Pattern Recognition on Oriented Matroids

List of Notation

–:= – equals by definition

–ø(s, t)–Kronecker delta, equal to 1 when s = t, and 0 otherwise

– – nonnegative integers

– – positive integers

–$\mathbb{Q}$ – rational numbers

– – real numbers

–gcd(·, ·) – greatest common divisor of two integers

–$\left(\begin{array}{l}j\\ l\end{array}\right)$ – binomial coefficient, equal to $\frac{j\left(j-1\right)\cdot \cdot \cdot \left(j-i+1\right)}{i\left(i-1\right)\cdot \cdot \cdot 1}$

–${\left(\begin{array}{l}j\\ l\end{array}\right)}_q$ – q-binomial coefficient, equal to $\frac{\left(q\text{'}-1\right)\left(q\text{'}-q\right)\cdot \cdot \cdot (q\text{'}-q^{}}{}$