# Thread: Any way to reduce this into a simple formula?

1. ## 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?

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

3. 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.