A key way to understand triangulated categories is to look at generators. In the context of positive Calabi-Yau (CY) triangulated categories, such as cluster categories, the most interesting generators seem to be cluster-tilting objects. There are some triangulated categories which are naturally negative CY. In this context, it is unclear which generator we should study. Higher Hom-configurations appear to be a natural candidate and seem to play a similar role as that of cluster-tilting objects. In this talk, we will focus on a special class of negative CY triangulated categories and give a combinatorial classification of higher Hom-configurations in those categories in terms of noncrossing partitions.