  We present a detailed investigation to establish that lepton-number (L)
violating supersymmetry (SUSY) can be effectively probed at the LHC in the
practically background-free same-sign trilepton (SS3l) and same-sign
four-lepton (SS4l) channels. With this in view, we extend our earlier analysis
of SS3l and SS4l signals by considering situations based on minimal
supergravity as well as a phenomenological SUSY model. We find that the
R-parity violating scenario predicts large event rates, for both the 7 and 14
TeV runs. Furthermore, we show that it is extremely unlikely to ever achieve
similar rates in R-parity conserving SUSY. In addition, we show how SS3l and
SS4l, in conjunction with the mixed-sign trilepton and four-lepton channels,
can be used to extract dynamical information about the underlying SUSY theory,
namely, the Majorana character of the decaying lightest neutralino and the
nature of L-violating couplings. We define suitable variables and relationships
between them which can be verified experimentally and which are largely
independent of the SUSY production cross-sections and the cascade decay
branching fractions. These theoretical predictions are validated by Monte Carlo
simulations including detector and background effects.
