Probing R-parity violation in the production of t bar{c}(c bar{t}) on the lepton colliders

We studied the process $e^{+}e^{-} \to t\bar{c}+c\bar{t}$ in a R_{p} violating supersymmetric model with effects from both B- and L-violating interactions. The calculation shows that it is possible to either detect the R_{p} violating signal at the Next Linear Collider or get more stringent constraints on the heavy-flavor $\rlap/R_{p}$ couplings. A comparision with results from $\gamma\gamma \to t\bar{c}+ c\bar{t}$ may allow to distinguish between B- and L-violating interactions. For very clean background conditions and R_{p} violation parameters close to present limits, a future detection of B-violating interactions should be possible. The process of $\mu ^{+} \mu ^{-} \to t \bar{c}+c\bar{t}$ is also considered.