THE BROKEN CIRCUIT COMPLEX AND THE HYPERSOLVABLE PARTITION COMPLEX

In this paper we construct the broken circuit complex of a hypersolvable r -arrangement  by using the hypersolvable partition analogue and the hypersolvable ordering which respects the hypersolvable structure .We used the minimal informations that encoded in the intersection lattice pattern up to codimension two to define an isomorphism between the broken circuit complexes of any two supersolvable arrangements which enable us to produce a comparison between the structures of the broken circuit complexes of a hypersolvable arrangement and their Jambu s- Papadima s deformed supersolvable arrangements.