Yield ratio of hypertriton to light nuclei in heavy-ion collisions from \begin{document}${ \sqrt{{ s}_{{NN}}}}$\end{document} = 4.9 GeV to 2.76 TeV

We argue that the difference in the yield ratio \begin{document}${{{S}}_{\rm{3}}} = \dfrac{{{{{N}}_{_\Lambda ^3{\rm{H}}}}/{{{N}}_\Lambda }}}{{{{{N}}_{^3{\rm{He}}}}/{{{N}}_{{p}}}}}$\end{document} measured in Au+Au collisions at \begin{document}$\rm \sqrt{s_{NN}}$\end{document} = 200 GeV and in Pb-Pb collisions at \begin{document}$\rm \sqrt{s_{NN}}$\end{document} = 2.76 TeV is mainly owing to the different treatment of the weak decay contribution to the proton yield in the Au+Au collisions at \begin{document}$\rm \sqrt{s_{NN}}$\end{document} = 200 GeV. We then use the coalescence model to extract from measured \begin{document}$\rm S_3$\end{document} the information about the \begin{document}$\Lambda$\end{document} and nucleon density fluctuations at the kinetic freeze-out of heavy-ion collisions. We also show, using available experimental data, that the yield ratio \begin{document}${{{S}}_{\rm{2}}} = \dfrac{{{{{N}}_{_\Lambda ^3{\rm{H}}}}}}{{{{{N}}_\Lambda }{{{N}}_{{d}}}}}$\end{document} is a more promising observable than \begin{document}$\rm S_3$\end{document} for probing the local baryon-strangeness correlation in the produced medium.