  We numerically study vortex ordering and pinning in Archimedean tiling
substrates composed of square and triangular plaquettes. The two different
plaquettes become occupied at different vortex densities, producing
commensurate peaks in the magnetization at non-integer matching fields. We find
that as the field increases, in some cases the fraction of occupied pins can
decrease due to the competition between fillings of the different plaquette
types. We also identify a number of different types of vortex orderings as
function of field at integer and non-integer commensurate fillings.
