Category:Gaussian Binomial Coefficients
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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:
| \(\ds \binom r m_q\) | \(:=\) | \(\ds \prod_{k \mathop = 0}^{m - 1} \dfrac {1 - q^{r - k} } {1 - q^{k + 1} }\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \dfrac {\paren {1 - q^r} \paren {1 - q^{r - 1} } \cdots \paren {1 - q^{r - m + 1} } } {\paren {1 - q^m} \paren {1 - q^{m - 1} } \cdots \paren {1 - q^1} }\) |
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.