  In the framework of the color-magnetic interaction model, we have
systematically calculated the mass splittings for the S-wave triply heavy
pentaquark states with the configuration $qqQQ\bar{Q}$ $(Q=c,b;q=u,d,s)$. Their
masses are estimated and their stabilities are discussed according to possible
rearrangement decay patterns. Our results indicate that there may exist several
stable or narrow such states. We hope the present study can help
experimentalists to search for exotic pentaquarks.
