Exact self-similar solutions to the fragmentation equation with homogeneous discrete kernel

New large time asymptotic (self-similar) solutions of the fragmentation (breakage) equation are derived in closed form for the case of certain homogeneous discrete fragmentation kernel. A fragmentation kernel is called homogeneous and discrete if it allows only certain ratios between the size of the fragments and that of parent particle. In this case the fragmentation kernel is not a continuous function. The present solutions are the first explicit self-similarity distributions for discontinuous breakage functions.