Dinv and Area

We give a new combinatorial proof of the well known result that the dinv of an (m,n)-Dyck path is equal to the area of its sweep map image. The first proof of this remarkable identity for co-prime (m,n) is due to Loehr and Warrington. There is also a second proof (in the co-prime case) due to Gorsky and Mazin and a third proof due to Mazin.