On the packing dimension of box-like self-affine sets in the plane

We consider a class of planar self-affine sets which we call 'box-like'. A boxlike self-affine set is the attractor of an iterated function system (IFS) consisting of contracting affine maps which take the unit square, [0, 1](2), to a rectangle with sides parallel to the axes. This class contains the Bedford-McMullen carpets and the generalizations thereof considered by Lalley-Gatzouras, Baranski and Feng-Wang as well as many other sets. In particular, we allow the mappings in the IFS to have non-trivial rotational and reflectional components. Assuming a rectangular open set condition, we compute the packing and box-counting dimensions by means of a pressure type formula based on the singular values of the maps.