Neutrino mixing and leptogenesis in the type II seesaw mechanism

In the framework of the type II seesaw mechanism we propose two simple but instructive ans\"atze for neutrino mixing and leptogenesis. In each ansatz, the effective Majorana neutrino mass matrix is composed of two parts---the part with Z₂ symmetry arises from the ordinary type I seesaw mechanism and the part with S₃ symmetry arises from an additional Higgs triplet vacuum expectation value. The two ans\"atze can simultaneously account for the current neutrino oscillation data and the cosmological baryon number asymmetry via leptogenesis.