Polygraph Arrangements

A class of subspace arrangements, Z(n, m), known as polygraph arrangements was exploited by Haiman in order to prove the n! theorem. By showing that their intersection lattices,L (Z(n, m)), are EL-shellable, we determine the cohomology groups of the complements of the arrangements. Moreover, we generalize the shellability results to a class of lattices which deserve to be called Dowling generalizations of L(Z(n, m)). As a consequence, we obtain the cohomology groups of the complements of certain Dowling analogues of polygraph arrangements.