Lamarsh, D & H, and other texts will have some discussion of reflected cores in plate, box, cylindrical, or spherical geometries.
The criticality is determined by what neutron flux/current leaks out of core and what is reflected, and what is absorbed in the core. In general, the neutron (fission) sources are exclusive to the core, and the reflector does not contain fission sources, but only those neutron leaking from the core. The reflector simply reflects some portion of the neutrons which leave the core. Neutrons in the reflector either scatter back into the core, out of the reflector through the outer surface, or are absorbed (usually without producing more neutrons). Some reflectors may provide (n, 2n) reactions, but there is an energy dependence.
Serber's primer deals primarily with certain types of core/reflectors (tampers). I found a copy of the LA-173, and it discusses some of the details. Basically Serber's equations contain some empirical coefficients which are system specific/dependent.
