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Math Help - Any way to reduce this into a simple formula?

  1. #1
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    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?
    Last edited by cubrikal; September 19th 2009 at 08:18 PM. Reason: mistake
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  2. #2
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    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!.
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  3. #3
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    Quote Originally Posted by Opalg View Post
    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.
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