genericArrangement(ZZ,ZZ,Ring) -- realize the uniform matroid using points on the monomial curve

Synopsis

Function: genericArrangement
Usage:

genericArrangement(r,n,K)

genericArrangement(r,n)
Inputs:
- r, an integer, the rank of the arrangement
- n, an integer, the number of hyperplanes
- K, a ring, a coefficient ring: $\QQ$ by default
Outputs:
- a hyperplane arrangement, the arrangement with linear forms normal to $(1,j,j^2,\cdots,j^{r-1})$, for $1\leq j\leq n$.

Description

By definition, a generic arrangement is a realization of a uniform matroid $U_{r,n}$, which is characterized by the property that all subsets of the ground set of size at most $r$ are independent. Points on the monomial curve have this property.

i1 : poincare genericArrangement(3,5,QQ)

                 2     3
o1 = 1 + 5T + 10T  + 6T

o1 : ZZ[T]

Ways to use this method: