  Our understanding of neutrino flavor conversion in the supernova core is
still preliminary, despite its likely relevance to the neutrino-driven
supernova mechanism. We present multi-angle and multi-energy numerical
simulations of neutrino quantum kinetics within a spherically symmetric shell
in the proximity of the region of neutrino decoupling. We rely on inputs from a
one-dimensional core-collapse supernova model with a mass of $18.6\ M_\odot$
and find that, at early post-bounce times ($t_{\mathrm pb} \lesssim 0.5$ s), no
crossing is present in the angular distribution of the electron neutrino lepton
number and flavor conversion develops due to vacuum mixing. Angular crossings
appear for $t_{\textrm{pb}} \gtrsim 0.5$ s and fast flavor conversion leads to
flavor equipartition, with the spectral energy distribution of $\nu_{e}$
($\bar{\nu}_{e}$) and $\nu_{x}$ ($\bar{\nu}_{x}$) becoming comparable. Notably,
flavor equipartition is not a generic outcome of fast flavor conversion, but
rather a consequence of the relatively similar properties of neutrinos of
different flavors characterizing the late accretion phase. Artificially
tweaking the collision term to introduce an electron lepton number angular
crossing for $t_{\mathrm{pb}} \lesssim 0.05$ s, we observe that flavor
equipartition is not achieved. While our findings are restricted to a specific
supernova model, they suggest a rich phenomenology of flavor conversion in the
supernova core as a function of the post-bounce time which needs to be further
explored to assess its impact on the explosion mechanism.
