  Results are presented from a search for charged-lepton flavor violating
(CLFV) interactions in top quark production and decay in pp collisions at a
center-of-mass energy of 13 TeV. The events are required to contain one
oppositely charged electron-muon pair in the final state, along with at least
one jet identified as originating from a bottom quark. The data correspond to
an integrated luminosity of 138 fb$^{-1}$, collected by the CMS experiment at
the LHC. This analysis includes both the production (q $\to$ e$\mu$t) and decay
(t $\to$ e$\mu$q) modes of the top quark through CLFV interactions, with q
referring to a u or c quark. These interactions are parametrized using an
effective field theory approach. With no significant excess over the standard
model expectation, the results are interpreted in terms of vector-, scalar-,
and tensor-like CLFV four-fermion effective interactions. Finally, observed
exclusion limits are set at 95% confidence levels on the respective branching
fractions of a top quark to an e$\mu$ pair and an up (charm) quark of 0.13
$\times$ 10$^{-6}$ (1.31 $\times$ 10$^{-6}$), 0.07 $\times$ 10$^{-6}$ (0.89
$\times$ 10$^{-6}$), and 0.25 $\times$ 10$^{-6}$ (2.59 $\times$ 10$^{-6}$) for
vector, scalar, and tensor CLFV interactions, respectively.
