  In this article we give a computational study of combinatorics of the
discriminantal arrangements. The discriminantal arrangements are parametrized
by two positive integers n and k such that n>k. The intersection lattice of the
discriminantal arrangement with the parameter (n,k) is isomorphic to the
intersection lattice of the hyperplane arrangement generated by n generic
points in the d-dimensional vector space where d=n-k-1. The combinatorics of
the discriminantal arrangements is very hard, except for the special cases of
the Boolean arrangements (k=0) and the braid arrangements (k=1). We review some
results on the intersection lattices of the arrangements generated by generic
points and use them to obtain some computational results on the characteristic
polynomials of the discriminantal arrangements.
