It appears that a, b, c and d are just a means of identifying the coils. There doesn't seem to be any indication that this generator has some peculiar number of phases, but the winding scheme is not described sufficiently to tell much about the design. The paper is really not about the motor design.
There is no information about why a coreless stator was chosen. In the photo, it appears that the magnetic flux path may consist entirely of air and plastic. Considerably better performance could be obtained by using a magnetic material in the core and around the magnets.
Upon further consideration
Although a coreless design seems to be inherently inefficient, the advantages apparently outweigh the disadvantages in some applications. One advantage is that a lighter weight machine is possible. That may have been a factor for the application described in the referenced paper. A disadvantage is that more NeFeB material is needed for a given output.
The highest power output for a given component volume will be obtained by operating the generator at the highest possible speed. There may be a better magnet coil arrangement that is better than the one presented. I suspect that the optimum coil and magnet shape may be something more like segments of a circle rather than small circles.
Other technical papers written on the subject and a detailed analysis of possible designs would probably provide a better answer.