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Is there a known identity that expresses the $q$-binomial coefficients (also known as Gaussian binomial coefficients) in terms of the (ordinary) binomial coefficients?

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I'd guess no. For the other direction, I'm sure you know that evaluation at $q=1$ gives the ordinary binomial coefficients. –  Tony Huynh Sep 27 '11 at 14:04
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No, there is not. –  Igor Rivin Sep 27 '11 at 15:23
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