$$\frac{\binom{n}{j}_q\binom{n+1}{j}_q \cdots\binom{n+k-1}{j}_q}{\binom{j}{j}_q\binom{j+1}{j}_q\cdots\binom{j+k-1}{j}_q}$$ where $n,j,k$ are non-negative integers.
Is the following product of $q$-binomial coefficients a polynomial in $q$?
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combinatorics
q-analogs
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0What do the $q$ subscripts on the binomial coefficients mean? – 2011-12-28
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1It means it is q binomial coefficient and here is the link to its definition http://mathworld.wolfram.com/q-BinomialCoefficient.html – 2011-12-28