On the area bisectors of a polygon

We consider the family of lines that are area bisectors of a polygon (possi bly with holes) in the plane. We say that two bisectors of a polygon P are combinatorially distinct if they induce different partitionings of the vert ices of P. We derive an algebraic characterization of area bisectors. We th en show that there are simple polygons with n vertices that have Omega (n(2 )) combinatorially distinct area bisectors (matching the obvious upper boun d), and present an output-sensitive algorithm for computing an explicit rep resentation of all the bisectors of a given polygon.