# Category:Gaussian Binomial Coefficients

This category contains results about Gaussian Binomial Coefficients.

Let $q \in \R_{\ne 1}$, $r \in \R$, $m \in \Z_{\ge 0}$.

The Gaussian binomial coefficient is an extension of the more conventional binomial coefficient as follows:

 $\displaystyle \binom r m_q$ $:=$ $\displaystyle \prod_{k \mathop = 0}^{m - 1} \dfrac {1 - q^{r - k} } {1 - q^{k + 1} }$ $\displaystyle$ $=$ $\displaystyle \dfrac {\paren {1 - q^r} \paren {1 - q^{r - 1} } \cdots \paren {1 - q^{r - m + 1} } } {\paren {1 - q^m} \paren {1 - q^{m - 1} } \cdots \paren {1 - q^1} }$

## Subcategories

This category has the following 2 subcategories, out of 2 total.

## Pages in category "Gaussian Binomial Coefficients"

The following 10 pages are in this category, out of 10 total.