On an explicit correspondence between nbc-basis, chambers and minimal complex for real supersolvable arrangements

In this paper we give a very natural description of the bijections between the set of cells in the minimal CW-complex homotopy equivalent to the complement of a complexified real supersolvable arrangement A, the nbc-basis of the Orlik-Solomon algebra associated to A and the set of chambers of A. We use these bijections to describe a bijection between the symmetric group and the nbc-basis of the braid arrangement.