Measurement of the absolute branching fraction of the three-body decay ${\mathrm{\Lambda }}_c^{+}\to {\mathrm{\Xi }}^0{K}^{+}{\pi }^0$ and search for ${\mathrm{\Lambda }}_c^{+}\to n{K}^{+}{\pi }^0$, ${\mathrm{\Sigma }}^0{K}^{+}{\pi }^0$ and $\mathrm{\Lambda }{K}^{+}{\pi }^0$

The Cabbibo-favored decay ${\mathrm{\Lambda }}_c^{+}\to {\mathrm{\Xi }}^0{K}^{+}{\pi }^0$ is studied for the first time using 6.1 fb${}^{-1}$ of $e^{+}{e}^{-}$ collision data at center-of-mass energies between 4.600 and 4.840 GeV, collected with the BESIII detector at the BEPCII collider. With a double-tag method, the branching fraction of the three-body decay ${\mathrm{\Lambda }}_c^{+}\to {\mathrm{\Xi }}^0{K}^{+}{\pi }^0$ is measured to be $(7.79\pm {1.46}_{}\pm {0.71}_{})\times {10}^{-3}$, where the first and second uncertainties are statistical and systematic, respectively. The branching fraction of the two-body decay ${\mathrm{\Lambda }}_c^{+}\to \mathrm{\Xi }(1530{)}^0{K}^{+}$ is $(5.99\pm 1.04\pm 0.29)\times {10}^{-3}$, which is consistent with the previous result of $(5.02\pm 0.99\pm 0.31)\times {10}^{-3}$. In addition, the upper limit on the branching fraction of the doubly Cabbibo-suppressed decay ${\mathrm{\Lambda }}_c^{+}\to n{K}^{+}{\pi }^0$ is $7.1\times {10}^{-4}$ at the 90$\mathrm{\%}$ confidence level. The upper limits on the branching fractions of ${\mathrm{\Lambda }}_c^{+}\to {\mathrm{\Sigma }}^0{K}^{+}{\pi }^0$ and $\mathrm{\Lambda }{K}^{+}{\pi }^0$ are also determined to be $1.8\times {10}^{-3}$ and $2.0\times {10}^{-3}$, respectively.