R-parity-violating supersymmetry effects and signals in single top quark production at the Fermilab Tevatron

We discuss single top quark production via $u^i{\overline{d}}^j\to t\overline{b}$ at the Fermilab Tevatron in the minimal supersymmetric model with $R$-parity violation. We find that within the allowed range of coupling constants, the lepton-number-violating couplings can give rise to observable effects when the slepton mass lies in a specific narrow range. For the baryon-number-violating couplings, the contribution to the production rate can be quite large in the presently allowed range of the coupling constants. We show that the measurement of single top quark production at the upgraded Tevatron can be used to constrain a linear combination of products of the $R$-parity-violating couplings.