  We calculate the cumulants and correlation functions of net-kaon multiplicity
distributions in Au+Au collisions at $\sqrt{s_{NN}} = 7.7$ GeV using a
multiphase transport model (AMPT) with both a new coalescence mechanism and all
charge conservation laws. The AMPT model can qualitatively describe the
centrality dependences of the net-kaon cumulants and cumulant ratios measured
by the STAR experiment. By focusing on the stage evolution of the cumulants,
cumulant ratios, and correlation functions, we reveal several key effects on
the fluctuations and correlations of strangeness during the dynamical evolution
of relativistic heavy-ion collisions, including strangeness production and
diffusion, hadronization, hadronic rescatterings, and weak decays. Without
considering the quantum chromodynamics critical fluctuations in the dynamic
model, we demonstrate that the net-kaon fluctuations can largely represent the
net-strangeness fluctuations. Our results provide a baseline for understanding
the net-kaon and net-strangeness fluctuations, which help to search for the
possible critical behaviors at the critical end point in relativistic heavy-ion
collisions.
