  A search is reported for heavy resonances decaying into e$\mu$ final states
in proton-proton collisions recorded by the CMS experiment at the CERN LHC at
$\sqrt{s}=$ 13 TeV, corresponding to an integrated luminosity of 35.9
fb$^{-1}$. The search focuses on resonance masses above 200 GeV. With no
evidence found for physics beyond the standard model in the e$\mu$ mass
spectrum, upper limits are set at 95% confidence level on the product of the
cross section and branching fraction for this lepton-flavor violating signal.
Based on these results, resonant $\tau$ sneutrino production in R-parity
violating supersymmetric models is excluded for masses below 1.7 TeV, for
couplings $\lambda_{132} = \lambda_{231} = \lambda'_{311} = 0.01$. Heavy Z$'$
gauge bosons with lepton-flavor violating transitions are excluded for masses
up to 4.4 TeV. The e$\mu$ mass spectrum is also interpreted in terms of
non-resonant contributions from quantum black-hole production in models with
one to six extra spatial dimensions, and lower mass limits are found between
3.6 and 5.6 TeV. In all interpretations used in this analysis, the results of
this search improve previous limits by about 1 TeV. These limits correspond to
the most sensitive values obtained at colliders.
