bothering with a reference or a proof. $\endgroup$
    – Ben Webster
    Feb 8, 2016 at 16:56

2 Answers 2

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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.

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  • $\begingroup$ That's exactly what I want. Thank you. $\endgroup$
    – var
    Feb 8, 2016 at 19:23
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See Vogan's notes. And here are more characters.

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  • $\begingroup$ I know his notes. But actually I want a "published" reference. Thank you. $\endgroup$
    – var
    Feb 8, 2016 at 19:22

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