  One of the most puzzling questions in particle physics concerns the status of
the baryon (B) and lepton (L) quantum numbers. On the theoretical side, most
new physics scenarios naturally lead to their non-conservation and some amount
of violation is actually needed to explain the baryon asymmetry of the
Universe. On the experimental side, low-energy constraints such as those on
proton decay are so stringent that it is generally believed that no B and L
violation will ever be seen in laboratories. We observe that this apparent
contradiction, however, disappears when the flavor symmetries involving all
three generations are taken into account. We then identify model-independent
classes of B and/or L violating six-fermion-based processes that indeed
simultaneously satisfy low-energy constraints and produce clearly identifiable
signals at the LHC. Finally, through simplified models, we study two classes
characterized by (\Delta B;\Delta L) = (\pm 1;\pm 3) and (\pm 2; 0), that lead
to particularly striking signatures (t \mu^+ e^+ and \bar t \bar t + jets,
respectively).
