3
$\begingroup$

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.

$\endgroup$
  • 5
    $\begingroup$ I would just write the result without bothering with a reference or a proof. $\endgroup$ – Ben Webster Feb 8 '16 at 16:56
4
$\begingroup$

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.

| cite | improve this answer | |
$\endgroup$
  • $\begingroup$ That's exactly what I want. Thank you. $\endgroup$ – var Feb 8 '16 at 19:23
0
$\begingroup$

See Vogan's notes. And here are more characters.

| cite | improve this answer | |
$\endgroup$
  • $\begingroup$ I know his notes. But actually I want a "published" reference. Thank you. $\endgroup$ – var Feb 8 '16 at 19:22

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.