An Algorithm For Deriving Characteristic Polynomials Of Hyperplane Arrangements
Oral Defence Date:
Dr. Mathias Beck, Dr. Rahul Singh, Dr. Dragutin Petkovic
A hyperplane arrangement is a finite set of hyperplanes. Much of the combinatorial structure of a hyperplane arrangement is encoded in its characteristic polynomial, which is defined recursively through the intersection lattice of the hyperplanes. For example, the number of regions that are cut out in space by the hyperplane arrangement is a special evaluation of the characteristic polynomial. This thesis aims to develop an algorithm and software to compute characteristic polynomials of hyperplane arrangements. While mathematicians have computed the characteristic polynomials of hyperplane arrangements by hand for decades, it is believed that this thesis will be the first software solution to this problem.
Hyperplane arrangement, Characteristic polynomial, Mobius function, Meet-semilattice, Dynamic programming