Triple parton scattering effects in $D$-meson production at the LHC

We study triple-parton scattering effects in open charm production in proton-proton collisions at the LHC. Predictions for one, two and three $c\bar c$ pairs production are given for $\sqrt{s}= 7$ TeV and $\sqrt{s}= 13$ TeV. Quite large cross sections, of the order of milibarns, for the triple-parton scattering mechanism are obtained. We suggest a measurement of three $D^{0}$ or three $\bar{D^{0}}$ mesons by the LHCb collaboration. The predicted visible cross sections are of the order of a few nanobarns. The counting rates including $D^{0} \to K^{-}\pi^{+}$ branching fractions are also given. We predict that at $\sqrt{s}= 13$ TeV a few thousands of events of triple-$D^{0}$ production can be observed by the LHCb collaboration.