# Any way to reduce this into a simple formula?

• September 19th 2009, 07:13 PM
cubrikal
Any way to reduce this into a simple formula?
$(q^{n} - q^{r-1})(q^{n} - q^{r-2})...(q^{n}-1)$

Off topic, but does this gives the permutation of sequences with r linearly independent vectors in a dimension n vector space over $F_{q}$? Unless, the formula I solved for was incorrect, I think this should involve combinations?
• September 20th 2009, 12:14 AM
Opalg
I'm not sure if this is what you're looking for, but in terms of q-factorials you could write this as $(q-1)^{n-r+1}q^{r(r-1)/2}[n-r+1]_q!$.
• September 20th 2009, 09:28 AM
cubrikal
Quote:

Originally Posted by Opalg
I'm not sure if this is what you're looking for, but in terms of q-factorials you could write this as $(q-1)^{n-r+1}q^{r(r-1)/2}[n-r+1]_q!$.

Thanks, I didn't know about q-factorials. I guess I thought it would involve combinations for some reason.