$R$-Parity Violation in Flavor Changing Neutral Current Processes and Top Quark Decays

We show that supersymmetric $R$-parity breaking ($\not R_p$) interactions always result in Flavor Changing Neutral Current (FCNC) processes. Within a single coupling scheme, these processes can be avoided in either the charge $+2/3$ or the charge $-1/3$ quark sector, but not both. These processes are used to place constraints on \Rp couplings. The constraints on the first and the second generations are better than those existing in the literature. The \Rp interactions may result in new top quark decays. Some of these violate electron-muon universality or produce a surplus of $b$ quark events in $t\bar{t}$ decays. Results from the CDF experiment are used to bound these \Rp couplings.