  Eisenk"olbl gave a formula for the number of lozenge tilings of a hexagon on
the triangular lattice with three unit triangles removed from along alternating
sides. In earlier work, the first author extended this to the situation when an
arbitrary set of unit triangles is removed from along alternating sides of the
hexagon. In this paper we address the general case when an arbitrary set of
unit triangles is removed from along the boundary of the hexagon.
