  An important step towards the classification of finite-dimensional pointed
Hopf algebras is the classification of finite-dimensional Nichols algebras
arising from braided vector spaces of group type. This question is
fundamentally linked with the structure of algebraic objects called racks. Of
particular interest to this classification is the type D condition on racks, a
sufficient condition for a rack to not be the source of a finite-dimensional
Nichols algebra. In this paper, we study the type D condition in simple racks
arising from the alternating groups. Expanding upon previous work in this
direction, we make progress towards a general classification of twisted
homogeneous racks of type D by proving that several families of twisted
homogeneous racks arising from alternating groups are of type D.
