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We report on a search for the lepton-flavor-violating processes ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\tau}}^{\ensuremath{-}}$ and ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{e}^{+}{\ensuremath{\tau}}^{\ensuremath{-}}$. The data sample corresponds to an integrated luminosity of $211\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ recorded by the BABAR experiment at the SLAC PEP-II asymmetric-energy $B$ Factory at a center-of-mass energy of $\sqrt{s}=10.58\text{ }\text{ }\mathrm{GeV}$. We find no evidence for a …