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In [[mathematics]], the '''Gaussian binomial coefficients''' (also called '''Gaussian coefficients''', '''Gaussian polynomials''', or '''''q''-binomial coefficients''') are [[q-analog|''q''-analog]]s of the [[binomial coefficients]]. The Gaussian binomial coefficient <math>\textstyle\binom nk_q</math> is a polynomial in ''q'' with integer coefficient, whose value when ''q'' is set to a prime power counts the number of subspaces of dimension ''k'' in a vector space of dimension ''n'' over a finite filed with ''q'' elements.
==Definition==
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