Search for $\mathrm{\Delta }S=2$ nonleptonic hyperon decays ${\mathrm{\Omega }}^{-}\to {\mathrm{\Sigma }}^0{\pi }^{-}$ and ${\mathrm{\Omega }}^{-}\to n{K}^{-}$

Using $(27.12\pm 0.14)\times {10}^8$ $\psi (3686)$ events collected by the BESIII detector at the center-of-mass energy of $\sqrt{s}=3.686$ GeV, we search for the first time for two nonleptonic hyperon decays that change strangeness by two units, ${\mathrm{\Omega }}^{-}\to {\mathrm{\Sigma }}^0{\pi }^{-}$ and ${\mathrm{\Omega }}^{-}\to n{K}^{-}$. No significant signal is observed. The upper limits on their decay branching fractions are determined to be $\mathcal{B}({\mathrm{\Omega }}^{-}\to {\mathrm{\Sigma }}^0{\pi }^{-})<5.4\times {10}^{-4}$ and $\mathcal{B}({\mathrm{\Omega }}^{-}\to n{K}^{-})<2.4\times {10}^{-4}$ at the $90\mathrm{\%}$ confidence level.