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The nonmesonic weak decay of $\Lambda$ hypernuclei is studied within amicroscopic diagrammatic approach which is extended to include thethree--nucleon induced mechanism. We adopt a nuclear matter formalism which,through the local density approximation, allows us to model finite hypernuclei,a one--meson--exchange weak transition potential and a Bonn nucleon--nucleonstrong potential. One--, two-- and three--nucleon induced weak decay rates arepredicted for $^{12}_\Lambda$C by including ground state correlations up tosecond order in the nucleon--nucleon potential and the recoil of the residualnucleus. Three--nucleon stimulated decays, $\Lambda NNN\to nNNN$ ($N=n$ or$p$), are considered here for the first time. The obtained decay rates comparewell with the latest KEK and FINUDA data. The three--nucleon induced rate turnsout to be dominated by $nnp$-- and $npp$--induced decays, it amounts to $\sim$7\% of the total nonmesonic rate and it is $\sim 1/2$ of the neutron--induceddecay rate. The reduction effect of the nuclear recoil is particularly relevantfor the three--nucleon induced rates ($\sim$ 15\%), less important for thetwo--nucleon induced rates ($\sim$ 4\%) and negligible for the one--nucleoninduced rates. Given the non--negligible size of the three--nucleon inducedcontribution and consequently its importance in the precise determination ofthe complete set of decay rates, new measurements and/or experimental analysisare encouraged.

Nonmesonic Weak Decay of $\Lambda$ Hypernuclei: The Three--Nucleon Induced Mode