Lower and upper bounds on the total weight of semi-rich acyclic arrangements of oriented lines in the plane Original Research Article

The ‘concept of cutting vectors’, developed by the author, is used to investigate the weight of the faces of arrangements of lines. Explicit formulas are given in the case of semi-rich acyclic arrangements. Special mappings are defined which allow to ‘move’ in the set of cutting vectors. Using this possibility we obtain lower and upper bounds for the total weights.